Triangle源程序
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<pre name="code" class="cpp">/*****************************************************************************//* *//* 888888888 ,o, / 888 *//* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o *//* 888 888 888 88b 888 888 888 888 888 d888 88b *//* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 *//* 888 888 888 C888 888 888 888 / 888 q888 *//* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" *//* "8oo8D *//* *//* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. *//* (triangle.c) *//* *//* Version 1.6 *//* July 28, 2005 *//* *//* Copyright 1993, 1995, 1997, 1998, 2002, 2005 *//* Jonathan Richard Shewchuk *//* 2360 Woolsey #H *//* Berkeley, California 94705-1927 *//* jrs@cs.berkeley.edu *//* *//* This program may be freely redistributed under the condition that the *//* copyright notices (including this entire header and the copyright *//* notice printed when the `-h' switch is selected) are not removed, and *//* no compensation is received. Private, research, and institutional *//* use is free. You may distribute modified versions of this code UNDER *//* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE *//* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE *//* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR *//* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as *//* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT *//* WITH THE AUTHOR. (If you are not directly supplying this code to a *//* customer, and you are instead telling them how they can obtain it for *//* free, then you are not required to make any arrangement with me.) *//* *//* Hypertext instructions for Triangle are available on the Web at *//* *//* http://www.cs.cmu.edu/~quake/triangle.html *//* *//* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way *//* whatsoever. This code is provided "as-is". Use at your own risk. *//* *//* Some of the references listed below are marked with an asterisk. [*] *//* These references are available for downloading from the Web page *//* *//* http://www.cs.cmu.edu/~quake/triangle.research.html *//* *//* Three papers discussing aspects of Triangle are available. A short *//* overview appears in "Triangle: Engineering a 2D Quality Mesh *//* Generator and Delaunay Triangulator," in Applied Computational *//* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh *//* Manocha, editors, Lecture Notes in Computer Science volume 1148, *//* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM *//* Workshop on Applied Computational Geometry). [*] *//* *//* The algorithms are discussed in the greatest detail in "Delaunay *//* Refinement Algorithms for Triangular Mesh Generation," Computational *//* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] *//* *//* More detail about the data structures may be found in my dissertation: *//* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report *//* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, *//* Pittsburgh, Pennsylvania, 18 May 1997. [*] *//* *//* Triangle was created as part of the Quake Project in the School of *//* Computer Science at Carnegie Mellon University. For further *//* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. *//* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, *//* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous *//* Media on Parallel Computers," Computer Methods in Applied Mechanics *//* and Engineering 152(1-2):85-102, 22 January 1998. *//* *//* Triangle's Delaunay refinement algorithm for quality mesh generation is *//* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm *//* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms *//* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- *//* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth *//* Annual Symposium on Computational Geometry (San Diego, California), *//* pages 274-280, Association for Computing Machinery, May 1993, *//* http://portal.acm.org/citation.cfm?id=161150 . *//* *//* The Delaunay refinement algorithm has been modified so that it meshes *//* domains with small input angles well, as described in Gary L. Miller, *//* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's *//* Algorithm Works," Twelfth International Meshing Roundtable, pages *//* 91-102, Sandia National Laboratories, September 2003. [*] *//* *//* My implementation of the divide-and-conquer and incremental Delaunay *//* triangulation algorithms follows closely the presentation of Guibas *//* and Stolfi, even though I use a triangle-based data structure instead *//* of their quad-edge data structure. (In fact, I originally implemented *//* Triangle using the quad-edge data structure, but the switch to a *//* triangle-based data structure sped Triangle by a factor of two.) The *//* mesh manipulation primitives and the two aforementioned Delaunay *//* triangulation algorithms are described by Leonidas J. Guibas and Jorge *//* Stolfi, "Primitives for the Manipulation of General Subdivisions and *//* the Computation of Voronoi Diagrams," ACM Transactions on Graphics *//* 4(2):74-123, April 1985, http://portal.acm.org/citation.cfm?id=282923 .*//* *//* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai *//* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the *//* Delaunay Triangulation," International Journal of Computer and *//* Information Science 9(3):219-242, 1980. Triangle's improvement of the *//* divide-and-conquer algorithm by alternating between vertical and *//* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- *//* Conquer Algorithm for Constructing Delaunay Triangulations," *//* Algorithmica 2(2):137-151, 1987. *//* *//* The incremental insertion algorithm was first proposed by C. L. Lawson, *//* "Software for C1 Surface Interpolation," in Mathematical Software III, *//* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. *//* For point location, I use the algorithm of Ernst P. Mucke, Isaac *//* Saias, and Binhai Zhu, "Fast Randomized Point Location Without *//* Preprocessing in Two- and Three-Dimensional Delaunay Triangulations," *//* Proceedings of the Twelfth Annual Symposium on Computational Geometry, *//* ACM, May 1996. [*] If I were to randomize the order of vertex *//* insertion (I currently don't bother), their result combined with the *//* result of Kenneth L. Clarkson and Peter W. Shor, "Applications of *//* Random Sampling in Computational Geometry II," Discrete & *//* Computational Geometry 4(1):387-421, 1989, would yield an expected *//* O(n^{4/3}) bound on running time. *//* *//* The O(n log n) sweepline Delaunay triangulation algorithm is taken from *//* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", *//* Algorithmica 2(2):153-174, 1987. A random sample of edges on the *//* boundary of the triangulation are maintained in a splay tree for the *//* purpose of point location. Splay trees are described by Daniel *//* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search *//* Trees," Journal of the ACM 32(3):652-686, July 1985, *//* http://portal.acm.org/citation.cfm?id=3835 . *//* *//* The algorithms for exact computation of the signs of determinants are *//* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- *//* Point Arithmetic and Fast Robust Geometric Predicates," Discrete & *//* Computational Geometry 18(3):305-363, October 1997. (Also available *//* as Technical Report CMU-CS-96-140, School of Computer Science, *//* Carnegie Mellon University, Pittsburgh, Pennsylvania, May 1996.) [*] *//* An abbreviated version appears as Jonathan Richard Shewchuk, "Robust *//* Adaptive Floating-Point Geometric Predicates," Proceedings of the *//* Twelfth Annual Symposium on Computational Geometry, ACM, May 1996. [*] *//* Many of the ideas for my exact arithmetic routines originate with *//* Douglas M. Priest, "Algorithms for Arbitrary Precision Floating Point *//* Arithmetic," Tenth Symposium on Computer Arithmetic, pp. 132-143, IEEE *//* Computer Society Press, 1991. [*] Many of the ideas for the correct *//* evaluation of the signs of determinants are taken from Steven Fortune *//* and Christopher J. Van Wyk, "Efficient Exact Arithmetic for Computa- *//* tional Geometry," Proceedings of the Ninth Annual Symposium on *//* Computational Geometry, ACM, pp. 163-172, May 1993, and from Steven *//* Fortune, "Numerical Stability of Algorithms for 2D Delaunay Triangu- *//* lations," International Journal of Computational Geometry & Applica- *//* tions 5(1-2):193-213, March-June 1995. *//* *//* The method of inserting new vertices off-center (not precisely at the *//* circumcenter of every poor-quality triangle) is from Alper Ungor, *//* "Off-centers: A New Type of Steiner Points for Computing Size-Optimal *//* Quality-Guaranteed Delaunay Triangulations," Proceedings of LATIN *//* 2004 (Buenos Aires, Argentina), April 2004. *//* *//* For definitions of and results involving Delaunay triangulations, *//* constrained and conforming versions thereof, and other aspects of *//* triangular mesh generation, see the excellent survey by Marshall Bern *//* and David Eppstein, "Mesh Generation and Optimal Triangulation," in *//* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, *//* editors, World Scientific, Singapore, pp. 23-90, 1992. [*] *//* *//* The time for incrementally adding PSLG (planar straight line graph) *//* segments to create a constrained Delaunay triangulation is probably *//* O(t^2) per segment in the worst case and O(t) per segment in the *//* common case, where t is the number of triangles that intersect the *//* segment before it is inserted. This doesn't count point location, *//* which can be much more expensive. I could improve this to O(d log d) *//* time, but d is usually quite small, so it's not worth the bother. *//* (This note does not apply when the -s switch is used, invoking a *//* different method is used to insert segments.) *//* *//* The time for deleting a vertex from a Delaunay triangulation is O(d^2) *//* in the worst case and O(d) in the common case, where d is the degree *//* of the vertex being deleted. I could improve this to O(d log d) time, *//* but d is usually quite small, so it's not worth the bother. *//* *//* Ruppert's Delaunay refinement algorithm typically generates triangles *//* at a linear rate (constant time per triangle) after the initial *//* triangulation is formed. There may be pathological cases where *//* quadratic time is required, but these never arise in practice. *//* *//* The geometric predicates (circumcenter calculations, segment *//* intersection formulae, etc.) appear in my "Lecture Notes on Geometric *//* Robustness" at http://www.cs.berkeley.edu/~jrs/mesh . *//* *//* If you make any improvements to this code, please please please let me *//* know, so that I may obtain the improvements. Even if you don't change *//* the code, I'd still love to hear what it's being used for. *//* *//*****************************************************************************//* For single precision (which will save some memory and reduce paging), *//* define the symbol SINGLE by using the -DSINGLE compiler switch or by *//* writing "#define SINGLE" below. *//* *//* For double precision (which will allow you to refine meshes to a smaller *//* edge length), leave SINGLE undefined. *//* *//* Double precision uses more memory, but improves the resolution of the *//* meshes you can generate with Triangle. It also reduces the likelihood *//* of a floating exception due to overflow. Finally, it is much faster *//* than single precision on 64-bit architectures like the DEC Alpha. I *//* recommend double precision unless you want to generate a mesh for which *//* you do not have enough memory. *//* #define SINGLE */#ifdef SINGLE#define REAL float#else /* not SINGLE */#define REAL double#endif /* not SINGLE *//* If yours is not a Unix system, define the NO_TIMER compiler switch to *//* remove the Unix-specific timing code. *//* #define NO_TIMER *//* To insert lots of self-checks for internal errors, define the SELF_CHECK *//* symbol. This will slow down the program significantly. It is best to *//* define the symbol using the -DSELF_CHECK compiler switch, but you could *//* write "#define SELF_CHECK" below. If you are modifying this code, I *//* recommend you turn self-checks on until your work is debugged. *//* #define SELF_CHECK *//* To compile Triangle as a callable object library (triangle.o), define the *//* TRILIBRARY symbol. Read the file triangle.h for details on how to call *//* the procedure triangulate() that results. *//* #define TRILIBRARY *//* It is possible to generate a smaller version of Triangle using one or *//* both of the following symbols. Define the REDUCED symbol to eliminate *//* all features that are primarily of research interest; specifically, the *//* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate *//* all meshing algorithms above and beyond constrained Delaunay *//* triangulation; specifically, the -r, -q, -a, -u, -D, -S, and -s *//* switches. These reductions are most likely to be useful when *//* generating an object library (triangle.o) by defining the TRILIBRARY *//* symbol. *//* #define REDUCED *//* #define CDT_ONLY *//* On some machines, my exact arithmetic routines might be defeated by the *//* use of internal extended precision floating-point registers. The best *//* way to solve this problem is to set the floating-point registers to use *//* single or double precision internally. On 80x86 processors, this may *//* be accomplished by setting the CPU86 symbol for the Microsoft C *//* compiler, or the LINUX symbol for the gcc compiler running on Linux. *//* *//* An inferior solution is to declare certain values as `volatile', thus *//* forcing them to be stored to memory and rounded off. Unfortunately, *//* this solution might slow Triangle down quite a bit. To use volatile *//* values, write "#define INEXACT volatile" below. Normally, however, *//* INEXACT should be defined to be nothing. ("#define INEXACT".) *//* *//* For more discussion, see http://www.cs.cmu.edu/~quake/robust.pc.html . *//* For yet more discussion, see Section 5 of my paper, "Adaptive Precision *//* Floating-Point Arithmetic and Fast Robust Geometric Predicates" (also *//* available as Section 6.6 of my dissertation). *//* #define CPU86 *//* #define LINUX */#define NO_TIMER#define INEXACT /* Nothing *//* #define INEXACT volatile *//* Maximum number of characters in a file name (including the null). */#define FILENAMESIZE 2048/* Maximum number of characters in a line read from a file (including the *//* null). */#define INPUTLINESIZE 1024/* For efficiency, a variety of data structures are allocated in bulk. The *//* following constants determine how many of each structure is allocated *//* at once. */#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */#define SUBSEGPERBLOCK 508 /* Number of subsegments allocated at once. */#define VERTEXPERBLOCK 4092 /* Number of vertices allocated at once. */#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. *//* Number of encroached subsegments allocated at once. */#define BADSUBSEGPERBLOCK 252/* Number of skinny triangles allocated at once. */#define BADTRIPERBLOCK 4092/* Number of flipped triangles allocated at once. */#define FLIPSTACKERPERBLOCK 252/* Number of splay tree nodes allocated at once. */#define SPLAYNODEPERBLOCK 508/* The vertex types. A DEADVERTEX has been deleted entirely. An *//* UNDEADVERTEX is not part of the mesh, but is written to the output *//* .node file and affects the node indexing in the other output files. */#define INPUTVERTEX 0#define SEGMENTVERTEX 1#define FREEVERTEX 2#define DEADVERTEX -32768#define UNDEADVERTEX -32767/* The next line is used to outsmart some very stupid compilers. If your *//* compiler is smarter, feel free to replace the "int" with "void". *//* Not that it matters. */#define VOID int/* Two constants for algorithms based on random sampling. Both constants *//* have been chosen empirically to optimize their respective algorithms. *//* Used for the point location scheme of Mucke, Saias, and Zhu, to decide *//* how large a random sample of triangles to inspect. */#define SAMPLEFACTOR 11/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction *//* of boundary edges should be maintained in the splay tree for point *//* location on the front. */#define SAMPLERATE 10/* A number that speaks for itself, every kissable digit. */#define PI 3.141592653589793238462643383279502884197169399375105820974944592308/* Another fave. */#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732/* And here's one for those of you who are intimidated by math. */#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333#include <stdio.h>#include <stdlib.h>#include <string.h>#include <math.h>#ifndef NO_TIMER#include <sys/time.h>#endif /* not NO_TIMER */#ifdef CPU86#include <float.h>#endif /* CPU86 */#ifdef LINUX#include <fpu_control.h>#endif /* LINUX */#ifdef TRILIBRARY#include "triangle.h"#endif /* TRILIBRARY *//* A few forward declarations. */#ifndef TRILIBRARYchar *readline();char *findfield();#endif /* not TRILIBRARY *//* Labels that signify the result of point location. The result of a *//* search indicates that the point falls in the interior of a triangle, on *//* an edge, on a vertex, or outside the mesh. */enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};/* Labels that signify the result of vertex insertion. The result indicates *//* that the vertex was inserted with complete success, was inserted but *//* encroaches upon a subsegment, was not inserted because it lies on a *//* segment, or was not inserted because another vertex occupies the same *//* location. */enum insertvertexresult {SUCCESSFULVERTEX, ENCROACHINGVERTEX, VIOLATINGVERTEX, DUPLICATEVERTEX};/* Labels that signify the result of direction finding. The result *//* indicates that a segment connecting the two query points falls within *//* the direction triangle, along the left edge of the direction triangle, *//* or along the right edge of the direction triangle. */enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};/*****************************************************************************//* *//* The basic mesh data structures *//* *//* There are three: vertices, triangles, and subsegments (abbreviated *//* `subseg'). These three data structures, linked by pointers, comprise *//* the mesh. A vertex simply represents a mesh vertex and its properties. *//* A triangle is a triangle. A subsegment is a special data structure used *//* to represent an impenetrable edge of the mesh (perhaps on the outer *//* boundary, on the boundary of a hole, or part of an internal boundary *//* separating two triangulated regions). Subsegments represent boundaries, *//* defined by the user, that triangles may not lie across. *//* *//* A triangle consists of a list of three vertices, a list of three *//* adjoining triangles, a list of three adjoining subsegments (when *//* segments exist), an arbitrary number of optional user-defined *//* floating-point attributes, and an optional area constraint. The latter *//* is an upper bound on the permissible area of each triangle in a region, *//* used for mesh refinement. *//* *//* For a triangle on a boundary of the mesh, some or all of the neighboring *//* triangles may not be present. For a triangle in the interior of the *//* mesh, often no neighboring subsegments are present. Such absent *//* triangles and subsegments are never represented by NULL pointers; they *//* are represented by two special records: `dummytri', the triangle that *//* fills "outer space", and `dummysub', the omnipresent subsegment. *//* `dummytri' and `dummysub' are used for several reasons; for instance, *//* they can be dereferenced and their contents examined without violating *//* protected memory. *//* *//* However, it is important to understand that a triangle includes other *//* information as well. The pointers to adjoining vertices, triangles, and *//* subsegments are ordered in a way that indicates their geometric relation *//* to each other. Furthermore, each of these pointers contains orientation *//* information. Each pointer to an adjoining triangle indicates which face *//* of that triangle is contacted. Similarly, each pointer to an adjoining *//* subsegment indicates which side of that subsegment is contacted, and how *//* the subsegment is oriented relative to the triangle. *//* *//* The data structure representing a subsegment may be thought to be *//* abutting the edge of one or two triangle data structures: either *//* sandwiched between two triangles, or resting against one triangle on an *//* exterior boundary or hole boundary. *//* *//* A subsegment consists of a list of four vertices--the vertices of the *//* subsegment, and the vertices of the segment it is a part of--a list of *//* two adjoining subsegments, and a list of two adjoining triangles. One *//* of the two adjoining triangles may not be present (though there should *//* always be one), and neighboring subsegments might not be present. *//* Subsegments also store a user-defined integer "boundary marker". *//* Typically, this integer is used to indicate what boundary conditions are *//* to be applied at that location in a finite element simulation. *//* *//* Like triangles, subsegments maintain information about the relative *//* orientation of neighboring objects. *//* *//* Vertices are relatively simple. A vertex is a list of floating-point *//* numbers, starting with the x, and y coordinates, followed by an *//* arbitrary number of optional user-defined floating-point attributes, *//* followed by an integer boundary marker. During the segment insertion *//* phase, there is also a pointer from each vertex to a triangle that may *//* contain it. Each pointer is not always correct, but when one is, it *//* speeds up segment insertion. These pointers are assigned values once *//* at the beginning of the segment insertion phase, and are not used or *//* updated except during this phase. Edge flipping during segment *//* insertion will render some of them incorrect. Hence, don't rely upon *//* them for anything. *//* *//* Other than the exception mentioned above, vertices have no information *//* about what triangles, subfacets, or subsegments they are linked to. *//* *//*****************************************************************************//*****************************************************************************//* *//* Handles *//* *//* The oriented triangle (`otri') and oriented subsegment (`osub') data *//* structures defined below do not themselves store any part of the mesh. *//* The mesh itself is made of `triangle's, `subseg's, and `vertex's. *//* *//* Oriented triangles and oriented subsegments will usually be referred to *//* as "handles." A handle is essentially a pointer into the mesh; it *//* allows you to "hold" one particular part of the mesh. Handles are used *//* to specify the regions in which one is traversing and modifying the mesh.*//* A single `triangle' may be held by many handles, or none at all. (The *//* latter case is not a memory leak, because the triangle is still *//* connected to other triangles in the mesh.) *//* *//* An `otri' is a handle that holds a triangle. It holds a specific edge *//* of the triangle. An `osub' is a handle that holds a subsegment. It *//* holds either the left or right side of the subsegment. *//* *//* Navigation about the mesh is accomplished through a set of mesh *//* manipulation primitives, further below. Many of these primitives take *//* a handle and produce a new handle that holds the mesh near the first *//* handle. Other primitives take two handles and glue the corresponding *//* parts of the mesh together. The orientation of the handles is *//* important. For instance, when two triangles are glued together by the *//* bond() primitive, they are glued at the edges on which the handles lie. *//* *//* Because vertices have no information about which triangles they are *//* attached to, I commonly represent a vertex by use of a handle whose *//* origin is the vertex. A single handle can simultaneously represent a *//* triangle, an edge, and a vertex. *//* *//*****************************************************************************//* The triangle data structure. Each triangle contains three pointers to *//* adjoining triangles, plus three pointers to vertices, plus three *//* pointers to subsegments (declared below; these pointers are usually *//* `dummysub'). It may or may not also contain user-defined attributes *//* and/or a floating-point "area constraint." It may also contain extra *//* pointers for nodes, when the user asks for high-order elements. *//* Because the size and structure of a `triangle' is not decided until *//* runtime, I haven't simply declared the type `triangle' as a struct. */typedef REAL **triangle; /* Really: typedef triangle *triangle *//* An oriented triangle: includes a pointer to a triangle and orientation. *//* The orientation denotes an edge of the triangle. Hence, there are *//* three possible orientations. By convention, each edge always points *//* counterclockwise about the corresponding triangle. */struct otri { triangle *tri; int orient; /* Ranges from 0 to 2. */};/* The subsegment data structure. Each subsegment contains two pointers to *//* adjoining subsegments, plus four pointers to vertices, plus two *//* pointers to adjoining triangles, plus one boundary marker, plus one *//* segment number. */typedef REAL **subseg; /* Really: typedef subseg *subseg *//* An oriented subsegment: includes a pointer to a subsegment and an *//* orientation. The orientation denotes a side of the edge. Hence, there *//* are two possible orientations. By convention, the edge is always *//* directed so that the "side" denoted is the right side of the edge. */struct osub { subseg *ss; int ssorient; /* Ranges from 0 to 1. */};/* The vertex data structure. Each vertex is actually an array of REALs. *//* The number of REALs is unknown until runtime. An integer boundary *//* marker, and sometimes a pointer to a triangle, is appended after the *//* REALs. */typedef REAL *vertex;/* A queue used to store encroached subsegments. Each subsegment's vertices *//* are stored so that we can check whether a subsegment is still the same. */struct badsubseg { subseg encsubseg; /* An encroached subsegment. */ vertex subsegorg, subsegdest; /* Its two vertices. */};/* A queue used to store bad triangles. The key is the square of the cosine *//* of the smallest angle of the triangle. Each triangle's vertices are *//* stored so that one can check whether a triangle is still the same. */struct badtriang { triangle poortri; /* A skinny or too-large triangle. */ REAL key; /* cos^2 of smallest (apical) angle. */ vertex triangorg, triangdest, triangapex; /* Its three vertices. */ struct badtriang *nexttriang; /* Pointer to next bad triangle. */};/* A stack of triangles flipped during the most recent vertex insertion. *//* The stack is used to undo the vertex insertion if the vertex encroaches *//* upon a subsegment. */struct flipstacker { triangle flippedtri; /* A recently flipped triangle. */ struct flipstacker *prevflip; /* Previous flip in the stack. */};/* A node in a heap used to store events for the sweepline Delaunay *//* algorithm. Nodes do not point directly to their parents or children in *//* the heap. Instead, each node knows its position in the heap, and can *//* look up its parent and children in a separate array. The `eventptr' *//* points either to a `vertex' or to a triangle (in encoded format, so *//* that an orientation is included). In the latter case, the origin of *//* the oriented triangle is the apex of a "circle event" of the sweepline *//* algorithm. To distinguish site events from circle events, all circle *//* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */struct event { REAL xkey, ykey; /* Coordinates of the event. */ VOID *eventptr; /* Can be a vertex or the location of a circle event. */ int heapposition; /* Marks this event's position in the heap. */};/* A node in the splay tree. Each node holds an oriented ghost triangle *//* that represents a boundary edge of the growing triangulation. When a *//* circle event covers two boundary edges with a triangle, so that they *//* are no longer boundary edges, those edges are not immediately deleted *//* from the tree; rather, they are lazily deleted when they are next *//* encountered. (Since only a random sample of boundary edges are kept *//* in the tree, lazy deletion is faster.) `keydest' is used to verify *//* that a triangle is still the same as when it entered the splay tree; if *//* it has been rotated (due to a circle event), it no longer represents a *//* boundary edge and should be deleted. */struct splaynode { struct otri keyedge; /* Lprev of an edge on the front. */ vertex keydest; /* Used to verify that splay node is still live. */ struct splaynode *lchild, *rchild; /* Children in splay tree. */}; /* A type used to allocate memory. firstblock is the first block of items. *//* nowblock is the block from which items are currently being allocated. *//* nextitem points to the next slab of free memory for an item. *//* deaditemstack is the head of a linked list (stack) of deallocated items *//* that can be recycled. unallocateditems is the number of items that *//* remain to be allocated from nowblock. *//* *//* Traversal is the process of walking through the entire list of items, and *//* is separate from allocation. Note that a traversal will visit items on *//* the "deaditemstack" stack as well as live items. pathblock points to *//* the block currently being traversed. pathitem points to the next item *//* to be traversed. pathitemsleft is the number of items that remain to *//* be traversed in pathblock. *//* *//* alignbytes determines how new records should be aligned in memory. *//* itembytes is the length of a record in bytes (after rounding up). *//* itemsperblock is the number of items allocated at once in a single *//* block. itemsfirstblock is the number of items in the first block, *//* which can vary from the others. items is the number of currently *//* allocated items. maxitems is the maximum number of items that have *//* been allocated at once; it is the current number of items plus the *//* number of records kept on deaditemstack. */struct memorypool { VOID **firstblock, **nowblock; VOID *nextitem; VOID *deaditemstack; VOID **pathblock; VOID *pathitem; int alignbytes; int itembytes; int itemsperblock; int itemsfirstblock; long items, maxitems; int unallocateditems; int pathitemsleft;};/* Global constants. */REAL splitter; /* Used to split REAL factors for exact multiplication. */REAL epsilon; /* Floating-point machine epsilon. */REAL resulterrbound;REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;REAL iccerrboundA, iccerrboundB, iccerrboundC;REAL o3derrboundA, o3derrboundB, o3derrboundC;/* Random number seed is not constant, but I've made it global anyway. */unsigned long randomseed; /* Current random number seed. *//* Mesh data structure. Triangle operates on only one mesh, but the mesh *//* structure is used (instead of global variables) to allow reentrancy. */struct mesh {/* Variables used to allocate memory for triangles, subsegments, vertices, *//* viri (triangles being eaten), encroached segments, bad (skinny or too *//* large) triangles, and splay tree nodes. */ struct memorypool triangles; struct memorypool subsegs; struct memorypool vertices; struct memorypool viri; struct memorypool badsubsegs; struct memorypool badtriangles; struct memorypool flipstackers; struct memorypool splaynodes;/* Variables that maintain the bad triangle queues. The queues are *//* ordered from 4095 (highest priority) to 0 (lowest priority). */ struct badtriang *queuefront[4096]; struct badtriang *queuetail[4096]; int nextnonemptyq[4096]; int firstnonemptyq;/* Variable that maintains the stack of recently flipped triangles. */ struct flipstacker *lastflip;/* Other variables. */ REAL xmin, xmax, ymin, ymax; /* x and y bounds. */ REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */ int invertices; /* Number of input vertices. */ int inelements; /* Number of input triangles. */ int insegments; /* Number of input segments. */ int holes; /* Number of input holes. */ int regions; /* Number of input regions. */ int undeads; /* Number of input vertices that don't appear in the mesh. */ long edges; /* Number of output edges. */ int mesh_dim; /* Dimension (ought to be 2). */ int nextras; /* Number of attributes per vertex. */ int eextras; /* Number of attributes per triangle. */ long hullsize; /* Number of edges in convex hull. */ int steinerleft; /* Number of Steiner points not yet used. */ int vertexmarkindex; /* Index to find boundary marker of a vertex. */ int vertex2triindex; /* Index to find a triangle adjacent to a vertex. */ int highorderindex; /* Index to find extra nodes for high-order elements. */ int elemattribindex; /* Index to find attributes of a triangle. */ int areaboundindex; /* Index to find area bound of a triangle. */ int checksegments; /* Are there segments in the triangulation yet? */ int checkquality; /* Has quality triangulation begun yet? */ int readnodefile; /* Has a .node file been read? */ long samples; /* Number of random samples for point location. */ long incirclecount; /* Number of incircle tests performed. */ long counterclockcount; /* Number of counterclockwise tests performed. */ long orient3dcount; /* Number of 3D orientation tests performed. */ long hyperbolacount; /* Number of right-of-hyperbola tests performed. */ long circumcentercount; /* Number of circumcenter calculations performed. */ long circletopcount; /* Number of circle top calculations performed. *//* Triangular bounding box vertices. */ vertex infvertex1, infvertex2, infvertex3;/* Pointer to the `triangle' that occupies all of "outer space." */ triangle *dummytri; triangle *dummytribase; /* Keep base address so we can free() it later. *//* Pointer to the omnipresent subsegment. Referenced by any triangle or *//* subsegment that isn't really connected to a subsegment at that *//* location. */ subseg *dummysub; subseg *dummysubbase; /* Keep base address so we can free() it later. *//* Pointer to a recently visited triangle. Improves point location if *//* proximate vertices are inserted sequentially. */ struct otri recenttri;}; /* End of `struct mesh'. *//* Data structure for command line switches and file names. This structure *//* is used (instead of global variables) to allow reentrancy. */struct behavior {/* Switches for the triangulator. *//* poly: -p switch. refine: -r switch. *//* quality: -q switch. *//* minangle: minimum angle bound, specified after -q switch. *//* goodangle: cosine squared of minangle. *//* offconstant: constant used to place off-center Steiner points. *//* vararea: -a switch without number. *//* fixedarea: -a switch with number. *//* maxarea: maximum area bound, specified after -a switch. *//* usertest: -u switch. *//* regionattrib: -A switch. convex: -c switch. *//* weighted: 1 for -w switch, 2 for -W switch. jettison: -j switch *//* firstnumber: inverse of -z switch. All items are numbered starting *//* from `firstnumber'. *//* edgesout: -e switch. voronoi: -v switch. *//* neighbors: -n switch. geomview: -g switch. *//* nobound: -B switch. nopolywritten: -P switch. *//* nonodewritten: -N switch. noelewritten: -E switch. *//* noiterationnum: -I switch. noholes: -O switch. *//* noexact: -X switch. *//* order: element order, specified after -o switch. *//* nobisect: count of how often -Y switch is selected. *//* steiner: maximum number of Steiner points, specified after -S switch. *//* incremental: -i switch. sweepline: -F switch. *//* dwyer: inverse of -l switch. *//* splitseg: -s switch. *//* conformdel: -D switch. docheck: -C switch. *//* quiet: -Q switch. verbose: count of how often -V switch is selected. *//* usesegments: -p, -r, -q, or -c switch; determines whether segments are *//* used at all. *//* *//* Read the instructions to find out the meaning of these switches. */ int poly, refine, quality, vararea, fixedarea, usertest; int regionattrib, convex, weighted, jettison; int firstnumber; int edgesout, voronoi, neighbors, geomview; int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum; int noholes, noexact, conformdel; int incremental, sweepline, dwyer; int splitseg; int docheck; int quiet, verbose; int usesegments; int order; int nobisect; int steiner; REAL minangle, goodangle, offconstant; REAL maxarea;/* Variables for file names. */#ifndef TRILIBRARY char innodefilename[FILENAMESIZE]; char inelefilename[FILENAMESIZE]; char inpolyfilename[FILENAMESIZE]; char areafilename[FILENAMESIZE]; char outnodefilename[FILENAMESIZE]; char outelefilename[FILENAMESIZE]; char outpolyfilename[FILENAMESIZE]; char edgefilename[FILENAMESIZE]; char vnodefilename[FILENAMESIZE]; char vedgefilename[FILENAMESIZE]; char neighborfilename[FILENAMESIZE]; char offfilename[FILENAMESIZE];#endif /* not TRILIBRARY */}; /* End of `struct behavior'. *//*****************************************************************************//* *//* Mesh manipulation primitives. Each triangle contains three pointers to *//* other triangles, with orientations. Each pointer points not to the *//* first byte of a triangle, but to one of the first three bytes of a *//* triangle. It is necessary to extract both the triangle itself and the *//* orientation. To save memory, I keep both pieces of information in one *//* pointer. To make this possible, I assume that all triangles are aligned *//* to four-byte boundaries. The decode() routine below decodes a pointer, *//* extracting an orientation (in the range 0 to 2) and a pointer to the *//* beginning of a triangle. The encode() routine compresses a pointer to a *//* triangle and an orientation into a single pointer. My assumptions that *//* triangles are four-byte-aligned and that the `unsigned long' type is *//* long enough to hold a pointer are two of the few kludges in this program.*//* *//* Subsegments are manipulated similarly. A pointer to a subsegment *//* carries both an address and an orientation in the range 0 to 1. *//* *//* The other primitives take an oriented triangle or oriented subsegment, *//* and return an oriented triangle or oriented subsegment or vertex; or *//* they change the connections in the data structure. *//* *//* Below, triangles and subsegments are denoted by their vertices. The *//* triangle abc has origin (org) a, destination (dest) b, and apex (apex) *//* c. These vertices occur in counterclockwise order about the triangle. *//* The handle abc may simultaneously denote vertex a, edge ab, and triangle *//* abc. *//* *//* Similarly, the subsegment ab has origin (sorg) a and destination (sdest) *//* b. If ab is thought to be directed upward (with b directly above a), *//* then the handle ab is thought to grasp the right side of ab, and may *//* simultaneously denote vertex a and edge ab. *//* *//* An asterisk (*) denotes a vertex whose identity is unknown. *//* *//* Given this notation, a partial list of mesh manipulation primitives *//* follows. *//* *//* *//* For triangles: *//* *//* sym: Find the abutting triangle; same edge. *//* sym(abc) -> ba* *//* *//* lnext: Find the next edge (counterclockwise) of a triangle. *//* lnext(abc) -> bca *//* *//* lprev: Find the previous edge (clockwise) of a triangle. *//* lprev(abc) -> cab *//* *//* onext: Find the next edge counterclockwise with the same origin. *//* onext(abc) -> ac* *//* *//* oprev: Find the next edge clockwise with the same origin. *//* oprev(abc) -> a*b *//* *//* dnext: Find the next edge counterclockwise with the same destination. *//* dnext(abc) -> *ba *//* *//* dprev: Find the next edge clockwise with the same destination. *//* dprev(abc) -> cb* *//* *//* rnext: Find the next edge (counterclockwise) of the adjacent triangle. *//* rnext(abc) -> *a* *//* *//* rprev: Find the previous edge (clockwise) of the adjacent triangle. *//* rprev(abc) -> b** *//* *//* org: Origin dest: Destination apex: Apex *//* org(abc) -> a dest(abc) -> b apex(abc) -> c *//* *//* bond: Bond two triangles together at the resepective handles. *//* bond(abc, bad) *//* *//* *//* For subsegments: *//* *//* ssym: Reverse the orientation of a subsegment. *//* ssym(ab) -> ba *//* *//* spivot: Find adjoining subsegment with the same origin. *//* spivot(ab) -> a* *//* *//* snext: Find next subsegment in sequence. *//* snext(ab) -> b* *//* *//* sorg: Origin sdest: Destination *//* sorg(ab) -> a sdest(ab) -> b *//* *//* sbond: Bond two subsegments together at the respective origins. *//* sbond(ab, ac) *//* *//* *//* For interacting tetrahedra and subfacets: *//* *//* tspivot: Find a subsegment abutting a triangle. *//* tspivot(abc) -> ba *//* *//* stpivot: Find a triangle abutting a subsegment. *//* stpivot(ab) -> ba* *//* *//* tsbond: Bond a triangle to a subsegment. *//* tsbond(abc, ba) *//* *//*****************************************************************************//********* Mesh manipulation primitives begin here *********//** **//** **//* Fast lookup arrays to speed some of the mesh manipulation primitives. */int plus1mod3[3] = {1, 2, 0};int minus1mod3[3] = {2, 0, 1};/********* Primitives for triangles *********//* *//* *//* decode() converts a pointer to an oriented triangle. The orientation is *//* extracted from the two least significant bits of the pointer. */#define decode(ptr, otri) \ (otri).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \ (otri).tri = (triangle *) \ ((unsigned long) (ptr) ^ (unsigned long) (otri).orient)/* encode() compresses an oriented triangle into a single pointer. It *//* relies on the assumption that all triangles are aligned to four-byte *//* boundaries, so the two least significant bits of (otri).tri are zero. */#define encode(otri) \ (triangle) ((unsigned long) (otri).tri | (unsigned long) (otri).orient) /* The following handle manipulation primitives are all described by Guibas *//* and Stolfi. However, Guibas and Stolfi use an edge-based data *//* structure, whereas I use a triangle-based data structure. *//* sym() finds the abutting triangle, on the same edge. Note that the edge *//* direction is necessarily reversed, because the handle specified by an *//* oriented triangle is directed counterclockwise around the triangle. */#define sym(otri1, otri2) \ ptr = (otri1).tri[(otri1).orient]; \ decode(ptr, otri2);#define symself(otri) \ ptr = (otri).tri[(otri).orient]; \ decode(ptr, otri);/* lnext() finds the next edge (counterclockwise) of a triangle. */#define lnext(otri1, otri2) \ (otri2).tri = (otri1).tri; \ (otri2).orient = plus1mod3[(otri1).orient]#define lnextself(otri) \ (otri).orient = plus1mod3[(otri).orient]/* lprev() finds the previous edge (clockwise) of a triangle. */#define lprev(otri1, otri2) \ (otri2).tri = (otri1).tri; \ (otri2).orient = minus1mod3[(otri1).orient]#define lprevself(otri) \ (otri).orient = minus1mod3[(otri).orient]/* onext() spins counterclockwise around a vertex; that is, it finds the *//* next edge with the same origin in the counterclockwise direction. This *//* edge is part of a different triangle. */#define onext(otri1, otri2) \ lprev(otri1, otri2); \ symself(otri2);#define onextself(otri) \ lprevself(otri); \ symself(otri);/* oprev() spins clockwise around a vertex; that is, it finds the next edge *//* with the same origin in the clockwise direction. This edge is part of *//* a different triangle. */#define oprev(otri1, otri2) \ sym(otri1, otri2); \ lnextself(otri2);#define oprevself(otri) \ symself(otri); \ lnextself(otri);/* dnext() spins counterclockwise around a vertex; that is, it finds the *//* next edge with the same destination in the counterclockwise direction. *//* This edge is part of a different triangle. */#define dnext(otri1, otri2) \ sym(otri1, otri2); \ lprevself(otri2);#define dnextself(otri) \ symself(otri); \ lprevself(otri);/* dprev() spins clockwise around a vertex; that is, it finds the next edge *//* with the same destination in the clockwise direction. This edge is *//* part of a different triangle. */#define dprev(otri1, otri2) \ lnext(otri1, otri2); \ symself(otri2);#define dprevself(otri) \ lnextself(otri); \ symself(otri);/* rnext() moves one edge counterclockwise about the adjacent triangle. *//* (It's best understood by reading Guibas and Stolfi. It involves *//* changing triangles twice.) */#define rnext(otri1, otri2) \ sym(otri1, otri2); \ lnextself(otri2); \ symself(otri2);#define rnextself(otri) \ symself(otri); \ lnextself(otri); \ symself(otri);/* rprev() moves one edge clockwise about the adjacent triangle. *//* (It's best understood by reading Guibas and Stolfi. It involves *//* changing triangles twice.) */#define rprev(otri1, otri2) \ sym(otri1, otri2); \ lprevself(otri2); \ symself(otri2);#define rprevself(otri) \ symself(otri); \ lprevself(otri); \ symself(otri);/* These primitives determine or set the origin, destination, or apex of a *//* triangle. */#define org(otri, vertexptr) \ vertexptr = (vertex) (otri).tri[plus1mod3[(otri).orient] + 3]#define dest(otri, vertexptr) \ vertexptr = (vertex) (otri).tri[minus1mod3[(otri).orient] + 3]#define apex(otri, vertexptr) \ vertexptr = (vertex) (otri).tri[(otri).orient + 3]#define setorg(otri, vertexptr) \ (otri).tri[plus1mod3[(otri).orient] + 3] = (triangle) vertexptr#define setdest(otri, vertexptr) \ (otri).tri[minus1mod3[(otri).orient] + 3] = (triangle) vertexptr#define setapex(otri, vertexptr) \ (otri).tri[(otri).orient + 3] = (triangle) vertexptr/* Bond two triangles together. */#define bond(otri1, otri2) \ (otri1).tri[(otri1).orient] = encode(otri2); \ (otri2).tri[(otri2).orient] = encode(otri1)/* Dissolve a bond (from one side). Note that the other triangle will still *//* think it's connected to this triangle. Usually, however, the other *//* triangle is being deleted entirely, or bonded to another triangle, so *//* it doesn't matter. */#define dissolve(otri) \ (otri).tri[(otri).orient] = (triangle) m->dummytri/* Copy an oriented triangle. */#define otricopy(otri1, otri2) \ (otri2).tri = (otri1).tri; \ (otri2).orient = (otri1).orient/* Test for equality of oriented triangles. */#define otriequal(otri1, otri2) \ (((otri1).tri == (otri2).tri) && \ ((otri1).orient == (otri2).orient))/* Primitives to infect or cure a triangle with the virus. These rely on *//* the assumption that all subsegments are aligned to four-byte boundaries.*/#define infect(otri) \ (otri).tri[6] = (triangle) \ ((unsigned long) (otri).tri[6] | (unsigned long) 2l)#define uninfect(otri) \ (otri).tri[6] = (triangle) \ ((unsigned long) (otri).tri[6] & ~ (unsigned long) 2l)/* Test a triangle for viral infection. */#define infected(otri) \ (((unsigned long) (otri).tri[6] & (unsigned long) 2l) != 0l)/* Check or set a triangle's attributes. */#define elemattribute(otri, attnum) \ ((REAL *) (otri).tri)[m->elemattribindex + (attnum)]#define setelemattribute(otri, attnum, value) \ ((REAL *) (otri).tri)[m->elemattribindex + (attnum)] = value/* Check or set a triangle's maximum area bound. */#define areabound(otri) ((REAL *) (otri).tri)[m->areaboundindex]#define setareabound(otri, value) \ ((REAL *) (otri).tri)[m->areaboundindex] = value/* Check or set a triangle's deallocation. Its second pointer is set to *//* NULL to indicate that it is not allocated. (Its first pointer is used *//* for the stack of dead items.) Its fourth pointer (its first vertex) *//* is set to NULL in case a `badtriang' structure points to it. */#define deadtri(tria) ((tria)[1] == (triangle) NULL)#define killtri(tria) \ (tria)[1] = (triangle) NULL; \ (tria)[3] = (triangle) NULL/********* Primitives for subsegments *********//* *//* *//* sdecode() converts a pointer to an oriented subsegment. The orientation *//* is extracted from the least significant bit of the pointer. The two *//* least significant bits (one for orientation, one for viral infection) *//* are masked out to produce the real pointer. */#define sdecode(sptr, osub) \ (osub).ssorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \ (osub).ss = (subseg *) \ ((unsigned long) (sptr) & ~ (unsigned long) 3l)/* sencode() compresses an oriented subsegment into a single pointer. It *//* relies on the assumption that all subsegments are aligned to two-byte *//* boundaries, so the least significant bit of (osub).ss is zero. */#define sencode(osub) \ (subseg) ((unsigned long) (osub).ss | (unsigned long) (osub).ssorient)/* ssym() toggles the orientation of a subsegment. */#define ssym(osub1, osub2) \ (osub2).ss = (osub1).ss; \ (osub2).ssorient = 1 - (osub1).ssorient#define ssymself(osub) \ (osub).ssorient = 1 - (osub).ssorient/* spivot() finds the other subsegment (from the same segment) that shares *//* the same origin. */#define spivot(osub1, osub2) \ sptr = (osub1).ss[(osub1).ssorient]; \ sdecode(sptr, osub2)#define spivotself(osub) \ sptr = (osub).ss[(osub).ssorient]; \ sdecode(sptr, osub)/* snext() finds the next subsegment (from the same segment) in sequence; *//* one whose origin is the input subsegment's destination. */#define snext(osub1, osub2) \ sptr = (osub1).ss[1 - (osub1).ssorient]; \ sdecode(sptr, osub2)#define snextself(osub) \ sptr = (osub).ss[1 - (osub).ssorient]; \ sdecode(sptr, osub)/* These primitives determine or set the origin or destination of a *//* subsegment or the segment that includes it. */#define sorg(osub, vertexptr) \ vertexptr = (vertex) (osub).ss[2 + (osub).ssorient]#define sdest(osub, vertexptr) \ vertexptr = (vertex) (osub).ss[3 - (osub).ssorient]#define setsorg(osub, vertexptr) \ (osub).ss[2 + (osub).ssorient] = (subseg) vertexptr#define setsdest(osub, vertexptr) \ (osub).ss[3 - (osub).ssorient] = (subseg) vertexptr#define segorg(osub, vertexptr) \ vertexptr = (vertex) (osub).ss[4 + (osub).ssorient]#define segdest(osub, vertexptr) \ vertexptr = (vertex) (osub).ss[5 - (osub).ssorient]#define setsegorg(osub, vertexptr) \ (osub).ss[4 + (osub).ssorient] = (subseg) vertexptr#define setsegdest(osub, vertexptr) \ (osub).ss[5 - (osub).ssorient] = (subseg) vertexptr/* These primitives read or set a boundary marker. Boundary markers are *//* used to hold user-defined tags for setting boundary conditions in *//* finite element solvers. */#define mark(osub) (* (int *) ((osub).ss + 8))#define setmark(osub, value) \ * (int *) ((osub).ss + 8) = value/* Bond two subsegments together. */#define sbond(osub1, osub2) \ (osub1).ss[(osub1).ssorient] = sencode(osub2); \ (osub2).ss[(osub2).ssorient] = sencode(osub1)/* Dissolve a subsegment bond (from one side). Note that the other *//* subsegment will still think it's connected to this subsegment. */#define sdissolve(osub) \ (osub).ss[(osub).ssorient] = (subseg) m->dummysub/* Copy a subsegment. */#define subsegcopy(osub1, osub2) \ (osub2).ss = (osub1).ss; \ (osub2).ssorient = (osub1).ssorient/* Test for equality of subsegments. */#define subsegequal(osub1, osub2) \ (((osub1).ss == (osub2).ss) && \ ((osub1).ssorient == (osub2).ssorient))/* Check or set a subsegment's deallocation. Its second pointer is set to *//* NULL to indicate that it is not allocated. (Its first pointer is used *//* for the stack of dead items.) Its third pointer (its first vertex) *//* is set to NULL in case a `badsubseg' structure points to it. */#define deadsubseg(sub) ((sub)[1] == (subseg) NULL)#define killsubseg(sub) \ (sub)[1] = (subseg) NULL; \ (sub)[2] = (subseg) NULL/********* Primitives for interacting triangles and subsegments *********//* *//* *//* tspivot() finds a subsegment abutting a triangle. */#define tspivot(otri, osub) \ sptr = (subseg) (otri).tri[6 + (otri).orient]; \ sdecode(sptr, osub)/* stpivot() finds a triangle abutting a subsegment. It requires that the *//* variable `ptr' of type `triangle' be defined. */#define stpivot(osub, otri) \ ptr = (triangle) (osub).ss[6 + (osub).ssorient]; \ decode(ptr, otri)/* Bond a triangle to a subsegment. */#define tsbond(otri, osub) \ (otri).tri[6 + (otri).orient] = (triangle) sencode(osub); \ (osub).ss[6 + (osub).ssorient] = (subseg) encode(otri)/* Dissolve a bond (from the triangle side). */#define tsdissolve(otri) \ (otri).tri[6 + (otri).orient] = (triangle) m->dummysub/* Dissolve a bond (from the subsegment side). */#define stdissolve(osub) \ (osub).ss[6 + (osub).ssorient] = (subseg) m->dummytri/********* Primitives for vertices *********//* *//* */#define vertexmark(vx) ((int *) (vx))[m->vertexmarkindex]#define setvertexmark(vx, value) \ ((int *) (vx))[m->vertexmarkindex] = value#define vertextype(vx) ((int *) (vx))[m->vertexmarkindex + 1]#define setvertextype(vx, value) \ ((int *) (vx))[m->vertexmarkindex + 1] = value#define vertex2tri(vx) ((triangle *) (vx))[m->vertex2triindex]#define setvertex2tri(vx, value) \ ((triangle *) (vx))[m->vertex2triindex] = value/** **//** **//********* Mesh manipulation primitives end here *********//********* User-defined triangle evaluation routine begins here *********//** **//** **//*****************************************************************************//* *//* triunsuitable() Determine if a triangle is unsuitable, and thus must *//* be further refined. *//* *//* You may write your own procedure that decides whether or not a selected *//* triangle is too big (and needs to be refined). There are two ways to do *//* this. *//* *//* (1) Modify the procedure `triunsuitable' below, then recompile *//* Triangle. *//* *//* (2) Define the symbol EXTERNAL_TEST (either by adding the definition *//* to this file, or by using the appropriate compiler switch). This way, *//* you can compile triangle.c separately from your test. Write your own *//* `triunsuitable' procedure in a separate C file (using the same prototype *//* as below). Compile it and link the object code with triangle.o. *//* *//* This procedure returns 1 if the triangle is too large and should be *//* refined; 0 otherwise. *//* *//*****************************************************************************/#ifdef EXTERNAL_TESTint triunsuitable();#else /* not EXTERNAL_TEST */#ifdef ANSI_DECLARATORSint triunsuitable(vertex triorg, vertex tridest, vertex triapex, REAL area)#else /* not ANSI_DECLARATORS */int triunsuitable(triorg, tridest, triapex, area)vertex triorg; /* The triangle's origin vertex. */vertex tridest; /* The triangle's destination vertex. */vertex triapex; /* The triangle's apex vertex. */REAL area; /* The area of the triangle. */#endif /* not ANSI_DECLARATORS */{ REAL dxoa, dxda, dxod; REAL dyoa, dyda, dyod; REAL oalen, dalen, odlen; REAL maxlen; dxoa = triorg[0] - triapex[0]; dyoa = triorg[1] - triapex[1]; dxda = tridest[0] - triapex[0]; dyda = tridest[1] - triapex[1]; dxod = triorg[0] - tridest[0]; dyod = triorg[1] - tridest[1]; /* Find the squares of the lengths of the triangle's three edges. */ oalen = dxoa * dxoa + dyoa * dyoa; dalen = dxda * dxda + dyda * dyda; odlen = dxod * dxod + dyod * dyod; /* Find the square of the length of the longest edge. */ maxlen = (dalen > oalen) ? dalen : oalen; maxlen = (odlen > maxlen) ? odlen : maxlen; if (maxlen > 0.05 * (triorg[0] * triorg[0] + triorg[1] * triorg[1]) + 0.02) { return 1; } else { return 0; }}#endif /* not EXTERNAL_TEST *//** **//** **//********* User-defined triangle evaluation routine ends here *********//********* Memory allocation and program exit wrappers begin here *********//** **//** **/#ifdef ANSI_DECLARATORSvoid triexit(int status)#else /* not ANSI_DECLARATORS */void triexit(status)int status;#endif /* not ANSI_DECLARATORS */{ exit(status);}#ifdef ANSI_DECLARATORSVOID *trimalloc(int size)#else /* not ANSI_DECLARATORS */VOID *trimalloc(size)int size;#endif /* not ANSI_DECLARATORS */{ VOID *memptr; memptr = (VOID *) malloc((unsigned int) size); if (memptr == (VOID *) NULL) { printf("Error: Out of memory.\n"); triexit(1); } return(memptr);}#ifdef ANSI_DECLARATORSvoid trifree(VOID *memptr)#else /* not ANSI_DECLARATORS */void trifree(memptr)VOID *memptr;#endif /* not ANSI_DECLARATORS */{ free(memptr);}/** **//** **//********* Memory allocation and program exit wrappers end here *********//********* User interaction routines begin here *********//** **//** **//*****************************************************************************//* *//* syntax() Print list of command line switches. *//* *//*****************************************************************************/#ifndef TRILIBRARYvoid syntax(){#ifdef CDT_ONLY#ifdef REDUCED printf("triangle [-pAcjevngBPNEIOXzo_lQVh] input_file\n");#else /* not REDUCED */ printf("triangle [-pAcjevngBPNEIOXzo_iFlCQVh] input_file\n");#endif /* not REDUCED */#else /* not CDT_ONLY */#ifdef REDUCED printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__lQVh] input_file\n");#else /* not REDUCED */ printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");#endif /* not REDUCED */#endif /* not CDT_ONLY */ printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");#ifndef CDT_ONLY printf(" -r Refines a previously generated mesh.\n"); printf( " -q Quality mesh generation. A minimum angle may be specified.\n"); printf(" -a Applies a maximum triangle area constraint.\n"); printf(" -u Applies a user-defined triangle constraint.\n");#endif /* not CDT_ONLY */ printf( " -A Applies attributes to identify triangles in certain regions.\n"); printf(" -c Encloses the convex hull with segments.\n");#ifndef CDT_ONLY printf(" -D Conforming Delaunay: all triangles are truly Delaunay.\n");#endif /* not CDT_ONLY *//* printf(" -w Weighted Delaunay triangulation.\n"); printf(" -W Regular triangulation (lower hull of a height field).\n");*/ printf(" -j Jettison unused vertices from output .node file.\n"); printf(" -e Generates an edge list.\n"); printf(" -v Generates a Voronoi diagram.\n"); printf(" -n Generates a list of triangle neighbors.\n"); printf(" -g Generates an .off file for Geomview.\n"); printf(" -B Suppresses output of boundary information.\n"); printf(" -P Suppresses output of .poly file.\n"); printf(" -N Suppresses output of .node file.\n"); printf(" -E Suppresses output of .ele file.\n"); printf(" -I Suppresses mesh iteration numbers.\n"); printf(" -O Ignores holes in .poly file.\n"); printf(" -X Suppresses use of exact arithmetic.\n"); printf(" -z Numbers all items starting from zero (rather than one).\n"); printf(" -o2 Generates second-order subparametric elements.\n");#ifndef CDT_ONLY printf(" -Y Suppresses boundary segment splitting.\n"); printf(" -S Specifies maximum number of added Steiner points.\n");#endif /* not CDT_ONLY */#ifndef REDUCED printf(" -i Uses incremental method, rather than divide-and-conquer.\n"); printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");#endif /* not REDUCED */ printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");#ifndef REDUCED#ifndef CDT_ONLY printf( " -s Force segments into mesh by splitting (instead of using CDT).\n");#endif /* not CDT_ONLY */ printf(" -C Check consistency of final mesh.\n");#endif /* not REDUCED */ printf(" -Q Quiet: No terminal output except errors.\n"); printf(" -V Verbose: Detailed information on what I'm doing.\n"); printf(" -h Help: Detailed instructions for Triangle.\n"); triexit(0);}#endif /* not TRILIBRARY *//*****************************************************************************//* *//* info() Print out complete instructions. *//* *//*****************************************************************************/#ifndef TRILIBRARYvoid info(){ printf("Triangle\n"); printf("A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n"); printf("Version 1.6\n\n"); printf("Copyright 1993, 1995, 1997, 1998, 2002, 2005 Jonathan Richard Shewchuk\n"); printf("2360 Woolsey #H / Berkeley, California 94705-1927\n"); printf("Bugs/comments to jrs@cs.berkeley.edu\n"); printf("Created as part of the Quake project (tools for earthquake simulation).\n"); printf("Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n"); printf("There is no warranty whatsoever. Use at your own risk.\n");#ifdef SINGLE printf("This executable is compiled for single precision arithmetic.\n\n\n");#else /* not SINGLE */ printf("This executable is compiled for double precision arithmetic.\n\n\n");#endif /* not SINGLE */ printf("Triangle generates exact Delaunay triangulations, constrained Delaunay\n"); printf("triangulations, conforming Delaunay triangulations, Voronoi diagrams, and\n"); printf("high-quality triangular meshes. The latter can be generated with no small\n"); printf("or large angles, and are thus suitable for finite element analysis. If no\n"); printf("command line switch is specified, your .node input file is read, and the\n"); printf("Delaunay triangulation is returned in .node and .ele output files. The\n"); printf("command syntax is:\n\n"); printf("triangle [-prq__a__uAcDjevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n"); printf("Underscores indicate that numbers may optionally follow certain switches.\n"); printf("Do not leave any space between a switch and its numeric parameter.\n"); printf("input_file must be a file with extension .node, or extension .poly if the\n"); printf("-p switch is used. If -r is used, you must supply .node and .ele files,\n"); printf("and possibly a .poly file and an .area file as well. The formats of these\n"); printf("files are described below.\n\n"); printf("Command Line Switches:\n\n"); printf(" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"); printf(" vertices, segments, holes, regional attributes, and regional area\n"); printf(" constraints. Generates a constrained Delaunay triangulation (CDT)\n"); printf(" fitting the input; or, if -s, -q, -a, or -u is used, a conforming\n"); printf(" constrained Delaunay triangulation (CCDT). If you want a truly\n"); printf(" Delaunay (not just constrained Delaunay) triangulation, use -D as\n"); printf(" well. When -p is not used, Triangle reads a .node file by default.\n"); printf(" -r Refines a previously generated mesh. The mesh is read from a .node\n"); printf(" file and an .ele file. If -p is also used, a .poly file is read\n"); printf(" and used to constrain segments in the mesh. If -a is also used\n"); printf(" (with no number following), an .area file is read and used to\n"); printf(" impose area constraints on the mesh. Further details on refinement\n"); printf(" appear below.\n"); printf(" -q Quality mesh generation by Delaunay refinement (a hybrid of Paul\n"); printf(" Chew's and Jim Ruppert's algorithms). Adds vertices to the mesh to\n"); printf(" ensure that all angles are between 20 and 140 degrees. An\n"); printf(" alternative bound on the minimum angle, replacing 20 degrees, may\n"); printf(" be specified after the `q'. The specified angle may include a\n"); printf(" decimal point, but not exponential notation. Note that a bound of\n"); printf(" theta degrees on the smallest angle also implies a bound of\n"); printf(" (180 - 2 theta) on the largest angle. If the minimum angle is 28.6\n"); printf(" degrees or smaller, Triangle is mathematically guaranteed to\n"); printf(" terminate (assuming infinite precision arithmetic--Triangle may\n"); printf(" fail to terminate if you run out of precision). In practice,\n"); printf(" Triangle often succeeds for minimum angles up to 34 degrees. For\n"); printf(" some meshes, however, you might need to reduce the minimum angle to\n"); printf(" avoid problems associated with insufficient floating-point\n"); printf(" precision.\n"); printf(" -a Imposes a maximum triangle area. If a number follows the `a', no\n"); printf(" triangle is generated whose area is larger than that number. If no\n"); printf(" number is specified, an .area file (if -r is used) or .poly file\n"); printf(" (if -r is not used) specifies a set of maximum area constraints.\n"); printf(" An .area file contains a separate area constraint for each\n"); printf(" triangle, and is useful for refining a finite element mesh based on\n"); printf(" a posteriori error estimates. A .poly file can optionally contain\n"); printf(" an area constraint for each segment-bounded region, thereby\n"); printf(" controlling triangle densities in a first triangulation of a PSLG.\n"); printf(" You can impose both a fixed area constraint and a varying area\n"); printf(" constraint by invoking the -a switch twice, once with and once\n"); printf(" without a number following. Each area specified may include a\n"); printf(" decimal point.\n"); printf(" -u Imposes a user-defined constraint on triangle size. There are two\n"); printf(" ways to use this feature. One is to edit the triunsuitable()\n"); printf(" procedure in triangle.c to encode any constraint you like, then\n"); printf(" recompile Triangle. The other is to compile triangle.c with the\n"); printf(" EXTERNAL_TEST symbol set (compiler switch -DEXTERNAL_TEST), then\n"); printf(" link Triangle with a separate object file that implements\n"); printf(" triunsuitable(). In either case, the -u switch causes the user-\n"); printf(" defined test to be applied to every triangle.\n"); printf(" -A Assigns an additional floating-point attribute to each triangle\n"); printf(" that identifies what segment-bounded region each triangle belongs\n"); printf(" to. Attributes are assigned to regions by the .poly file. If a\n"); printf(" region is not explicitly marked by the .poly file, triangles in\n"); printf(" that region are assigned an attribute of zero. The -A switch has\n"); printf(" an effect only when the -p switch is used and the -r switch is not.\n"); printf(" -c Creates segments on the convex hull of the triangulation. If you\n"); printf(" are triangulating a vertex set, this switch causes a .poly file to\n"); printf(" be written, containing all edges of the convex hull. If you are\n"); printf(" triangulating a PSLG, this switch specifies that the whole convex\n"); printf(" hull of the PSLG should be triangulated, regardless of what\n"); printf(" segments the PSLG has. If you do not use this switch when\n"); printf(" triangulating a PSLG, Triangle assumes that you have identified the\n"); printf(" region to be triangulated by surrounding it with segments of the\n"); printf(" input PSLG. Beware: if you are not careful, this switch can cause\n"); printf(" the introduction of an extremely thin angle between a PSLG segment\n"); printf(" and a convex hull segment, which can cause overrefinement (and\n"); printf(" possibly failure if Triangle runs out of precision). If you are\n"); printf(" refining a mesh, the -c switch works differently: it causes a\n"); printf(" .poly file to be written containing the boundary edges of the mesh\n"); printf(" (useful if no .poly file was read).\n"); printf(" -D Conforming Delaunay triangulation: use this switch if you want to\n"); printf(" ensure that all the triangles in the mesh are Delaunay, and not\n"); printf(" merely constrained Delaunay; or if you want to ensure that all the\n"); printf(" Voronoi vertices lie within the triangulation. (Some finite volume\n"); printf(" methods have this requirement.) This switch invokes Ruppert's\n"); printf(" original algorithm, which splits every subsegment whose diametral\n"); printf(" circle is encroached. It usually increases the number of vertices\n"); printf(" and triangles.\n"); printf(" -j Jettisons vertices that are not part of the final triangulation\n"); printf(" from the output .node file. By default, Triangle copies all\n"); printf(" vertices in the input .node file to the output .node file, in the\n"); printf(" same order, so their indices do not change. The -j switch prevents\n"); printf(" duplicated input vertices, or vertices `eaten' by holes, from\n"); printf(" appearing in the output .node file. Thus, if two input vertices\n"); printf(" have exactly the same coordinates, only the first appears in the\n"); printf(" output. If any vertices are jettisoned, the vertex numbering in\n"); printf(" the output .node file differs from that of the input .node file.\n"); printf(" -e Outputs (to an .edge file) a list of edges of the triangulation.\n"); printf(" -v Outputs the Voronoi diagram associated with the triangulation.\n"); printf(" Does not attempt to detect degeneracies, so some Voronoi vertices\n"); printf(" may be duplicated. See the discussion of Voronoi diagrams below.\n"); printf(" -n Outputs (to a .neigh file) a list of triangles neighboring each\n"); printf(" triangle.\n"); printf(" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"); printf(" viewing with the Geometry Center's Geomview package.\n"); printf(" -B No boundary markers in the output .node, .poly, and .edge output\n"); printf(" files. See the detailed discussion of boundary markers below.\n"); printf(" -P No output .poly file. Saves disk space, but you lose the ability\n"); printf(" to maintain constraining segments on later refinements of the mesh.\n"); printf(" -N No output .node file.\n"); printf(" -E No output .ele file.\n"); printf(" -I No iteration numbers. Suppresses the output of .node and .poly\n"); printf(" files, so your input files won't be overwritten. (If your input is\n"); printf(" a .poly file only, a .node file is written.) Cannot be used with\n"); printf(" the -r switch, because that would overwrite your input .ele file.\n"); printf(" Shouldn't be used with the -q, -a, -u, or -s switch if you are\n"); printf(" using a .node file for input, because no .node file is written, so\n"); printf(" there is no record of any added Steiner points.\n"); printf(" -O No holes. Ignores the holes in the .poly file.\n"); printf(" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"); printf(" arithmetic for certain tests if it thinks the inexact tests are not\n"); printf(" accurate enough. Exact arithmetic ensures the robustness of the\n"); printf(" triangulation algorithms, despite floating-point roundoff error.\n"); printf(" Disabling exact arithmetic with the -X switch causes a small\n"); printf(" improvement in speed and creates the possibility that Triangle will\n"); printf(" fail to produce a valid mesh. Not recommended.\n"); printf(" -z Numbers all items starting from zero (rather than one). Note that\n"); printf(" this switch is normally overridden by the value used to number the\n"); printf(" first vertex of the input .node or .poly file. However, this\n"); printf(" switch is useful when calling Triangle from another program.\n"); printf(" -o2 Generates second-order subparametric elements with six nodes each.\n"); printf(" -Y No new vertices on the boundary. This switch is useful when the\n"); printf(" mesh boundary must be preserved so that it conforms to some\n"); printf(" adjacent mesh. Be forewarned that you will probably sacrifice much\n"); printf(" of the quality of the mesh; Triangle will try, but the resulting\n"); printf(" mesh may contain poorly shaped triangles. Works well if all the\n"); printf(" boundary vertices are closely spaced. Specify this switch twice\n"); printf(" (`-YY') to prevent all segment splitting, including internal\n"); printf(" boundaries.\n"); printf(" -S Specifies the maximum number of Steiner points (vertices that are\n"); printf(" not in the input, but are added to meet the constraints on minimum\n"); printf(" angle and maximum area). The default is to allow an unlimited\n"); printf(" number. If you specify this switch with no number after it,\n"); printf(" the limit is set to zero. Triangle always adds vertices at segment\n"); printf(" intersections, even if it needs to use more vertices than the limit\n"); printf(" you set. When Triangle inserts segments by splitting (-s), it\n"); printf(" always adds enough vertices to ensure that all the segments of the\n"); printf(" PLSG are recovered, ignoring the limit if necessary.\n"); printf(" -i Uses an incremental rather than a divide-and-conquer algorithm to\n"); printf(" construct a Delaunay triangulation. Try it if the divide-and-\n"); printf(" conquer algorithm fails.\n"); printf(" -F Uses Steven Fortune's sweepline algorithm to construct a Delaunay\n"); printf(" triangulation. Warning: does not use exact arithmetic for all\n"); printf(" calculations. An exact result is not guaranteed.\n"); printf(" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n"); printf(" default, Triangle alternates between vertical and horizontal cuts,\n"); printf(" which usually improve the speed except with vertex sets that are\n"); printf(" small or short and wide. This switch is primarily of theoretical\n"); printf(" interest.\n"); printf(" -s Specifies that segments should be forced into the triangulation by\n"); printf(" recursively splitting them at their midpoints, rather than by\n"); printf(" generating a constrained Delaunay triangulation. Segment splitting\n"); printf(" is true to Ruppert's original algorithm, but can create needlessly\n"); printf(" small triangles. This switch is primarily of theoretical interest.\n"); printf(" -C Check the consistency of the final mesh. Uses exact arithmetic for\n"); printf(" checking, even if the -X switch is used. Useful if you suspect\n"); printf(" Triangle is buggy.\n"); printf(" -Q Quiet: Suppresses all explanation of what Triangle is doing,\n"); printf(" unless an error occurs.\n"); printf(" -V Verbose: Gives detailed information about what Triangle is doing.\n"); printf(" Add more `V's for increasing amount of detail. `-V' is most\n"); printf(" useful; itgives information on algorithmic progress and much more\n"); printf(" detailed statistics. `-VV' gives vertex-by-vertex details, and\n"); printf(" prints so much that Triangle runs much more slowly. `-VVVV' gives\n"); printf(" information only a debugger could love.\n"); printf(" -h Help: Displays these instructions.\n"); printf("\n"); printf("Definitions:\n"); printf("\n"); printf(" A Delaunay triangulation of a vertex set is a triangulation whose\n"); printf(" vertices are the vertex set, that covers the convex hull of the vertex\n"); printf(" set. A Delaunay triangulation has the property that no vertex lies\n"); printf(" inside the circumscribing circle (circle that passes through all three\n"); printf(" vertices) of any triangle in the triangulation.\n\n"); printf(" A Voronoi diagram of a vertex set is a subdivision of the plane into\n"); printf(" polygonal cells (some of which may be unbounded, meaning infinitely\n"); printf(" large), where each cell is the set of points in the plane that are closer\n"); printf(" to some input vertex than to any other input vertex. The Voronoi diagram\n"); printf(" is a geometric dual of the Delaunay triangulation.\n\n"); printf(" A Planar Straight Line Graph (PSLG) is a set of vertices and segments.\n"); printf(" Segments are simply edges, whose endpoints are all vertices in the PSLG.\n"); printf(" Segments may intersect each other only at their endpoints. The file\n"); printf(" format for PSLGs (.poly files) is described below.\n\n"); printf(" A constrained Delaunay triangulation (CDT) of a PSLG is similar to a\n"); printf(" Delaunay triangulation, but each PSLG segment is present as a single edge\n"); printf(" of the CDT. (A constrained Delaunay triangulation is not truly a\n"); printf(" Delaunay triangulation, because some of its triangles might not be\n"); printf(" Delaunay.) By definition, a CDT does not have any vertices other than\n"); printf(" those specified in the input PSLG. Depending on context, a CDT might\n"); printf(" cover the convex hull of the PSLG, or it might cover only a segment-\n"); printf(" bounded region (e.g. a polygon).\n\n"); printf(" A conforming Delaunay triangulation of a PSLG is a triangulation in which\n"); printf(" each triangle is truly Delaunay, and each PSLG segment is represented by\n"); printf(" a linear contiguous sequence of edges of the triangulation. New vertices\n"); printf(" (not part of the PSLG) may appear, and each input segment may have been\n"); printf(" subdivided into shorter edges (subsegments) by these additional vertices.\n"); printf(" The new vertices are frequently necessary to maintain the Delaunay\n"); printf(" property while ensuring that every segment is represented.\n\n"); printf(" A conforming constrained Delaunay triangulation (CCDT) of a PSLG is a\n"); printf(" triangulation of a PSLG whose triangles are constrained Delaunay. New\n"); printf(" vertices may appear, and input segments may be subdivided into\n"); printf(" subsegments, but not to guarantee that segments are respected; rather, to\n"); printf(" improve the quality of the triangles. The high-quality meshes produced\n"); printf(" by the -q switch are usually CCDTs, but can be made conforming Delaunay\n"); printf(" with the -D switch.\n\n"); printf("File Formats:\n\n"); printf(" All files may contain comments prefixed by the character '#'. Vertices,\n"); printf(" triangles, edges, holes, and maximum area constraints must be numbered\n"); printf(" consecutively, starting from either 1 or 0. Whichever you choose, all\n"); printf(" input files must be consistent; if the vertices are numbered from 1, so\n"); printf(" must be all other objects. Triangle automatically detects your choice\n"); printf(" while reading the .node (or .poly) file. (When calling Triangle from\n"); printf(" another program, use the -z switch if you wish to number objects from\n"); printf(" zero.) Examples of these file formats are given below.\n\n"); printf(" .node files:\n"); printf(" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"); printf(" <# of boundary markers (0 or 1)>\n"); printf(" Remaining lines: <vertex #> <x> <y> [attributes] [boundary marker]\n"); printf("\n"); printf(" The attributes, which are typically floating-point values of physical\n"); printf(" quantities (such as mass or conductivity) associated with the nodes of\n"); printf(" a finite element mesh, are copied unchanged to the output mesh. If -q,\n"); printf(" -a, -u, -D, or -s is selected, each new Steiner point added to the mesh\n"); printf(" has attributes assigned to it by linear interpolation.\n\n"); printf(" If the fourth entry of the first line is `1', the last column of the\n"); printf(" remainder of the file is assumed to contain boundary markers. Boundary\n"); printf(" markers are used to identify boundary vertices and vertices resting on\n"); printf(" PSLG segments; a complete description appears in a section below. The\n"); printf(" .node file produced by Triangle contains boundary markers in the last\n"); printf(" column unless they are suppressed by the -B switch.\n\n"); printf(" .ele files:\n"); printf(" First line: <# of triangles> <nodes per triangle> <# of attributes>\n"); printf(" Remaining lines: <triangle #> <node> <node> <node> ... [attributes]\n"); printf("\n"); printf(" Nodes are indices into the corresponding .node file. The first three\n"); printf(" nodes are the corner vertices, and are listed in counterclockwise order\n"); printf(" around each triangle. (The remaining nodes, if any, depend on the type\n"); printf(" of finite element used.)\n\n"); printf(" The attributes are just like those of .node files. Because there is no\n"); printf(" simple mapping from input to output triangles, Triangle attempts to\n"); printf(" interpolate attributes, and may cause a lot of diffusion of attributes\n"); printf(" among nearby triangles as the triangulation is refined. Attributes do\n"); printf(" not diffuse across segments, so attributes used to identify\n"); printf(" segment-bounded regions remain intact.\n\n"); printf(" In .ele files produced by Triangle, each triangular element has three\n"); printf(" nodes (vertices) unless the -o2 switch is used, in which case\n"); printf(" subparametric quadratic elements with six nodes each are generated.\n"); printf(" The first three nodes are the corners in counterclockwise order, and\n"); printf(" the fourth, fifth, and sixth nodes lie on the midpoints of the edges\n"); printf(" opposite the first, second, and third vertices, respectively.\n"); printf("\n"); printf(" .poly files:\n"); printf(" First line: <# of vertices> <dimension (must be 2)> <# of attributes>\n"); printf(" <# of boundary markers (0 or 1)>\n"); printf(" Following lines: <vertex #> <x> <y> [attributes] [boundary marker]\n"); printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n"); printf(" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n"); printf(" One line: <# of holes>\n"); printf(" Following lines: <hole #> <x> <y>\n"); printf(" Optional line: <# of regional attributes and/or area constraints>\n"); printf(" Optional following lines: <region #> <x> <y> <attribute> <max area>\n"); printf("\n"); printf(" A .poly file represents a PSLG, as well as some additional information.\n"); printf(" The first section lists all the vertices, and is identical to the\n"); printf(" format of .node files. <# of vertices> may be set to zero to indicate\n"); printf(" that the vertices are listed in a separate .node file; .poly files\n"); printf(" produced by Triangle always have this format. A vertex set represented\n"); printf(" this way has the advantage that it may easily be triangulated with or\n"); printf(" without segments (depending on whether the -p switch is invoked).\n"); printf("\n"); printf(" The second section lists the segments. Segments are edges whose\n"); printf(" presence in the triangulation is enforced. (Depending on the choice of\n"); printf(" switches, segment might be subdivided into smaller edges). Each\n"); printf(" segment is specified by listing the indices of its two endpoints. This\n"); printf(" means that you must include its endpoints in the vertex list. Each\n"); printf(" segment, like each point, may have a boundary marker.\n\n"); printf(" If -q, -a, -u, and -s are not selected, Triangle produces a constrained\n"); printf(" Delaunay triangulation (CDT), in which each segment appears as a single\n"); printf(" edge in the triangulation. If -q, -a, -u, or -s is selected, Triangle\n"); printf(" produces a conforming constrained Delaunay triangulation (CCDT), in\n"); printf(" which segments may be subdivided into smaller edges. If -D is\n"); printf(" selected, Triangle produces a conforming Delaunay triangulation, so\n"); printf(" that every triangle is Delaunay, and not just constrained Delaunay.\n"); printf("\n"); printf(" The third section lists holes (and concavities, if -c is selected) in\n"); printf(" the triangulation. Holes are specified by identifying a point inside\n"); printf(" each hole. After the triangulation is formed, Triangle creates holes\n"); printf(" by eating triangles, spreading out from each hole point until its\n"); printf(" progress is blocked by segments in the PSLG. You must be careful to\n"); printf(" enclose each hole in segments, or your whole triangulation might be\n"); printf(" eaten away. If the two triangles abutting a segment are eaten, the\n"); printf(" segment itself is also eaten. Do not place a hole directly on a\n"); printf(" segment; if you do, Triangle chooses one side of the segment\n"); printf(" arbitrarily.\n\n"); printf(" The optional fourth section lists regional attributes (to be assigned\n"); printf(" to all triangles in a region) and regional constraints on the maximum\n"); printf(" triangle area. Triangle reads this section only if the -A switch is\n"); printf(" used or the -a switch is used without a number following it, and the -r\n"); printf(" switch is not used. Regional attributes and area constraints are\n"); printf(" propagated in the same manner as holes: you specify a point for each\n"); printf(" attribute and/or constraint, and the attribute and/or constraint\n"); printf(" affects the whole region (bounded by segments) containing the point.\n"); printf(" If two values are written on a line after the x and y coordinate, the\n"); printf(" first such value is assumed to be a regional attribute (but is only\n"); printf(" applied if the -A switch is selected), and the second value is assumed\n"); printf(" to be a regional area constraint (but is only applied if the -a switch\n"); printf(" is selected). You may specify just one value after the coordinates,\n"); printf(" which can serve as both an attribute and an area constraint, depending\n"); printf(" on the choice of switches. If you are using the -A and -a switches\n"); printf(" simultaneously and wish to assign an attribute to some region without\n"); printf(" imposing an area constraint, use a negative maximum area.\n\n"); printf(" When a triangulation is created from a .poly file, you must either\n"); printf(" enclose the entire region to be triangulated in PSLG segments, or\n"); printf(" use the -c switch, which automatically creates extra segments that\n"); printf(" enclose the convex hull of the PSLG. If you do not use the -c switch,\n"); printf(" Triangle eats all triangles that are not enclosed by segments; if you\n"); printf(" are not careful, your whole triangulation may be eaten away. If you do\n"); printf(" use the -c switch, you can still produce concavities by the appropriate\n"); printf(" placement of holes just inside the boundary of the convex hull.\n"); printf("\n"); printf(" An ideal PSLG has no intersecting segments, nor any vertices that lie\n"); printf(" upon segments (except, of course, the endpoints of each segment). You\n"); printf(" aren't required to make your .poly files ideal, but you should be aware\n"); printf(" of what can go wrong. Segment intersections are relatively safe--\n"); printf(" Triangle calculates the intersection points for you and adds them to\n"); printf(" the triangulation--as long as your machine's floating-point precision\n"); printf(" doesn't become a problem. You are tempting the fates if you have three\n"); printf(" segments that cross at the same location, and expect Triangle to figure\n"); printf(" out where the intersection point is. Thanks to floating-point roundoff\n"); printf(" error, Triangle will probably decide that the three segments intersect\n"); printf(" at three different points, and you will find a minuscule triangle in\n"); printf(" your output--unless Triangle tries to refine the tiny triangle, uses\n"); printf(" up the last bit of machine precision, and fails to terminate at all.\n"); printf(" You're better off putting the intersection point in the input files,\n"); printf(" and manually breaking up each segment into two. Similarly, if you\n"); printf(" place a vertex at the middle of a segment, and hope that Triangle will\n"); printf(" break up the segment at that vertex, you might get lucky. On the other\n"); printf(" hand, Triangle might decide that the vertex doesn't lie precisely on\n"); printf(" the segment, and you'll have a needle-sharp triangle in your output--or\n"); printf(" a lot of tiny triangles if you're generating a quality mesh.\n"); printf("\n"); printf(" When Triangle reads a .poly file, it also writes a .poly file, which\n"); printf(" includes all the subsegments--the edges that are parts of input\n"); printf(" segments. If the -c switch is used, the output .poly file also\n"); printf(" includes all of the edges on the convex hull. Hence, the output .poly\n"); printf(" file is useful for finding edges associated with input segments and for\n"); printf(" setting boundary conditions in finite element simulations. Moreover,\n"); printf(" you will need the output .poly file if you plan to refine the output\n"); printf(" mesh, and don't want segments to be missing in later triangulations.\n"); printf("\n"); printf(" .area files:\n"); printf(" First line: <# of triangles>\n"); printf(" Following lines: <triangle #> <maximum area>\n"); printf("\n"); printf(" An .area file associates with each triangle a maximum area that is used\n"); printf(" for mesh refinement. As with other file formats, every triangle must\n"); printf(" be represented, and the triangles must be numbered consecutively. A\n"); printf(" triangle may be left unconstrained by assigning it a negative maximum\n"); printf(" area.\n\n"); printf(" .edge files:\n"); printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n"); printf(" Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n"); printf("\n"); printf(" Endpoints are indices into the corresponding .node file. Triangle can\n"); printf(" produce .edge files (use the -e switch), but cannot read them. The\n"); printf(" optional column of boundary markers is suppressed by the -B switch.\n"); printf("\n"); printf(" In Voronoi diagrams, one also finds a special kind of edge that is an\n"); printf(" infinite ray with only one endpoint. For these edges, a different\n"); printf(" format is used:\n\n"); printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n"); printf(" The `direction' is a floating-point vector that indicates the direction\n"); printf(" of the infinite ray.\n\n"); printf(" .neigh files:\n"); printf(" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"); printf(" Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n"); printf("\n"); printf(" Neighbors are indices into the corresponding .ele file. An index of -1\n"); printf(" indicates no neighbor (because the triangle is on an exterior\n"); printf(" boundary). The first neighbor of triangle i is opposite the first\n"); printf(" corner of triangle i, and so on.\n\n"); printf(" Triangle can produce .neigh files (use the -n switch), but cannot read\n"); printf(" them.\n\n"); printf("Boundary Markers:\n\n"); printf(" Boundary markers are tags used mainly to identify which output vertices\n"); printf(" and edges are associated with which PSLG segment, and to identify which\n"); printf(" vertices and edges occur on a boundary of the triangulation. A common\n"); printf(" use is to determine where boundary conditions should be applied to a\n"); printf(" finite element mesh. You can prevent boundary markers from being written\n"); printf(" into files produced by Triangle by using the -B switch.\n\n"); printf(" The boundary marker associated with each segment in an output .poly file\n"); printf(" and each edge in an output .edge file is chosen as follows:\n"); printf(" - If an output edge is part or all of a PSLG segment with a nonzero\n"); printf(" boundary marker, then the edge is assigned the same marker.\n"); printf(" - Otherwise, if the edge lies on a boundary of the triangulation\n"); printf(" (even the boundary of a hole), then the edge is assigned the marker\n"); printf(" one (1).\n"); printf(" - Otherwise, the edge is assigned the marker zero (0).\n"); printf(" The boundary marker associated with each vertex in an output .node file\n"); printf(" is chosen as follows:\n"); printf(" - If a vertex is assigned a nonzero boundary marker in the input file,\n"); printf(" then it is assigned the same marker in the output .node file.\n"); printf(" - Otherwise, if the vertex lies on a PSLG segment (even if it is an\n"); printf(" endpoint of the segment) with a nonzero boundary marker, then the\n"); printf(" vertex is assigned the same marker. If the vertex lies on several\n"); printf(" such segments, one of the markers is chosen arbitrarily.\n"); printf(" - Otherwise, if the vertex occurs on a boundary of the triangulation,\n"); printf(" then the vertex is assigned the marker one (1).\n"); printf(" - Otherwise, the vertex is assigned the marker zero (0).\n"); printf("\n"); printf(" If you want Triangle to determine for you which vertices and edges are on\n"); printf(" the boundary, assign them the boundary marker zero (or use no markers at\n"); printf(" all) in your input files. In the output files, all boundary vertices,\n"); printf(" edges, and segments will be assigned the value one.\n\n"); printf("Triangulation Iteration Numbers:\n\n"); printf(" Because Triangle can read and refine its own triangulations, input\n"); printf(" and output files have iteration numbers. For instance, Triangle might\n"); printf(" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n"); printf(" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n"); printf(" mesh.4.poly. Files with no iteration number are treated as if\n"); printf(" their iteration number is zero; hence, Triangle might read the file\n"); printf(" points.node, triangulate it, and produce the files points.1.node and\n"); printf(" points.1.ele.\n\n"); printf(" Iteration numbers allow you to create a sequence of successively finer\n"); printf(" meshes suitable for multigrid methods. They also allow you to produce a\n"); printf(" sequence of meshes using error estimate-driven mesh refinement.\n"); printf("\n"); printf(" If you're not using refinement or quality meshing, and you don't like\n"); printf(" iteration numbers, use the -I switch to disable them. This switch also\n"); printf(" disables output of .node and .poly files to prevent your input files from\n"); printf(" being overwritten. (If the input is a .poly file that contains its own\n"); printf(" points, a .node file is written. This can be quite convenient for\n"); printf(" computing CDTs or quality meshes.)\n\n"); printf("Examples of How to Use Triangle:\n\n"); printf(" `triangle dots' reads vertices from dots.node, and writes their Delaunay\n"); printf(" triangulation to dots.1.node and dots.1.ele. (dots.1.node is identical\n"); printf(" to dots.node.) `triangle -I dots' writes the triangulation to dots.ele\n"); printf(" instead. (No additional .node file is needed, so none is written.)\n"); printf("\n"); printf(" `triangle -pe object.1' reads a PSLG from object.1.poly (and possibly\n"); printf(" object.1.node, if the vertices are omitted from object.1.poly) and writes\n"); printf(" its constrained Delaunay triangulation to object.2.node and object.2.ele.\n"); printf(" The segments are copied to object.2.poly, and all edges are written to\n"); printf(" object.2.edge.\n\n"); printf(" `triangle -pq31.5a.1 object' reads a PSLG from object.poly (and possibly\n"); printf(" object.node), generates a mesh whose angles are all between 31.5 and 117\n"); printf(" degrees and whose triangles all have areas of 0.1 or less, and writes the\n"); printf(" mesh to object.1.node and object.1.ele. Each segment may be broken up\n"); printf(" into multiple subsegments; these are written to object.1.poly.\n"); printf("\n"); printf(" Here is a sample file `box.poly' describing a square with a square hole:\n"); printf("\n"); printf(" # A box with eight vertices in 2D, no attributes, one boundary marker.\n"); printf(" 8 2 0 1\n"); printf(" # Outer box has these vertices:\n"); printf(" 1 0 0 0\n"); printf(" 2 0 3 0\n"); printf(" 3 3 0 0\n"); printf(" 4 3 3 33 # A special marker for this vertex.\n"); printf(" # Inner square has these vertices:\n"); printf(" 5 1 1 0\n"); printf(" 6 1 2 0\n"); printf(" 7 2 1 0\n"); printf(" 8 2 2 0\n"); printf(" # Five segments with boundary markers.\n"); printf(" 5 1\n"); printf(" 1 1 2 5 # Left side of outer box.\n"); printf(" # Square hole has these segments:\n"); printf(" 2 5 7 0\n"); printf(" 3 7 8 0\n"); printf(" 4 8 6 10\n"); printf(" 5 6 5 0\n"); printf(" # One hole in the middle of the inner square.\n"); printf(" 1\n"); printf(" 1 1.5 1.5\n"); printf("\n"); printf(" Note that some segments are missing from the outer square, so you must\n"); printf(" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"); printf(" file `box.1.node', with twelve vertices. The last four vertices were\n"); printf(" added to meet the angle constraint. Vertices 1, 2, and 9 have markers\n"); printf(" from segment 1. Vertices 6 and 8 have markers from segment 4. All the\n"); printf(" other vertices but 4 have been marked to indicate that they lie on a\n"); printf(" boundary.\n\n"); printf(" 12 2 0 1\n"); printf(" 1 0 0 5\n"); printf(" 2 0 3 5\n"); printf(" 3 3 0 1\n"); printf(" 4 3 3 33\n"); printf(" 5 1 1 1\n"); printf(" 6 1 2 10\n"); printf(" 7 2 1 1\n"); printf(" 8 2 2 10\n"); printf(" 9 0 1.5 5\n"); printf(" 10 1.5 0 1\n"); printf(" 11 3 1.5 1\n"); printf(" 12 1.5 3 1\n"); printf(" # Generated by triangle -pqc box.poly\n"); printf("\n"); printf(" Here is the output file `box.1.ele', with twelve triangles.\n"); printf("\n"); printf(" 12 3 0\n"); printf(" 1 5 6 9\n"); printf(" 2 10 3 7\n"); printf(" 3 6 8 12\n"); printf(" 4 9 1 5\n"); printf(" 5 6 2 9\n"); printf(" 6 7 3 11\n"); printf(" 7 11 4 8\n"); printf(" 8 7 5 10\n"); printf(" 9 12 2 6\n"); printf(" 10 8 7 11\n"); printf(" 11 5 1 10\n"); printf(" 12 8 4 12\n"); printf(" # Generated by triangle -pqc box.poly\n\n"); printf(" Here is the output file `box.1.poly'. Note that segments have been added\n"); printf(" to represent the convex hull, and some segments have been subdivided by\n"); printf(" newly added vertices. Note also that <# of vertices> is set to zero to\n"); printf(" indicate that the vertices should be read from the .node file.\n"); printf("\n"); printf(" 0 2 0 1\n"); printf(" 12 1\n"); printf(" 1 1 9 5\n"); printf(" 2 5 7 1\n"); printf(" 3 8 7 1\n"); printf(" 4 6 8 10\n"); printf(" 5 5 6 1\n"); printf(" 6 3 10 1\n"); printf(" 7 4 11 1\n"); printf(" 8 2 12 1\n"); printf(" 9 9 2 5\n"); printf(" 10 10 1 1\n"); printf(" 11 11 3 1\n"); printf(" 12 12 4 1\n"); printf(" 1\n"); printf(" 1 1.5 1.5\n"); printf(" # Generated by triangle -pqc box.poly\n"); printf("\n"); printf("Refinement and Area Constraints:\n"); printf("\n"); printf(" The -r switch causes a mesh (.node and .ele files) to be read and\n"); printf(" refined. If the -p switch is also used, a .poly file is read and used to\n"); printf(" specify edges that are constrained and cannot be eliminated (although\n"); printf(" they can be subdivided into smaller edges) by the refinement process.\n"); printf("\n"); printf(" When you refine a mesh, you generally want to impose tighter constraints.\n"); printf(" One way to accomplish this is to use -q with a larger angle, or -a\n"); printf(" followed by a smaller area than you used to generate the mesh you are\n"); printf(" refining. Another way to do this is to create an .area file, which\n"); printf(" specifies a maximum area for each triangle, and use the -a switch\n"); printf(" (without a number following). Each triangle's area constraint is applied\n"); printf(" to that triangle. Area constraints tend to diffuse as the mesh is\n"); printf(" refined, so if there are large variations in area constraint between\n"); printf(" adjacent triangles, you may not get the results you want. In that case,\n"); printf(" consider instead using the -u switch and writing a C procedure that\n"); printf(" determines which triangles are too large.\n\n"); printf(" If you are refining a mesh composed of linear (three-node) elements, the\n"); printf(" output mesh contains all the nodes present in the input mesh, in the same\n"); printf(" order, with new nodes added at the end of the .node file. However, the\n"); printf(" refinement is not hierarchical: there is no guarantee that each output\n"); printf(" element is contained in a single input element. Often, an output element\n"); printf(" can overlap two or three input elements, and some input edges are not\n"); printf(" present in the output mesh. Hence, a sequence of refined meshes forms a\n"); printf(" hierarchy of nodes, but not a hierarchy of elements. If you refine a\n"); printf(" mesh of higher-order elements, the hierarchical property applies only to\n"); printf(" the nodes at the corners of an element; the midpoint nodes on each edge\n"); printf(" are discarded before the mesh is refined.\n\n"); printf(" Maximum area constraints in .poly files operate differently from those in\n"); printf(" .area files. A maximum area in a .poly file applies to the whole\n"); printf(" (segment-bounded) region in which a point falls, whereas a maximum area\n"); printf(" in an .area file applies to only one triangle. Area constraints in .poly\n"); printf(" files are used only when a mesh is first generated, whereas area\n"); printf(" constraints in .area files are used only to refine an existing mesh, and\n"); printf(" are typically based on a posteriori error estimates resulting from a\n"); printf(" finite element simulation on that mesh.\n\n"); printf(" `triangle -rq25 object.1' reads object.1.node and object.1.ele, then\n"); printf(" refines the triangulation to enforce a 25 degree minimum angle, and then\n"); printf(" writes the refined triangulation to object.2.node and object.2.ele.\n"); printf("\n"); printf(" `triangle -rpaa6.2 z.3' reads z.3.node, z.3.ele, z.3.poly, and z.3.area.\n"); printf(" After reconstructing the mesh and its subsegments, Triangle refines the\n"); printf(" mesh so that no triangle has area greater than 6.2, and furthermore the\n"); printf(" triangles satisfy the maximum area constraints in z.3.area. No angle\n"); printf(" bound is imposed at all. The output is written to z.4.node, z.4.ele, and\n"); printf(" z.4.poly.\n\n"); printf(" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n"); printf(" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n"); printf(" suitable for multigrid.\n\n"); printf("Convex Hulls and Mesh Boundaries:\n\n"); printf(" If the input is a vertex set (not a PSLG), Triangle produces its convex\n"); printf(" hull as a by-product in the output .poly file if you use the -c switch.\n"); printf(" There are faster algorithms for finding a two-dimensional convex hull\n"); printf(" than triangulation, of course, but this one comes for free.\n\n"); printf(" If the input is an unconstrained mesh (you are using the -r switch but\n"); printf(" not the -p switch), Triangle produces a list of its boundary edges\n"); printf(" (including hole boundaries) as a by-product when you use the -c switch.\n"); printf(" If you also use the -p switch, the output .poly file contains all the\n"); printf(" segments from the input .poly file as well.\n\n"); printf("Voronoi Diagrams:\n\n"); printf(" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n"); printf(" .v.edge. For example, `triangle -v points' reads points.node, produces\n"); printf(" its Delaunay triangulation in points.1.node and points.1.ele, and\n"); printf(" produces its Voronoi diagram in points.1.v.node and points.1.v.edge. The\n"); printf(" .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"); printf(" file contains a list of all Voronoi edges, some of which may be infinite\n"); printf(" rays. (The choice of filenames makes it easy to run the set of Voronoi\n"); printf(" vertices through Triangle, if so desired.)\n\n"); printf(" This implementation does not use exact arithmetic to compute the Voronoi\n"); printf(" vertices, and does not check whether neighboring vertices are identical.\n"); printf(" Be forewarned that if the Delaunay triangulation is degenerate or\n"); printf(" near-degenerate, the Voronoi diagram may have duplicate vertices or\n"); printf(" crossing edges.\n\n"); printf(" The result is a valid Voronoi diagram only if Triangle's output is a true\n"); printf(" Delaunay triangulation. The Voronoi output is usually meaningless (and\n"); printf(" may contain crossing edges and other pathology) if the output is a CDT or\n"); printf(" CCDT, or if it has holes or concavities. If the triangulated domain is\n"); printf(" convex and has no holes, you can use -D switch to force Triangle to\n"); printf(" construct a conforming Delaunay triangulation instead of a CCDT, so the\n"); printf(" Voronoi diagram will be valid.\n\n"); printf("Mesh Topology:\n\n"); printf(" You may wish to know which triangles are adjacent to a certain Delaunay\n"); printf(" edge in an .edge file, which Voronoi cells are adjacent to a certain\n"); printf(" Voronoi edge in a .v.edge file, or which Voronoi cells are adjacent to\n"); printf(" each other. All of this information can be found by cross-referencing\n"); printf(" output files with the recollection that the Delaunay triangulation and\n"); printf(" the Voronoi diagram are planar duals.\n\n"); printf(" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n"); printf(" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n"); printf(" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n"); printf(" vertex j of the corresponding .v.node file. Voronoi cell k is the dual\n"); printf(" of vertex k of the corresponding .node file.\n\n"); printf(" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n"); printf(" vertices of the corresponding Voronoi edge. If the endpoints of a\n"); printf(" Voronoi edge are Voronoi vertices 2 and 6 respectively, then triangles 2\n"); printf(" and 6 adjoin the left and right sides of the corresponding Delaunay edge,\n"); printf(" respectively. To find the Voronoi cells adjacent to a Voronoi edge, look\n"); printf(" at the endpoints of the corresponding Delaunay edge. If the endpoints of\n"); printf(" a Delaunay edge are input vertices 7 and 12, then Voronoi cells 7 and 12\n"); printf(" adjoin the right and left sides of the corresponding Voronoi edge,\n"); printf(" respectively. To find which Voronoi cells are adjacent to each other,\n"); printf(" just read the list of Delaunay edges.\n\n"); printf(" Triangle does not write a list of the edges adjoining each Voronoi cell,\n"); printf(" but you can reconstructed it straightforwardly. For instance, to find\n"); printf(" all the edges of Voronoi cell 1, search the output .edge file for every\n"); printf(" edge that has input vertex 1 as an endpoint. The corresponding dual\n"); printf(" edges in the output .v.edge file form the boundary of Voronoi cell 1.\n"); printf("\n"); printf(" For each Voronoi vertex, the .neigh file gives a list of the three\n"); printf(" Voronoi vertices attached to it. You might find this more convenient\n"); printf(" than the .v.edge file.\n\n"); printf("Quadratic Elements:\n\n"); printf(" Triangle generates meshes with subparametric quadratic elements if the\n"); printf(" -o2 switch is specified. Quadratic elements have six nodes per element,\n"); printf(" rather than three. `Subparametric' means that the edges of the triangles\n"); printf(" are always straight, so that subparametric quadratic elements are\n"); printf(" geometrically identical to linear elements, even though they can be used\n"); printf(" with quadratic interpolating functions. The three extra nodes of an\n"); printf(" element fall at the midpoints of the three edges, with the fourth, fifth,\n"); printf(" and sixth nodes appearing opposite the first, second, and third corners\n"); printf(" respectively.\n\n"); printf("Domains with Small Angles:\n\n"); printf(" If two input segments adjoin each other at a small angle, clearly the -q\n"); printf(" switch cannot remove the small angle. Moreover, Triangle may have no\n"); printf(" choice but to generate additional triangles whose smallest angles are\n"); printf(" smaller than the specified bound. However, these triangles only appear\n"); printf(" between input segments separated by small angles. Moreover, if you\n"); printf(" request a minimum angle of theta degrees, Triangle will generally produce\n"); printf(" no angle larger than 180 - 2 theta, even if it is forced to compromise on\n"); printf(" the minimum angle.\n\n"); printf("Statistics:\n\n"); printf(" After generating a mesh, Triangle prints a count of entities in the\n"); printf(" output mesh, including the number of vertices, triangles, edges, exterior\n"); printf(" boundary edges (i.e. subsegments on the boundary of the triangulation,\n"); printf(" including hole boundaries), interior boundary edges (i.e. subsegments of\n"); printf(" input segments not on the boundary), and total subsegments. If you've\n"); printf(" forgotten the statistics for an existing mesh, run Triangle on that mesh\n"); printf(" with the -rNEP switches to read the mesh and print the statistics without\n"); printf(" writing any files. Use -rpNEP if you've got a .poly file for the mesh.\n"); printf("\n"); printf(" The -V switch produces extended statistics, including a rough estimate\n"); printf(" of memory use, the number of calls to geometric predicates, and\n"); printf(" histograms of the angles and the aspect ratios of the triangles in the\n"); printf(" mesh.\n\n"); printf("Exact Arithmetic:\n\n"); printf(" Triangle uses adaptive exact arithmetic to perform what computational\n"); printf(" geometers call the `orientation' and `incircle' tests. If the floating-\n"); printf(" point arithmetic of your machine conforms to the IEEE 754 standard (as\n"); printf(" most workstations do), and does not use extended precision internal\n"); printf(" floating-point registers, then your output is guaranteed to be an\n"); printf(" absolutely true Delaunay or constrained Delaunay triangulation, roundoff\n"); printf(" error notwithstanding. The word `adaptive' implies that these arithmetic\n"); printf(" routines compute the result only to the precision necessary to guarantee\n"); printf(" correctness, so they are usually nearly as fast as their approximate\n"); printf(" counterparts.\n\n"); printf(" May CPUs, including Intel x86 processors, have extended precision\n"); printf(" floating-point registers. These must be reconfigured so their precision\n"); printf(" is reduced to memory precision. Triangle does this if it is compiled\n"); printf(" correctly. See the makefile for details.\n\n"); printf(" The exact tests can be disabled with the -X switch. On most inputs, this\n"); printf(" switch reduces the computation time by about eight percent--it's not\n"); printf(" worth the risk. There are rare difficult inputs (having many collinear\n"); printf(" and cocircular vertices), however, for which the difference in speed\n"); printf(" could be a factor of two. Be forewarned that these are precisely the\n"); printf(" inputs most likely to cause errors if you use the -X switch. Hence, the\n"); printf(" -X switch is not recommended.\n\n"); printf(" Unfortunately, the exact tests don't solve every numerical problem.\n"); printf(" Exact arithmetic is not used to compute the positions of new vertices,\n"); printf(" because the bit complexity of vertex coordinates would grow without\n"); printf(" bound. Hence, segment intersections aren't computed exactly; in very\n"); printf(" unusual cases, roundoff error in computing an intersection point might\n"); printf(" actually lead to an inverted triangle and an invalid triangulation.\n"); printf(" (This is one reason to specify your own intersection points in your .poly\n"); printf(" files.) Similarly, exact arithmetic is not used to compute the vertices\n"); printf(" of the Voronoi diagram.\n\n"); printf(" Another pair of problems not solved by the exact arithmetic routines is\n"); printf(" underflow and overflow. If Triangle is compiled for double precision\n"); printf(" arithmetic, I believe that Triangle's geometric predicates work correctly\n"); printf(" if the exponent of every input coordinate falls in the range [-148, 201].\n"); printf(" Underflow can silently prevent the orientation and incircle tests from\n"); printf(" being performed exactly, while overflow typically causes a floating\n"); printf(" exception.\n\n"); printf("Calling Triangle from Another Program:\n\n"); printf(" Read the file triangle.h for details.\n\n"); printf("Troubleshooting:\n\n"); printf(" Please read this section before mailing me bugs.\n\n"); printf(" `My output mesh has no triangles!'\n\n"); printf(" If you're using a PSLG, you've probably failed to specify a proper set\n"); printf(" of bounding segments, or forgotten to use the -c switch. Or you may\n"); printf(" have placed a hole badly, thereby eating all your triangles. To test\n"); printf(" these possibilities, try again with the -c and -O switches.\n"); printf(" Alternatively, all your input vertices may be collinear, in which case\n"); printf(" you can hardly expect to triangulate them.\n\n"); printf(" `Triangle doesn't terminate, or just crashes.'\n\n"); printf(" Bad things can happen when triangles get so small that the distance\n"); printf(" between their vertices isn't much larger than the precision of your\n"); printf(" machine's arithmetic. If you've compiled Triangle for single-precision\n"); printf(" arithmetic, you might do better by recompiling it for double-precision.\n"); printf(" Then again, you might just have to settle for more lenient constraints\n"); printf(" on the minimum angle and the maximum area than you had planned.\n"); printf("\n"); printf(" You can minimize precision problems by ensuring that the origin lies\n"); printf(" inside your vertex set, or even inside the densest part of your\n"); printf(" mesh. If you're triangulating an object whose x-coordinates all fall\n"); printf(" between 6247133 and 6247134, you're not leaving much floating-point\n"); printf(" precision for Triangle to work with.\n\n"); printf(" Precision problems can occur covertly if the input PSLG contains two\n"); printf(" segments that meet (or intersect) at an extremely small angle, or if\n"); printf(" such an angle is introduced by the -c switch. If you don't realize\n"); printf(" that a tiny angle is being formed, you might never discover why\n"); printf(" Triangle is crashing. To check for this possibility, use the -S switch\n"); printf(" (with an appropriate limit on the number of Steiner points, found by\n"); printf(" trial-and-error) to stop Triangle early, and view the output .poly file\n"); printf(" with Show Me (described below). Look carefully for regions where dense\n"); printf(" clusters of vertices are forming and for small angles between segments.\n"); printf(" Zoom in closely, as such segments might look like a single segment from\n"); printf(" a distance.\n\n"); printf(" If some of the input values are too large, Triangle may suffer a\n"); printf(" floating exception due to overflow when attempting to perform an\n"); printf(" orientation or incircle test. (Read the section on exact arithmetic\n"); printf(" above.) Again, I recommend compiling Triangle for double (rather\n"); printf(" than single) precision arithmetic.\n\n"); printf(" Unexpected problems can arise if you use quality meshing (-q, -a, or\n"); printf(" -u) with an input that is not segment-bounded--that is, if your input\n"); printf(" is a vertex set, or you're using the -c switch. If the convex hull of\n"); printf(" your input vertices has collinear vertices on its boundary, an input\n"); printf(" vertex that you think lies on the convex hull might actually lie just\n"); printf(" inside the convex hull. If so, the vertex and the nearby convex hull\n"); printf(" edge form an extremely thin triangle. When Triangle tries to refine\n"); printf(" the mesh to enforce angle and area constraints, Triangle might generate\n"); printf(" extremely tiny triangles, or it might fail because of insufficient\n"); printf(" floating-point precision.\n\n"); printf(" `The numbering of the output vertices doesn't match the input vertices.'\n"); printf("\n"); printf(" You may have had duplicate input vertices, or you may have eaten some\n"); printf(" of your input vertices with a hole, or by placing them outside the area\n"); printf(" enclosed by segments. In any case, you can solve the problem by not\n"); printf(" using the -j switch.\n\n"); printf(" `Triangle executes without incident, but when I look at the resulting\n"); printf(" mesh, it has overlapping triangles or other geometric inconsistencies.'\n"); printf("\n"); printf(" If you select the -X switch, Triangle occasionally makes mistakes due\n"); printf(" to floating-point roundoff error. Although these errors are rare,\n"); printf(" don't use the -X switch. If you still have problems, please report the\n"); printf(" bug.\n\n"); printf(" `Triangle executes without incident, but when I look at the resulting\n"); printf(" Voronoi diagram, it has overlapping edges or other geometric\n"); printf(" inconsistencies.'\n"); printf("\n"); printf(" If your input is a PSLG (-p), you can only expect a meaningful Voronoi\n"); printf(" diagram if the domain you are triangulating is convex and free of\n"); printf(" holes, and you use the -D switch to construct a conforming Delaunay\n"); printf(" triangulation (instead of a CDT or CCDT).\n\n"); printf(" Strange things can happen if you've taken liberties with your PSLG. Do\n"); printf(" you have a vertex lying in the middle of a segment? Triangle sometimes\n"); printf(" copes poorly with that sort of thing. Do you want to lay out a collinear\n"); printf(" row of evenly spaced, segment-connected vertices? Have you simply\n"); printf(" defined one long segment connecting the leftmost vertex to the rightmost\n"); printf(" vertex, and a bunch of vertices lying along it? This method occasionally\n"); printf(" works, especially with horizontal and vertical lines, but often it\n"); printf(" doesn't, and you'll have to connect each adjacent pair of vertices with a\n"); printf(" separate segment. If you don't like it, tough.\n\n"); printf(" Furthermore, if you have segments that intersect other than at their\n"); printf(" endpoints, try not to let the intersections fall extremely close to PSLG\n"); printf(" vertices or each other.\n\n"); printf(" If you have problems refining a triangulation not produced by Triangle:\n"); printf(" Are you sure the triangulation is geometrically valid? Is it formatted\n"); printf(" correctly for Triangle? Are the triangles all listed so the first three\n"); printf(" vertices are their corners in counterclockwise order? Are all of the\n"); printf(" triangles constrained Delaunay? Triangle's Delaunay refinement algorithm\n"); printf(" assumes that it starts with a CDT.\n\n"); printf("Show Me:\n\n"); printf(" Triangle comes with a separate program named `Show Me', whose primary\n"); printf(" purpose is to draw meshes on your screen or in PostScript. Its secondary\n"); printf(" purpose is to check the validity of your input files, and do so more\n"); printf(" thoroughly than Triangle does. Unlike Triangle, Show Me requires that\n"); printf(" you have the X Windows system. Sorry, Microsoft Windows users.\n"); printf("\n"); printf("Triangle on the Web:\n"); printf("\n"); printf(" To see an illustrated version of these instructions, check out\n"); printf("\n"); printf(" http://www.cs.cmu.edu/~quake/triangle.html\n"); printf("\n"); printf("A Brief Plea:\n"); printf("\n"); printf(" If you use Triangle, and especially if you use it to accomplish real\n"); printf(" work, I would like very much to hear from you. A short letter or email\n"); printf(" (to jrs@cs.berkeley.edu) describing how you use Triangle will mean a lot\n"); printf(" to me. The more people I know are using this program, the more easily I\n"); printf(" can justify spending time on improvements, which in turn will benefit\n"); printf(" you. Also, I can put you on a list to receive email whenever a new\n"); printf(" version of Triangle is available.\n\n"); printf(" If you use a mesh generated by Triangle in a publication, please include\n"); printf(" an acknowledgment as well. And please spell Triangle with a capital `T'!\n"); printf(" If you want to include a citation, use `Jonathan Richard Shewchuk,\n"); printf(" ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay\n"); printf(" Triangulator,'' in Applied Computational Geometry: Towards Geometric\n"); printf(" Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of\n"); printf(" Lecture Notes in Computer Science, pages 203-222, Springer-Verlag,\n"); printf(" Berlin, May 1996. (From the First ACM Workshop on Applied Computational\n"); printf(" Geometry.)'\n\n"); printf("Research credit:\n\n"); printf(" Of course, I can take credit for only a fraction of the ideas that made\n"); printf(" this mesh generator possible. Triangle owes its existence to the efforts\n"); printf(" of many fine computational geometers and other researchers, including\n"); printf(" Marshall Bern, L. Paul Chew, Kenneth L. Clarkson, Boris Delaunay, Rex A.\n"); printf(" Dwyer, David Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E.\n"); printf(" Knuth, Charles L. Lawson, Der-Tsai Lee, Gary L. Miller, Ernst P. Mucke,\n"); printf(" Steven E. Pav, Douglas M. Priest, Jim Ruppert, Isaac Saias, Bruce J.\n"); printf(" Schachter, Micha Sharir, Peter W. Shor, Daniel D. Sleator, Jorge Stolfi,\n"); printf(" Robert E. Tarjan, Alper Ungor, Christopher J. Van Wyk, Noel J.\n"); printf(" Walkington, and Binhai Zhu. See the comments at the beginning of the\n"); printf(" source code for references.\n\n"); triexit(0);}#endif /* not TRILIBRARY *//*****************************************************************************//* *//* internalerror() Ask the user to send me the defective product. Exit. *//* *//*****************************************************************************/void internalerror(){ printf(" Please report this bug to jrs@cs.berkeley.edu\n"); printf(" Include the message above, your input data set, and the exact\n"); printf(" command line you used to run Triangle.\n"); triexit(1);}/*****************************************************************************//* *//* parsecommandline() Read the command line, identify switches, and set *//* up options and file names. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid parsecommandline(int argc, char **argv, struct behavior *b)#else /* not ANSI_DECLARATORS */void parsecommandline(argc, argv, b)int argc;char **argv;struct behavior *b;#endif /* not ANSI_DECLARATORS */{#ifdef TRILIBRARY#define STARTINDEX 0#else /* not TRILIBRARY */#define STARTINDEX 1 int increment; int meshnumber;#endif /* not TRILIBRARY */ int i, j, k; char workstring[FILENAMESIZE]; b->poly = b->refine = b->quality = 0; b->vararea = b->fixedarea = b->usertest = 0; b->regionattrib = b->convex = b->weighted = b->jettison = 0; b->firstnumber = 1; b->edgesout = b->voronoi = b->neighbors = b->geomview = 0; b->nobound = b->nopolywritten = b->nonodewritten = b->noelewritten = 0; b->noiterationnum = 0; b->noholes = b->noexact = 0; b->incremental = b->sweepline = 0; b->dwyer = 1; b->splitseg = 0; b->docheck = 0; b->nobisect = 0; b->conformdel = 0; b->steiner = -1; b->order = 1; b->minangle = 0.0; b->maxarea = -1.0; b->quiet = b->verbose = 0;#ifndef TRILIBRARY b->innodefilename[0] = '\0';#endif /* not TRILIBRARY */ for (i = STARTINDEX; i < argc; i++) {#ifndef TRILIBRARY if (argv[i][0] == '-') {#endif /* not TRILIBRARY */ for (j = STARTINDEX; argv[i][j] != '\0'; j++) { if (argv[i][j] == 'p') { b->poly = 1;}#ifndef CDT_ONLY if (argv[i][j] == 'r') { b->refine = 1;} if (argv[i][j] == 'q') { b->quality = 1; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { j++; workstring[k] = argv[i][j]; k++; } workstring[k] = '\0'; b->minangle = (REAL) strtod(workstring, (char **) NULL); } else { b->minangle = 20.0; }} if (argv[i][j] == 'a'){ b->quality = 1; if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')) { b->fixedarea = 1; k = 0; while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) || (argv[i][j + 1] == '.')){ j++; workstring[k] = argv[i][j]; k++;} workstring[k] = '\0'; b->maxarea = (REAL) strtod(workstring, (char **) NULL); if (b->maxarea <= 0.0) { printf("Error: Maximum area must be greater than zero.\n"); triexit(1); } } else{ b->vararea = 1;}} if (argv[i][j] == 'u') { b->quality = 1; b->usertest = 1; }#endif /* not CDT_ONLY */ if (argv[i][j] == 'A') { b->regionattrib = 1; } if (argv[i][j] == 'c') { b->convex = 1; } if (argv[i][j] == 'w') { b->weighted = 1; } if (argv[i][j] == 'W') { b->weighted = 2; } if (argv[i][j] == 'j') { b->jettison = 1; } if (argv[i][j] == 'z') { b->firstnumber = 0; } if (argv[i][j] == 'e') { b->edgesout = 1;} if (argv[i][j] == 'v') { b->voronoi = 1;} if (argv[i][j] == 'n') { b->neighbors = 1;} if (argv[i][j] == 'g') { b->geomview = 1;} if (argv[i][j] == 'B') { b->nobound = 1;} if (argv[i][j] == 'P') { b->nopolywritten = 1;} if (argv[i][j] == 'N') { b->nonodewritten = 1;} if (argv[i][j] == 'E') { b->noelewritten = 1;}#ifndef TRILIBRARY if (argv[i][j] == 'I') { b->noiterationnum = 1;}#endif /* not TRILIBRARY */ if (argv[i][j] == 'O') { b->noholes = 1;} if (argv[i][j] == 'X') { b->noexact = 1;} if (argv[i][j] == 'o') { if (argv[i][j + 1] == '2') { j++; b->order = 2; }}#ifndef CDT_ONLY if (argv[i][j] == 'Y') { b->nobisect++;} if (argv[i][j] == 'S') { b->steiner = 0; while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) { j++; b->steiner = b->steiner * 10 + (int) (argv[i][j] - '0'); } }#endif /* not CDT_ONLY */#ifndef REDUCED if (argv[i][j] == 'i') { b->incremental = 1; } if (argv[i][j] == 'F') { b->sweepline = 1; }#endif /* not REDUCED */ if (argv[i][j] == 'l') { b->dwyer = 0; }#ifndef REDUCED#ifndef CDT_ONLY if (argv[i][j] == 's') { b->splitseg = 1; } if ((argv[i][j] == 'D') || (argv[i][j] == 'L')) { b->quality = 1; b->conformdel = 1; }#endif /* not CDT_ONLY */ if (argv[i][j] == 'C') { b->docheck = 1; }#endif /* not REDUCED */ if (argv[i][j] == 'Q') { b->quiet = 1; } if (argv[i][j] == 'V') { b->verbose++; }#ifndef TRILIBRARY if ((argv[i][j] == 'h') || (argv[i][j] == 'H') || (argv[i][j] == '?')) { info();}#endif /* not TRILIBRARY */ }#ifndef TRILIBRARY } else { strncpy(b->innodefilename, argv[i], FILENAMESIZE - 1); b->innodefilename[FILENAMESIZE - 1] = '\0'; }#endif /* not TRILIBRARY */ }#ifndef TRILIBRARY if (b->innodefilename[0] == '\0') { syntax(); } if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".node")) { b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; } if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".poly")) { b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; b->poly = 1; }#ifndef CDT_ONLY if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 4], ".ele")) { b->innodefilename[strlen(b->innodefilename) - 4] = '\0'; b->refine = 1; } if (!strcmp(&b->innodefilename[strlen(b->innodefilename) - 5], ".area")) { b->innodefilename[strlen(b->innodefilename) - 5] = '\0'; b->refine = 1; b->quality = 1; b->vararea = 1; }#endif /* not CDT_ONLY */#endif /* not TRILIBRARY */ b->usesegments = b->poly || b->refine || b->quality || b->convex; b->goodangle = cos(b->minangle * PI / 180.0); if (b->goodangle == 1.0) { b->offconstant = 0.0; } else { b->offconstant = 0.475 * sqrt((1.0 + b->goodangle) / (1.0 - b->goodangle)); } b->goodangle *= b->goodangle; if (b->refine && b->noiterationnum) { printf( "Error: You cannot use the -I switch when refining a triangulation.\n"); triexit(1); } /* Be careful not to allocate space for element area constraints that */ /* will never be assigned any value (other than the default -1.0). */ if (!b->refine && !b->poly) { b->vararea = 0; } /* Be careful not to add an extra attribute to each element unless the */ /* input supports it (PSLG in, but not refining a preexisting mesh). */ if (b->refine || !b->poly) { b->regionattrib = 0; } /* Regular/weighted triangulations are incompatible with PSLGs */ /* and meshing. */ if (b->weighted && (b->poly || b->quality)) { b->weighted = 0; if (!b->quiet) { printf("Warning: weighted triangulations (-w, -W) are incompatible\n"); printf(" with PSLGs (-p) and meshing (-q, -a, -u). Weights ignored.\n" ); } } if (b->jettison && b->nonodewritten && !b->quiet) { printf("Warning: -j and -N switches are somewhat incompatible.\n"); printf(" If any vertices are jettisoned, you will need the output\n"); printf(" .node file to reconstruct the new node indices."); }#ifndef TRILIBRARY strcpy(b->inpolyfilename, b->innodefilename); strcpy(b->inelefilename, b->innodefilename); strcpy(b->areafilename, b->innodefilename); increment = 0; strcpy(workstring, b->innodefilename); j = 1; while (workstring[j] != '\0') { if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) { increment = j + 1; } j++; } meshnumber = 0; if (increment > 0) { j = increment; do { if ((workstring[j] >= '0') && (workstring[j] <= '9')) { meshnumber = meshnumber * 10 + (int) (workstring[j] - '0'); } else { increment = 0; } j++; } while (workstring[j] != '\0'); } if (b->noiterationnum) { strcpy(b->outnodefilename, b->innodefilename); strcpy(b->outelefilename, b->innodefilename); strcpy(b->edgefilename, b->innodefilename); strcpy(b->vnodefilename, b->innodefilename); strcpy(b->vedgefilename, b->innodefilename); strcpy(b->neighborfilename, b->innodefilename); strcpy(b->offfilename, b->innodefilename); strcat(b->outnodefilename, ".node"); strcat(b->outelefilename, ".ele"); strcat(b->edgefilename, ".edge"); strcat(b->vnodefilename, ".v.node"); strcat(b->vedgefilename, ".v.edge"); strcat(b->neighborfilename, ".neigh"); strcat(b->offfilename, ".off"); } else if (increment == 0) { strcpy(b->outnodefilename, b->innodefilename); strcpy(b->outpolyfilename, b->innodefilename); strcpy(b->outelefilename, b->innodefilename); strcpy(b->edgefilename, b->innodefilename); strcpy(b->vnodefilename, b->innodefilename); strcpy(b->vedgefilename, b->innodefilename); strcpy(b->neighborfilename, b->innodefilename); strcpy(b->offfilename, b->innodefilename); strcat(b->outnodefilename, ".1.node"); strcat(b->outpolyfilename, ".1.poly"); strcat(b->outelefilename, ".1.ele"); strcat(b->edgefilename, ".1.edge"); strcat(b->vnodefilename, ".1.v.node"); strcat(b->vedgefilename, ".1.v.edge"); strcat(b->neighborfilename, ".1.neigh"); strcat(b->offfilename, ".1.off"); } else { workstring[increment] = '%'; workstring[increment + 1] = 'd'; workstring[increment + 2] = '\0'; sprintf(b->outnodefilename, workstring, meshnumber + 1); strcpy(b->outpolyfilename, b->outnodefilename); strcpy(b->outelefilename, b->outnodefilename); strcpy(b->edgefilename, b->outnodefilename); strcpy(b->vnodefilename, b->outnodefilename); strcpy(b->vedgefilename, b->outnodefilename); strcpy(b->neighborfilename, b->outnodefilename); strcpy(b->offfilename, b->outnodefilename); strcat(b->outnodefilename, ".node"); strcat(b->outpolyfilename, ".poly"); strcat(b->outelefilename, ".ele"); strcat(b->edgefilename, ".edge"); strcat(b->vnodefilename, ".v.node"); strcat(b->vedgefilename, ".v.edge"); strcat(b->neighborfilename, ".neigh"); strcat(b->offfilename, ".off"); } strcat(b->innodefilename, ".node"); strcat(b->inpolyfilename, ".poly"); strcat(b->inelefilename, ".ele"); strcat(b->areafilename, ".area");#endif /* not TRILIBRARY */}/** **//** **//********* User interaction routines begin here *********//********* Debugging routines begin here *********//** **//** **//*****************************************************************************//* *//* printtriangle() Print out the details of an oriented triangle. *//* *//* I originally wrote this procedure to simplify debugging; it can be *//* called directly from the debugger, and presents information about an *//* oriented triangle in digestible form. It's also used when the *//* highest level of verbosity (`-VVV') is specified. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid printtriangle(struct mesh *m, struct behavior *b, struct otri *t)#else /* not ANSI_DECLARATORS */void printtriangle(m, b, t)struct mesh *m;struct behavior *b;struct otri *t;#endif /* not ANSI_DECLARATORS */{ struct otri printtri; struct osub printsh; vertex printvertex; printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri, t->orient); decode(t->tri[0], printtri); if (printtri.tri == m->dummytri) { printf(" [0] = Outer space\n"); } else { printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } decode(t->tri[1], printtri); if (printtri.tri == m->dummytri) { printf(" [1] = Outer space\n"); } else { printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } decode(t->tri[2], printtri); if (printtri.tri == m->dummytri) { printf(" [2] = Outer space\n"); } else { printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } org(*t, printvertex); if (printvertex == (vertex) NULL) printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3); else printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", (t->orient + 1) % 3 + 3, (unsigned long) printvertex, printvertex[0], printvertex[1]); dest(*t, printvertex); if (printvertex == (vertex) NULL) printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3); else printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", (t->orient + 2) % 3 + 3, (unsigned long) printvertex, printvertex[0], printvertex[1]); apex(*t, printvertex); if (printvertex == (vertex) NULL) printf(" Apex [%d] = NULL\n", t->orient + 3); else printf(" Apex [%d] = x%lx (%.12g, %.12g)\n", t->orient + 3, (unsigned long) printvertex, printvertex[0], printvertex[1]); if (b->usesegments) { sdecode(t->tri[6], printsh); if (printsh.ss != m->dummysub) { printf(" [6] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sdecode(t->tri[7], printsh); if (printsh.ss != m->dummysub) { printf(" [7] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sdecode(t->tri[8], printsh); if (printsh.ss != m->dummysub) { printf(" [8] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } } if (b->vararea) { printf(" Area constraint: %.4g\n", areabound(*t)); }}/*****************************************************************************//* *//* printsubseg() Print out the details of an oriented subsegment. *//* *//* I originally wrote this procedure to simplify debugging; it can be *//* called directly from the debugger, and presents information about an *//* oriented subsegment in digestible form. It's also used when the highest *//* level of verbosity (`-VVV') is specified. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid printsubseg(struct mesh *m, struct behavior *b, struct osub *s)#else /* not ANSI_DECLARATORS */void printsubseg(m, b, s)struct mesh *m;struct behavior *b;struct osub *s;#endif /* not ANSI_DECLARATORS */{ struct osub printsh; struct otri printtri; vertex printvertex; printf("subsegment x%lx with orientation %d and mark %d:\n", (unsigned long) s->ss, s->ssorient, mark(*s)); sdecode(s->ss[0], printsh); if (printsh.ss == m->dummysub) { printf(" [0] = No subsegment\n"); } else { printf(" [0] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sdecode(s->ss[1], printsh); if (printsh.ss == m->dummysub) { printf(" [1] = No subsegment\n"); } else { printf(" [1] = x%lx %d\n", (unsigned long) printsh.ss, printsh.ssorient); } sorg(*s, printvertex); if (printvertex == (vertex) NULL) printf(" Origin[%d] = NULL\n", 2 + s->ssorient); else printf(" Origin[%d] = x%lx (%.12g, %.12g)\n", 2 + s->ssorient, (unsigned long) printvertex, printvertex[0], printvertex[1]); sdest(*s, printvertex); if (printvertex == (vertex) NULL) printf(" Dest [%d] = NULL\n", 3 - s->ssorient); else printf(" Dest [%d] = x%lx (%.12g, %.12g)\n", 3 - s->ssorient, (unsigned long) printvertex, printvertex[0], printvertex[1]); decode(s->ss[6], printtri); if (printtri.tri == m->dummytri) { printf(" [6] = Outer space\n"); } else { printf(" [6] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } decode(s->ss[7], printtri); if (printtri.tri == m->dummytri) { printf(" [7] = Outer space\n"); } else { printf(" [7] = x%lx %d\n", (unsigned long) printtri.tri, printtri.orient); } segorg(*s, printvertex); if (printvertex == (vertex) NULL) printf(" Segment origin[%d] = NULL\n", 4 + s->ssorient); else printf(" Segment origin[%d] = x%lx (%.12g, %.12g)\n", 4 + s->ssorient, (unsigned long) printvertex, printvertex[0], printvertex[1]); segdest(*s, printvertex); if (printvertex == (vertex) NULL) printf(" Segment dest [%d] = NULL\n", 5 - s->ssorient); else printf(" Segment dest [%d] = x%lx (%.12g, %.12g)\n", 5 - s->ssorient, (unsigned long) printvertex, printvertex[0], printvertex[1]);}/** **//** **//********* Debugging routines end here *********//********* Memory management routines begin here *********//** **//** **//*****************************************************************************//* *//* poolzero() Set all of a pool's fields to zero. *//* *//* This procedure should never be called on a pool that has any memory *//* allocated to it, as that memory would leak. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid poolzero(struct memorypool *pool)#else /* not ANSI_DECLARATORS */void poolzero(pool)struct memorypool *pool;#endif /* not ANSI_DECLARATORS */{ pool->firstblock = (VOID **) NULL; pool->nowblock = (VOID **) NULL; pool->nextitem = (VOID *) NULL; pool->deaditemstack = (VOID *) NULL; pool->pathblock = (VOID **) NULL; pool->pathitem = (VOID *) NULL; pool->alignbytes = 0; pool->itembytes = 0; pool->itemsperblock = 0; pool->itemsfirstblock = 0; pool->items = 0; pool->maxitems = 0; pool->unallocateditems = 0; pool->pathitemsleft = 0;}/*****************************************************************************//* *//* poolrestart() Deallocate all items in a pool. *//* *//* The pool is returned to its starting state, except that no memory is *//* freed to the operating system. Rather, the previously allocated blocks *//* are ready to be reused. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid poolrestart(struct memorypool *pool)#else /* not ANSI_DECLARATORS */void poolrestart(pool)struct memorypool *pool;#endif /* not ANSI_DECLARATORS */{ unsigned long alignptr; pool->items = 0; pool->maxitems = 0; /* Set the currently active block. */ pool->nowblock = pool->firstblock; /* Find the first item in the pool. Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->nowblock + 1); /* Align the item on an `alignbytes'-byte boundary. */ pool->nextitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* There are lots of unallocated items left in this block. */ pool->unallocateditems = pool->itemsfirstblock; /* The stack of deallocated items is empty. */ pool->deaditemstack = (VOID *) NULL;}/*****************************************************************************//* *//* poolinit() Initialize a pool of memory for allocation of items. *//* *//* This routine initializes the machinery for allocating items. A `pool' *//* is created whose records have size at least `bytecount'. Items will be *//* allocated in `itemcount'-item blocks. Each item is assumed to be a *//* collection of words, and either pointers or floating-point values are *//* assumed to be the "primary" word type. (The "primary" word type is used *//* to determine alignment of items.) If `alignment' isn't zero, all items *//* will be `alignment'-byte aligned in memory. `alignment' must be either *//* a multiple or a factor of the primary word size; powers of two are safe. *//* `alignment' is normally used to create a few unused bits at the bottom *//* of each item's pointer, in which information may be stored. *//* *//* Don't change this routine unless you understand it. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid poolinit(struct memorypool *pool, int bytecount, int itemcount, int firstitemcount, int alignment)#else /* not ANSI_DECLARATORS */void poolinit(pool, bytecount, itemcount, firstitemcount, alignment)struct memorypool *pool;int bytecount;int itemcount;int firstitemcount;int alignment;#endif /* not ANSI_DECLARATORS */{ /* Find the proper alignment, which must be at least as large as: */ /* - The parameter `alignment'. */ /* - sizeof(VOID *), so the stack of dead items can be maintained */ /* without unaligned accesses. */ if (alignment > sizeof(VOID *)) { pool->alignbytes = alignment; } else { pool->alignbytes = sizeof(VOID *); } pool->itembytes = ((bytecount - 1) / pool->alignbytes + 1) * pool->alignbytes; pool->itemsperblock = itemcount; if (firstitemcount == 0) { pool->itemsfirstblock = itemcount; } else { pool->itemsfirstblock = firstitemcount; } /* Allocate a block of items. Space for `itemsfirstblock' items and one */ /* pointer (to point to the next block) are allocated, as well as space */ /* to ensure alignment of the items. */ pool->firstblock = (VOID **) trimalloc(pool->itemsfirstblock * pool->itembytes + (int) sizeof(VOID *) + pool->alignbytes); /* Set the next block pointer to NULL. */ *(pool->firstblock) = (VOID *) NULL; poolrestart(pool);}/*****************************************************************************//* *//* pooldeinit() Free to the operating system all memory taken by a pool. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid pooldeinit(struct memorypool *pool)#else /* not ANSI_DECLARATORS */void pooldeinit(pool)struct memorypool *pool;#endif /* not ANSI_DECLARATORS */{ while (pool->firstblock != (VOID **) NULL) { pool->nowblock = (VOID **) *(pool->firstblock); trifree((VOID *) pool->firstblock); pool->firstblock = pool->nowblock; }}/*****************************************************************************//* *//* poolalloc() Allocate space for an item. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSVOID *poolalloc(struct memorypool *pool)#else /* not ANSI_DECLARATORS */VOID *poolalloc(pool)struct memorypool *pool;#endif /* not ANSI_DECLARATORS */{ VOID *newitem; VOID **newblock; unsigned long alignptr; /* First check the linked list of dead items. If the list is not */ /* empty, allocate an item from the list rather than a fresh one. */ if (pool->deaditemstack != (VOID *) NULL) { newitem = pool->deaditemstack; /* Take first item in list. */ pool->deaditemstack = * (VOID **) pool->deaditemstack; } else { /* Check if there are any free items left in the current block. */ if (pool->unallocateditems == 0) { /* Check if another block must be allocated. */ if (*(pool->nowblock) == (VOID *) NULL) { /* Allocate a new block of items, pointed to by the previous block. */ newblock = (VOID **) trimalloc(pool->itemsperblock * pool->itembytes + (int) sizeof(VOID *) + pool->alignbytes); *(pool->nowblock) = (VOID *) newblock; /* The next block pointer is NULL. */ *newblock = (VOID *) NULL; } /* Move to the new block. */ pool->nowblock = (VOID **) *(pool->nowblock); /* Find the first item in the block. */ /* Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->nowblock + 1); /* Align the item on an `alignbytes'-byte boundary. */ pool->nextitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* There are lots of unallocated items left in this block. */ pool->unallocateditems = pool->itemsperblock; } /* Allocate a new item. */ newitem = pool->nextitem; /* Advance `nextitem' pointer to next free item in block. */ pool->nextitem = (VOID *) ((char *) pool->nextitem + pool->itembytes); pool->unallocateditems--; pool->maxitems++; } pool->items++; return newitem;}/*****************************************************************************//* *//* pooldealloc() Deallocate space for an item. *//* *//* The deallocated space is stored in a queue for later reuse. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid pooldealloc(struct memorypool *pool, VOID *dyingitem)#else /* not ANSI_DECLARATORS */void pooldealloc(pool, dyingitem)struct memorypool *pool;VOID *dyingitem;#endif /* not ANSI_DECLARATORS */{ /* Push freshly killed item onto stack. */ *((VOID **) dyingitem) = pool->deaditemstack; pool->deaditemstack = dyingitem; pool->items--;}/*****************************************************************************//* *//* traversalinit() Prepare to traverse the entire list of items. *//* *//* This routine is used in conjunction with traverse(). *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid traversalinit(struct memorypool *pool)#else /* not ANSI_DECLARATORS */void traversalinit(pool)struct memorypool *pool;#endif /* not ANSI_DECLARATORS */{ unsigned long alignptr; /* Begin the traversal in the first block. */ pool->pathblock = pool->firstblock; /* Find the first item in the block. Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->pathblock + 1); /* Align with item on an `alignbytes'-byte boundary. */ pool->pathitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* Set the number of items left in the current block. */ pool->pathitemsleft = pool->itemsfirstblock;}/*****************************************************************************//* *//* traverse() Find the next item in the list. *//* *//* This routine is used in conjunction with traversalinit(). Be forewarned *//* that this routine successively returns all items in the list, including *//* deallocated ones on the deaditemqueue. It's up to you to figure out *//* which ones are actually dead. Why? I don't want to allocate extra *//* space just to demarcate dead items. It can usually be done more *//* space-efficiently by a routine that knows something about the structure *//* of the item. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSVOID *traverse(struct memorypool *pool)#else /* not ANSI_DECLARATORS */VOID *traverse(pool)struct memorypool *pool;#endif /* not ANSI_DECLARATORS */{ VOID *newitem; unsigned long alignptr; /* Stop upon exhausting the list of items. */ if (pool->pathitem == pool->nextitem) { return (VOID *) NULL; } /* Check whether any untraversed items remain in the current block. */ if (pool->pathitemsleft == 0) { /* Find the next block. */ pool->pathblock = (VOID **) *(pool->pathblock); /* Find the first item in the block. Increment by the size of (VOID *). */ alignptr = (unsigned long) (pool->pathblock + 1); /* Align with item on an `alignbytes'-byte boundary. */ pool->pathitem = (VOID *) (alignptr + (unsigned long) pool->alignbytes - (alignptr % (unsigned long) pool->alignbytes)); /* Set the number of items left in the current block. */ pool->pathitemsleft = pool->itemsperblock; } newitem = pool->pathitem; /* Find the next item in the block. */ pool->pathitem = (VOID *) ((char *) pool->pathitem + pool->itembytes); pool->pathitemsleft--; return newitem;}/*****************************************************************************//* *//* dummyinit() Initialize the triangle that fills "outer space" and the *//* omnipresent subsegment. *//* *//* The triangle that fills "outer space," called `dummytri', is pointed to *//* by every triangle and subsegment on a boundary (be it outer or inner) of *//* the triangulation. Also, `dummytri' points to one of the triangles on *//* the convex hull (until the holes and concavities are carved), making it *//* possible to find a starting triangle for point location. *//* *//* The omnipresent subsegment, `dummysub', is pointed to by every triangle *//* or subsegment that doesn't have a full complement of real subsegments *//* to point to. *//* *//* `dummytri' and `dummysub' are generally required to fulfill only a few *//* invariants: their vertices must remain NULL and `dummytri' must always *//* be bonded (at offset zero) to some triangle on the convex hull of the *//* mesh, via a boundary edge. Otherwise, the connections of `dummytri' and *//* `dummysub' may change willy-nilly. This makes it possible to avoid *//* writing a good deal of special-case code (in the edge flip, for example) *//* for dealing with the boundary of the mesh, places where no subsegment is *//* present, and so forth. Other entities are frequently bonded to *//* `dummytri' and `dummysub' as if they were real mesh entities, with no *//* harm done. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid dummyinit(struct mesh *m, struct behavior *b, int trianglebytes, int subsegbytes)#else /* not ANSI_DECLARATORS */void dummyinit(m, b, trianglebytes, subsegbytes)struct mesh *m;struct behavior *b;int trianglebytes;int subsegbytes;#endif /* not ANSI_DECLARATORS */{ unsigned long alignptr; /* Set up `dummytri', the `triangle' that occupies "outer space." */ m->dummytribase = (triangle *) trimalloc(trianglebytes + m->triangles.alignbytes); /* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */ alignptr = (unsigned long) m->dummytribase; m->dummytri = (triangle *) (alignptr + (unsigned long) m->triangles.alignbytes - (alignptr % (unsigned long) m->triangles.alignbytes)); /* Initialize the three adjoining triangles to be "outer space." These */ /* will eventually be changed by various bonding operations, but their */ /* values don't really matter, as long as they can legally be */ /* dereferenced. */ m->dummytri[0] = (triangle) m->dummytri; m->dummytri[1] = (triangle) m->dummytri; m->dummytri[2] = (triangle) m->dummytri; /* Three NULL vertices. */ m->dummytri[3] = (triangle) NULL; m->dummytri[4] = (triangle) NULL; m->dummytri[5] = (triangle) NULL; if (b->usesegments) { /* Set up `dummysub', the omnipresent subsegment pointed to by any */ /* triangle side or subsegment end that isn't attached to a real */ /* subsegment. */ m->dummysubbase = (subseg *) trimalloc(subsegbytes + m->subsegs.alignbytes); /* Align `dummysub' on a `subsegs.alignbytes'-byte boundary. */ alignptr = (unsigned long) m->dummysubbase; m->dummysub = (subseg *) (alignptr + (unsigned long) m->subsegs.alignbytes - (alignptr % (unsigned long) m->subsegs.alignbytes)); /* Initialize the two adjoining subsegments to be the omnipresent */ /* subsegment. These will eventually be changed by various bonding */ /* operations, but their values don't really matter, as long as they */ /* can legally be dereferenced. */ m->dummysub[0] = (subseg) m->dummysub; m->dummysub[1] = (subseg) m->dummysub; /* Four NULL vertices. */ m->dummysub[2] = (subseg) NULL; m->dummysub[3] = (subseg) NULL; m->dummysub[4] = (subseg) NULL; m->dummysub[5] = (subseg) NULL; /* Initialize the two adjoining triangles to be "outer space." */ m->dummysub[6] = (subseg) m->dummytri; m->dummysub[7] = (subseg) m->dummytri; /* Set the boundary marker to zero. */ * (int *) (m->dummysub + 8) = 0; /* Initialize the three adjoining subsegments of `dummytri' to be */ /* the omnipresent subsegment. */ m->dummytri[6] = (triangle) m->dummysub; m->dummytri[7] = (triangle) m->dummysub; m->dummytri[8] = (triangle) m->dummysub; }}/*****************************************************************************//* *//* initializevertexpool() Calculate the size of the vertex data structure *//* and initialize its memory pool. *//* *//* This routine also computes the `vertexmarkindex' and `vertex2triindex' *//* indices used to find values within each vertex. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid initializevertexpool(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void initializevertexpool(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ int vertexsize; /* The index within each vertex at which the boundary marker is found, */ /* followed by the vertex type. Ensure the vertex marker is aligned to */ /* a sizeof(int)-byte address. */ m->vertexmarkindex = ((m->mesh_dim + m->nextras) * sizeof(REAL) + sizeof(int) - 1) / sizeof(int); vertexsize = (m->vertexmarkindex + 2) * sizeof(int); if (b->poly) { /* The index within each vertex at which a triangle pointer is found. */ /* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */ m->vertex2triindex = (vertexsize + sizeof(triangle) - 1) / sizeof(triangle); vertexsize = (m->vertex2triindex + 1) * sizeof(triangle); } /* Initialize the pool of vertices. */ poolinit(&m->vertices, vertexsize, VERTEXPERBLOCK, m->invertices > VERTEXPERBLOCK ? m->invertices : VERTEXPERBLOCK, sizeof(REAL));}/*****************************************************************************//* *//* initializetrisubpools() Calculate the sizes of the triangle and *//* subsegment data structures and initialize *//* their memory pools. *//* *//* This routine also computes the `highorderindex', `elemattribindex', and *//* `areaboundindex' indices used to find values within each triangle. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid initializetrisubpools(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void initializetrisubpools(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ int trisize; /* The index within each triangle at which the extra nodes (above three) */ /* associated with high order elements are found. There are three */ /* pointers to other triangles, three pointers to corners, and possibly */ /* three pointers to subsegments before the extra nodes. */ m->highorderindex = 6 + (b->usesegments * 3); /* The number of bytes occupied by a triangle. */ trisize = ((b->order + 1) * (b->order + 2) / 2 + (m->highorderindex - 3)) * sizeof(triangle); /* The index within each triangle at which its attributes are found, */ /* where the index is measured in REALs. */ m->elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL); /* The index within each triangle at which the maximum area constraint */ /* is found, where the index is measured in REALs. Note that if the */ /* `regionattrib' flag is set, an additional attribute will be added. */ m->areaboundindex = m->elemattribindex + m->eextras + b->regionattrib; /* If triangle attributes or an area bound are needed, increase the number */ /* of bytes occupied by a triangle. */ if (b->vararea) { trisize = (m->areaboundindex + 1) * sizeof(REAL); } else if (m->eextras + b->regionattrib > 0) { trisize = m->areaboundindex * sizeof(REAL); } /* If a Voronoi diagram or triangle neighbor graph is requested, make */ /* sure there's room to store an integer index in each triangle. This */ /* integer index can occupy the same space as the subsegment pointers */ /* or attributes or area constraint or extra nodes. */ if ((b->voronoi || b->neighbors) && (trisize < 6 * sizeof(triangle) + sizeof(int))) { trisize = 6 * sizeof(triangle) + sizeof(int); } /* Having determined the memory size of a triangle, initialize the pool. */ poolinit(&m->triangles, trisize, TRIPERBLOCK, (2 * m->invertices - 2) > TRIPERBLOCK ? (2 * m->invertices - 2) : TRIPERBLOCK, 4); if (b->usesegments) { /* Initialize the pool of subsegments. Take into account all eight */ /* pointers and one boundary marker. */ poolinit(&m->subsegs, 8 * sizeof(triangle) + sizeof(int), SUBSEGPERBLOCK, SUBSEGPERBLOCK, 4); /* Initialize the "outer space" triangle and omnipresent subsegment. */ dummyinit(m, b, m->triangles.itembytes, m->subsegs.itembytes); } else { /* Initialize the "outer space" triangle. */ dummyinit(m, b, m->triangles.itembytes, 0); }}/*****************************************************************************//* *//* triangledealloc() Deallocate space for a triangle, marking it dead. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid triangledealloc(struct mesh *m, triangle *dyingtriangle)#else /* not ANSI_DECLARATORS */void triangledealloc(m, dyingtriangle)struct mesh *m;triangle *dyingtriangle;#endif /* not ANSI_DECLARATORS */{ /* Mark the triangle as dead. This makes it possible to detect dead */ /* triangles when traversing the list of all triangles. */ killtri(dyingtriangle); pooldealloc(&m->triangles, (VOID *) dyingtriangle);}/*****************************************************************************//* *//* triangletraverse() Traverse the triangles, skipping dead ones. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORStriangle *triangletraverse(struct mesh *m)#else /* not ANSI_DECLARATORS */triangle *triangletraverse(m)struct mesh *m;#endif /* not ANSI_DECLARATORS */{ triangle *newtriangle; do { newtriangle = (triangle *) traverse(&m->triangles); if (newtriangle == (triangle *) NULL) { return (triangle *) NULL; } } while (deadtri(newtriangle)); /* Skip dead ones. */ return newtriangle;}/*****************************************************************************//* *//* subsegdealloc() Deallocate space for a subsegment, marking it dead. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid subsegdealloc(struct mesh *m, subseg *dyingsubseg)#else /* not ANSI_DECLARATORS */void subsegdealloc(m, dyingsubseg)struct mesh *m;subseg *dyingsubseg;#endif /* not ANSI_DECLARATORS */{ /* Mark the subsegment as dead. This makes it possible to detect dead */ /* subsegments when traversing the list of all subsegments. */ killsubseg(dyingsubseg); pooldealloc(&m->subsegs, (VOID *) dyingsubseg);}/*****************************************************************************//* *//* subsegtraverse() Traverse the subsegments, skipping dead ones. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSsubseg *subsegtraverse(struct mesh *m)#else /* not ANSI_DECLARATORS */subseg *subsegtraverse(m)struct mesh *m;#endif /* not ANSI_DECLARATORS */{ subseg *newsubseg; do { newsubseg = (subseg *) traverse(&m->subsegs); if (newsubseg == (subseg *) NULL) { return (subseg *) NULL; } } while (deadsubseg(newsubseg)); /* Skip dead ones. */ return newsubseg;}/*****************************************************************************//* *//* vertexdealloc() Deallocate space for a vertex, marking it dead. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid vertexdealloc(struct mesh *m, vertex dyingvertex)#else /* not ANSI_DECLARATORS */void vertexdealloc(m, dyingvertex)struct mesh *m;vertex dyingvertex;#endif /* not ANSI_DECLARATORS */{ /* Mark the vertex as dead. This makes it possible to detect dead */ /* vertices when traversing the list of all vertices. */ setvertextype(dyingvertex, DEADVERTEX); pooldealloc(&m->vertices, (VOID *) dyingvertex);}/*****************************************************************************//* *//* vertextraverse() Traverse the vertices, skipping dead ones. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvertex vertextraverse(struct mesh *m)#else /* not ANSI_DECLARATORS */vertex vertextraverse(m)struct mesh *m;#endif /* not ANSI_DECLARATORS */{ vertex newvertex; do { newvertex = (vertex) traverse(&m->vertices); if (newvertex == (vertex) NULL) { return (vertex) NULL; } } while (vertextype(newvertex) == DEADVERTEX); /* Skip dead ones. */ return newvertex;}/*****************************************************************************//* *//* badsubsegdealloc() Deallocate space for a bad subsegment, marking it *//* dead. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid badsubsegdealloc(struct mesh *m, struct badsubseg *dyingseg)#else /* not ANSI_DECLARATORS */void badsubsegdealloc(m, dyingseg)struct mesh *m;struct badsubseg *dyingseg;#endif /* not ANSI_DECLARATORS */{ /* Set subsegment's origin to NULL. This makes it possible to detect dead */ /* badsubsegs when traversing the list of all badsubsegs . */ dyingseg->subsegorg = (vertex) NULL; pooldealloc(&m->badsubsegs, (VOID *) dyingseg);}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* badsubsegtraverse() Traverse the bad subsegments, skipping dead ones. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSstruct badsubseg *badsubsegtraverse(struct mesh *m)#else /* not ANSI_DECLARATORS */struct badsubseg *badsubsegtraverse(m)struct mesh *m;#endif /* not ANSI_DECLARATORS */{ struct badsubseg *newseg; do { newseg = (struct badsubseg *) traverse(&m->badsubsegs); if (newseg == (struct badsubseg *) NULL) { return (struct badsubseg *) NULL; } } while (newseg->subsegorg == (vertex) NULL); /* Skip dead ones. */ return newseg;}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* getvertex() Get a specific vertex, by number, from the list. *//* *//* The first vertex is number 'firstnumber'. *//* *//* Note that this takes O(n) time (with a small constant, if VERTEXPERBLOCK *//* is large). I don't care to take the trouble to make it work in constant *//* time. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvertex getvertex(struct mesh *m, struct behavior *b, int number)#else /* not ANSI_DECLARATORS */vertex getvertex(m, b, number)struct mesh *m;struct behavior *b;int number;#endif /* not ANSI_DECLARATORS */{ VOID **getblock; char *foundvertex; unsigned long alignptr; int current; getblock = m->vertices.firstblock; current = b->firstnumber; /* Find the right block. */ if (current + m->vertices.itemsfirstblock <= number) { getblock = (VOID **) *getblock; current += m->vertices.itemsfirstblock; while (current + m->vertices.itemsperblock <= number) { getblock = (VOID **) *getblock; current += m->vertices.itemsperblock; } } /* Now find the right vertex. */ alignptr = (unsigned long) (getblock + 1); foundvertex = (char *) (alignptr + (unsigned long) m->vertices.alignbytes - (alignptr % (unsigned long) m->vertices.alignbytes)); return (vertex) (foundvertex + m->vertices.itembytes * (number - current));}/*****************************************************************************//* *//* triangledeinit() Free all remaining allocated memory. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid triangledeinit(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void triangledeinit(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ pooldeinit(&m->triangles); trifree((VOID *) m->dummytribase); if (b->usesegments) { pooldeinit(&m->subsegs); trifree((VOID *) m->dummysubbase); } pooldeinit(&m->vertices);#ifndef CDT_ONLY if (b->quality) { pooldeinit(&m->badsubsegs); if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { pooldeinit(&m->badtriangles); pooldeinit(&m->flipstackers); } }#endif /* not CDT_ONLY */}/** **//** **//********* Memory management routines end here *********//********* Constructors begin here *********//** **//** **//*****************************************************************************//* *//* maketriangle() Create a new triangle with orientation zero. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid maketriangle(struct mesh *m, struct behavior *b, struct otri *newotri)#else /* not ANSI_DECLARATORS */void maketriangle(m, b, newotri)struct mesh *m;struct behavior *b;struct otri *newotri;#endif /* not ANSI_DECLARATORS */{ int i; newotri->tri = (triangle *) poolalloc(&m->triangles); /* Initialize the three adjoining triangles to be "outer space". */ newotri->tri[0] = (triangle) m->dummytri; newotri->tri[1] = (triangle) m->dummytri; newotri->tri[2] = (triangle) m->dummytri; /* Three NULL vertices. */ newotri->tri[3] = (triangle) NULL; newotri->tri[4] = (triangle) NULL; newotri->tri[5] = (triangle) NULL; if (b->usesegments) { /* Initialize the three adjoining subsegments to be the omnipresent */ /* subsegment. */ newotri->tri[6] = (triangle) m->dummysub; newotri->tri[7] = (triangle) m->dummysub; newotri->tri[8] = (triangle) m->dummysub; } for (i = 0; i < m->eextras; i++) { setelemattribute(*newotri, i, 0.0); } if (b->vararea) { setareabound(*newotri, -1.0); } newotri->orient = 0;}/*****************************************************************************//* *//* makesubseg() Create a new subsegment with orientation zero. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid makesubseg(struct mesh *m, struct osub *newsubseg)#else /* not ANSI_DECLARATORS */void makesubseg(m, newsubseg)struct mesh *m;struct osub *newsubseg;#endif /* not ANSI_DECLARATORS */{ newsubseg->ss = (subseg *) poolalloc(&m->subsegs); /* Initialize the two adjoining subsegments to be the omnipresent */ /* subsegment. */ newsubseg->ss[0] = (subseg) m->dummysub; newsubseg->ss[1] = (subseg) m->dummysub; /* Four NULL vertices. */ newsubseg->ss[2] = (subseg) NULL; newsubseg->ss[3] = (subseg) NULL; newsubseg->ss[4] = (subseg) NULL; newsubseg->ss[5] = (subseg) NULL; /* Initialize the two adjoining triangles to be "outer space." */ newsubseg->ss[6] = (subseg) m->dummytri; newsubseg->ss[7] = (subseg) m->dummytri; /* Set the boundary marker to zero. */ setmark(*newsubseg, 0); newsubseg->ssorient = 0;}/** **//** **//********* Constructors end here *********//********* Geometric primitives begin here *********//** **//** **//* The adaptive exact arithmetic geometric predicates implemented herein are *//* described in detail in my paper, "Adaptive Precision Floating-Point *//* Arithmetic and Fast Robust Geometric Predicates." See the header for a *//* full citation. *//* Which of the following two methods of finding the absolute values is *//* fastest is compiler-dependent. A few compilers can inline and optimize *//* the fabs() call; but most will incur the overhead of a function call, *//* which is disastrously slow. A faster way on IEEE machines might be to *//* mask the appropriate bit, but that's difficult to do in C without *//* forcing the value to be stored to memory (rather than be kept in the *//* register to which the optimizer assigned it). */#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))/* #define Absolute(a) fabs(a) *//* Many of the operations are broken up into two pieces, a main part that *//* performs an approximate operation, and a "tail" that computes the *//* roundoff error of that operation. *//* *//* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), *//* Split(), and Two_Product() are all implemented as described in the *//* reference. Each of these macros requires certain variables to be *//* defined in the calling routine. The variables `bvirt', `c', `abig', *//* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because *//* they store the result of an operation that may incur roundoff error. *//* The input parameter `x' (or the highest numbered `x_' parameter) must *//* also be declared `INEXACT'. */#define Fast_Two_Sum_Tail(a, b, x, y) \ bvirt = x - a; \ y = b - bvirt#define Fast_Two_Sum(a, b, x, y) \ x = (REAL) (a + b); \ Fast_Two_Sum_Tail(a, b, x, y)#define Two_Sum_Tail(a, b, x, y) \ bvirt = (REAL) (x - a); \ avirt = x - bvirt; \ bround = b - bvirt; \ around = a - avirt; \ y = around + bround#define Two_Sum(a, b, x, y) \ x = (REAL) (a + b); \ Two_Sum_Tail(a, b, x, y)#define Two_Diff_Tail(a, b, x, y) \ bvirt = (REAL) (a - x); \ avirt = x + bvirt; \ bround = bvirt - b; \ around = a - avirt; \ y = around + bround#define Two_Diff(a, b, x, y) \ x = (REAL) (a - b); \ Two_Diff_Tail(a, b, x, y)#define Split(a, ahi, alo) \ c = (REAL) (splitter * a); \ abig = (REAL) (c - a); \ ahi = c - abig; \ alo = a - ahi#define Two_Product_Tail(a, b, x, y) \ Split(a, ahi, alo); \ Split(b, bhi, blo); \ err1 = x - (ahi * bhi); \ err2 = err1 - (alo * bhi); \ err3 = err2 - (ahi * blo); \ y = (alo * blo) - err3#define Two_Product(a, b, x, y) \ x = (REAL) (a * b); \ Two_Product_Tail(a, b, x, y)/* Two_Product_Presplit() is Two_Product() where one of the inputs has *//* already been split. Avoids redundant splitting. */#define Two_Product_Presplit(a, b, bhi, blo, x, y) \ x = (REAL) (a * b); \ Split(a, ahi, alo); \ err1 = x - (ahi * bhi); \ err2 = err1 - (alo * bhi); \ err3 = err2 - (ahi * blo); \ y = (alo * blo) - err3/* Square() can be done more quickly than Two_Product(). */#define Square_Tail(a, x, y) \ Split(a, ahi, alo); \ err1 = x - (ahi * ahi); \ err3 = err1 - ((ahi + ahi) * alo); \ y = (alo * alo) - err3#define Square(a, x, y) \ x = (REAL) (a * a); \ Square_Tail(a, x, y)/* Macros for summing expansions of various fixed lengths. These are all *//* unrolled versions of Expansion_Sum(). */#define Two_One_Sum(a1, a0, b, x2, x1, x0) \ Two_Sum(a0, b , _i, x0); \ Two_Sum(a1, _i, x2, x1)#define Two_One_Diff(a1, a0, b, x2, x1, x0) \ Two_Diff(a0, b , _i, x0); \ Two_Sum( a1, _i, x2, x1)#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \ Two_One_Sum(a1, a0, b0, _j, _0, x0); \ Two_One_Sum(_j, _0, b1, x3, x2, x1)#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \ Two_One_Diff(a1, a0, b0, _j, _0, x0); \ Two_One_Diff(_j, _0, b1, x3, x2, x1)/* Macro for multiplying a two-component expansion by a single component. */#define Two_One_Product(a1, a0, b, x3, x2, x1, x0) \ Split(b, bhi, blo); \ Two_Product_Presplit(a0, b, bhi, blo, _i, x0); \ Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \ Two_Sum(_i, _0, _k, x1); \ Fast_Two_Sum(_j, _k, x3, x2)/*****************************************************************************//* *//* exactinit() Initialize the variables used for exact arithmetic. *//* *//* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in *//* floating-point arithmetic. `epsilon' bounds the relative roundoff *//* error. It is used for floating-point error analysis. *//* *//* `splitter' is used to split floating-point numbers into two half- *//* length significands for exact multiplication. *//* *//* I imagine that a highly optimizing compiler might be too smart for its *//* own good, and somehow cause this routine to fail, if it pretends that *//* floating-point arithmetic is too much like real arithmetic. *//* *//* Don't change this routine unless you fully understand it. *//* *//*****************************************************************************/void exactinit(){ REAL half; REAL check, lastcheck; int every_other;#ifdef LINUX int cword;#endif /* LINUX */#ifdef CPU86#ifdef SINGLE _control87(_PC_24, _MCW_PC); /* Set FPU control word for single precision. */#else /* not SINGLE */ _control87(_PC_53, _MCW_PC); /* Set FPU control word for double precision. */#endif /* not SINGLE */#endif /* CPU86 */#ifdef LINUX#ifdef SINGLE /* cword = 4223; */ cword = 4210; /* set FPU control word for single precision */#else /* not SINGLE */ /* cword = 4735; */ cword = 4722; /* set FPU control word for double precision */#endif /* not SINGLE */ _FPU_SETCW(cword);#endif /* LINUX */ every_other = 1; half = 0.5; epsilon = 1.0; splitter = 1.0; check = 1.0; /* Repeatedly divide `epsilon' by two until it is too small to add to */ /* one without causing roundoff. (Also check if the sum is equal to */ /* the previous sum, for machines that round up instead of using exact */ /* rounding. Not that these routines will work on such machines.) */ do { lastcheck = check; epsilon *= half; if (every_other) { splitter *= 2.0; } every_other = !every_other; check = 1.0 + epsilon; } while ((check != 1.0) && (check != lastcheck)); splitter += 1.0; /* Error bounds for orientation and incircle tests. */ resulterrbound = (3.0 + 8.0 * epsilon) * epsilon; ccwerrboundA = (3.0 + 16.0 * epsilon) * epsilon; ccwerrboundB = (2.0 + 12.0 * epsilon) * epsilon; ccwerrboundC = (9.0 + 64.0 * epsilon) * epsilon * epsilon; iccerrboundA = (10.0 + 96.0 * epsilon) * epsilon; iccerrboundB = (4.0 + 48.0 * epsilon) * epsilon; iccerrboundC = (44.0 + 576.0 * epsilon) * epsilon * epsilon; o3derrboundA = (7.0 + 56.0 * epsilon) * epsilon; o3derrboundB = (3.0 + 28.0 * epsilon) * epsilon; o3derrboundC = (26.0 + 288.0 * epsilon) * epsilon * epsilon;}/*****************************************************************************//* *//* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero *//* components from the output expansion. *//* *//* Sets h = e + f. See my Robust Predicates paper for details. *//* *//* If round-to-even is used (as with IEEE 754), maintains the strongly *//* nonoverlapping property. (That is, if e is strongly nonoverlapping, h *//* will be also.) Does NOT maintain the nonoverlapping or nonadjacent *//* properties. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSint fast_expansion_sum_zeroelim(int elen, REAL *e, int flen, REAL *f, REAL *h)#else /* not ANSI_DECLARATORS */int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */int elen;REAL *e;int flen;REAL *f;REAL *h;#endif /* not ANSI_DECLARATORS */{ REAL Q; INEXACT REAL Qnew; INEXACT REAL hh; INEXACT REAL bvirt; REAL avirt, bround, around; int eindex, findex, hindex; REAL enow, fnow; enow = e[0]; fnow = f[0]; eindex = findex = 0; if ((fnow > enow) == (fnow > -enow)) { Q = enow; enow = e[++eindex]; } else { Q = fnow; fnow = f[++findex]; } hindex = 0; if ((eindex < elen) && (findex < flen)) { if ((fnow > enow) == (fnow > -enow)) { Fast_Two_Sum(enow, Q, Qnew, hh); enow = e[++eindex]; } else { Fast_Two_Sum(fnow, Q, Qnew, hh); fnow = f[++findex]; } Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } while ((eindex < elen) && (findex < flen)) { if ((fnow > enow) == (fnow > -enow)) { Two_Sum(Q, enow, Qnew, hh); enow = e[++eindex]; } else { Two_Sum(Q, fnow, Qnew, hh); fnow = f[++findex]; } Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } } } while (eindex < elen) { Two_Sum(Q, enow, Qnew, hh); enow = e[++eindex]; Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } } while (findex < flen) { Two_Sum(Q, fnow, Qnew, hh); fnow = f[++findex]; Q = Qnew; if (hh != 0.0) { h[hindex++] = hh; } } if ((Q != 0.0) || (hindex == 0)) { h[hindex++] = Q; } return hindex;}/*****************************************************************************//* *//* scale_expansion_zeroelim() Multiply an expansion by a scalar, *//* eliminating zero components from the *//* output expansion. *//* *//* Sets h = be. See my Robust Predicates paper for details. *//* *//* Maintains the nonoverlapping property. If round-to-even is used (as *//* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent *//* properties as well. (That is, if e has one of these properties, so *//* will h.) *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSint scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)#else /* not ANSI_DECLARATORS */int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */int elen;REAL *e;REAL b;REAL *h;#endif /* not ANSI_DECLARATORS */{ INEXACT REAL Q, sum; REAL hh; INEXACT REAL product1; REAL product0; int eindex, hindex; REAL enow; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; Split(b, bhi, blo); Two_Product_Presplit(e[0], b, bhi, blo, Q, hh); hindex = 0; if (hh != 0) { h[hindex++] = hh; } for (eindex = 1; eindex < elen; eindex++) { enow = e[eindex]; Two_Product_Presplit(enow, b, bhi, blo, product1, product0); Two_Sum(Q, product0, sum, hh); if (hh != 0) { h[hindex++] = hh; } Fast_Two_Sum(product1, sum, Q, hh); if (hh != 0) { h[hindex++] = hh; } } if ((Q != 0.0) || (hindex == 0)) { h[hindex++] = Q; } return hindex;}/*****************************************************************************//* *//* estimate() Produce a one-word estimate of an expansion's value. *//* *//* See my Robust Predicates paper for details. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSREAL estimate(int elen, REAL *e)#else /* not ANSI_DECLARATORS */REAL estimate(elen, e)int elen;REAL *e;#endif /* not ANSI_DECLARATORS */{ REAL Q; int eindex; Q = e[0]; for (eindex = 1; eindex < elen; eindex++) { Q += e[eindex]; } return Q;}/*****************************************************************************//* *//* counterclockwise() Return a positive value if the points pa, pb, and *//* pc occur in counterclockwise order; a negative *//* value if they occur in clockwise order; and zero *//* if they are collinear. The result is also a rough *//* approximation of twice the signed area of the *//* triangle defined by the three points. *//* *//* Uses exact arithmetic if necessary to ensure a correct answer. The *//* result returned is the determinant of a matrix. This determinant is *//* computed adaptively, in the sense that exact arithmetic is used only to *//* the degree it is needed to ensure that the returned value has the *//* correct sign. Hence, this function is usually quite fast, but will run *//* more slowly when the input points are collinear or nearly so. *//* *//* See my Robust Predicates paper for details. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSREAL counterclockwiseadapt(vertex pa, vertex pb, vertex pc, REAL detsum)#else /* not ANSI_DECLARATORS */REAL counterclockwiseadapt(pa, pb, pc, detsum)vertex pa;vertex pb;vertex pc;REAL detsum;#endif /* not ANSI_DECLARATORS */{ INEXACT REAL acx, acy, bcx, bcy; REAL acxtail, acytail, bcxtail, bcytail; INEXACT REAL detleft, detright; REAL detlefttail, detrighttail; REAL det, errbound; REAL B[4], C1[8], C2[12], D[16]; INEXACT REAL B3; int C1length, C2length, Dlength; REAL u[4]; INEXACT REAL u3; INEXACT REAL s1, t1; REAL s0, t0; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; INEXACT REAL _i, _j; REAL _0; acx = (REAL) (pa[0] - pc[0]); bcx = (REAL) (pb[0] - pc[0]); acy = (REAL) (pa[1] - pc[1]); bcy = (REAL) (pb[1] - pc[1]); Two_Product(acx, bcy, detleft, detlefttail); Two_Product(acy, bcx, detright, detrighttail); Two_Two_Diff(detleft, detlefttail, detright, detrighttail, B3, B[2], B[1], B[0]); B[3] = B3; det = estimate(4, B); errbound = ccwerrboundB * detsum; if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Diff_Tail(pa[0], pc[0], acx, acxtail); Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail); Two_Diff_Tail(pa[1], pc[1], acy, acytail); Two_Diff_Tail(pb[1], pc[1], bcy, bcytail); if ((acxtail == 0.0) && (acytail == 0.0) && (bcxtail == 0.0) && (bcytail == 0.0)) { return det; } errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det); det += (acx * bcytail + bcy * acxtail) - (acy * bcxtail + bcx * acytail); if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Product(acxtail, bcy, s1, s0); Two_Product(acytail, bcx, t1, t0); Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); u[3] = u3; C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1); Two_Product(acx, bcytail, s1, s0); Two_Product(acy, bcxtail, t1, t0); Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); u[3] = u3; C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2); Two_Product(acxtail, bcytail, s1, s0); Two_Product(acytail, bcxtail, t1, t0); Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]); u[3] = u3; Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D); return(D[Dlength - 1]);}#ifdef ANSI_DECLARATORSREAL counterclockwise(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc)#else /* not ANSI_DECLARATORS */REAL counterclockwise(m, b, pa, pb, pc)struct mesh *m;struct behavior *b;vertex pa;vertex pb;vertex pc;#endif /* not ANSI_DECLARATORS */{ REAL detleft, detright, det; REAL detsum, errbound; m->counterclockcount++; detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]); detright = (pa[1] - pc[1]) * (pb[0] - pc[0]); det = detleft - detright; if (b->noexact) { return det; } if (detleft > 0.0) { if (detright <= 0.0) { return det; } else { detsum = detleft + detright; } } else if (detleft < 0.0) { if (detright >= 0.0) { return det; } else { detsum = -detleft - detright; } } else { return det; } errbound = ccwerrboundA * detsum; if ((det >= errbound) || (-det >= errbound)) { return det; } return counterclockwiseadapt(pa, pb, pc, detsum);}/*****************************************************************************//* *//* incircle() Return a positive value if the point pd lies inside the *//* circle passing through pa, pb, and pc; a negative value if *//* it lies outside; and zero if the four points are cocircular.*//* The points pa, pb, and pc must be in counterclockwise *//* order, or the sign of the result will be reversed. *//* *//* Uses exact arithmetic if necessary to ensure a correct answer. The *//* result returned is the determinant of a matrix. This determinant is *//* computed adaptively, in the sense that exact arithmetic is used only to *//* the degree it is needed to ensure that the returned value has the *//* correct sign. Hence, this function is usually quite fast, but will run *//* more slowly when the input points are cocircular or nearly so. *//* *//* See my Robust Predicates paper for details. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSREAL incircleadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL permanent)#else /* not ANSI_DECLARATORS */REAL incircleadapt(pa, pb, pc, pd, permanent)vertex pa;vertex pb;vertex pc;vertex pd;REAL permanent;#endif /* not ANSI_DECLARATORS */{ INEXACT REAL adx, bdx, cdx, ady, bdy, cdy; REAL det, errbound; INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; REAL bc[4], ca[4], ab[4]; INEXACT REAL bc3, ca3, ab3; REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32]; int axbclen, axxbclen, aybclen, ayybclen, alen; REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32]; int bxcalen, bxxcalen, bycalen, byycalen, blen; REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32]; int cxablen, cxxablen, cyablen, cyyablen, clen; REAL abdet[64]; int ablen; REAL fin1[1152], fin2[1152]; REAL *finnow, *finother, *finswap; int finlength; REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail; INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1; REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0; REAL aa[4], bb[4], cc[4]; INEXACT REAL aa3, bb3, cc3; INEXACT REAL ti1, tj1; REAL ti0, tj0; REAL u[4], v[4]; INEXACT REAL u3, v3; REAL temp8[8], temp16a[16], temp16b[16], temp16c[16]; REAL temp32a[32], temp32b[32], temp48[48], temp64[64]; int temp8len, temp16alen, temp16blen, temp16clen; int temp32alen, temp32blen, temp48len, temp64len; REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8]; int axtbblen, axtcclen, aytbblen, aytcclen; REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8]; int bxtaalen, bxtcclen, bytaalen, bytcclen; REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8]; int cxtaalen, cxtbblen, cytaalen, cytbblen; REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8]; int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen; REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16]; int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen; REAL axtbctt[8], aytbctt[8], bxtcatt[8]; REAL bytcatt[8], cxtabtt[8], cytabtt[8]; int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen; REAL abt[8], bct[8], cat[8]; int abtlen, bctlen, catlen; REAL abtt[4], bctt[4], catt[4]; int abttlen, bcttlen, cattlen; INEXACT REAL abtt3, bctt3, catt3; REAL negate; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; INEXACT REAL _i, _j; REAL _0; adx = (REAL) (pa[0] - pd[0]); bdx = (REAL) (pb[0] - pd[0]); cdx = (REAL) (pc[0] - pd[0]); ady = (REAL) (pa[1] - pd[1]); bdy = (REAL) (pb[1] - pd[1]); cdy = (REAL) (pc[1] - pd[1]); Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); bc[3] = bc3; axbclen = scale_expansion_zeroelim(4, bc, adx, axbc); axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc); aybclen = scale_expansion_zeroelim(4, bc, ady, aybc); ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc); alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet); Two_Product(cdx, ady, cdxady1, cdxady0); Two_Product(adx, cdy, adxcdy1, adxcdy0); Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); ca[3] = ca3; bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca); bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca); bycalen = scale_expansion_zeroelim(4, ca, bdy, byca); byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca); blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet); Two_Product(adx, bdy, adxbdy1, adxbdy0); Two_Product(bdx, ady, bdxady1, bdxady0); Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); ab[3] = ab3; cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab); cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab); cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab); cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab); clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet); ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); det = estimate(finlength, fin1); errbound = iccerrboundB * permanent; if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Diff_Tail(pa[0], pd[0], adx, adxtail); Two_Diff_Tail(pa[1], pd[1], ady, adytail); Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) { return det; } errbound = iccerrboundC * permanent + resulterrbound * Absolute(det); det += ((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) + 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx)) + ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) + 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx)) + ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) + 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx)); if ((det >= errbound) || (-det >= errbound)) { return det; } finnow = fin1; finother = fin2; if ((bdxtail != 0.0) || (bdytail != 0.0) || (cdxtail != 0.0) || (cdytail != 0.0)) { Square(adx, adxadx1, adxadx0); Square(ady, adyady1, adyady0); Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]); aa[3] = aa3; } if ((cdxtail != 0.0) || (cdytail != 0.0) || (adxtail != 0.0) || (adytail != 0.0)) { Square(bdx, bdxbdx1, bdxbdx0); Square(bdy, bdybdy1, bdybdy0); Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]); bb[3] = bb3; } if ((adxtail != 0.0) || (adytail != 0.0) || (bdxtail != 0.0) || (bdytail != 0.0)) { Square(cdx, cdxcdx1, cdxcdx0); Square(cdy, cdycdy1, cdycdy0); Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]); cc[3] = cc3; } if (adxtail != 0.0) { axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc); temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx, temp16a); axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc); temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b); axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb); temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adytail != 0.0) { aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc); temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady, temp16a); aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb); temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b); aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc); temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdxtail != 0.0) { bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca); temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx, temp16a); bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa); temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b); bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc); temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdytail != 0.0) { bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca); temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy, temp16a); bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc); temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b); bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa); temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdxtail != 0.0) { cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab); temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx, temp16a); cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb); temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b); cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa); temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdytail != 0.0) { cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab); temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy, temp16a); cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa); temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b); cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb); temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c); temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; } if ((adxtail != 0.0) || (adytail != 0.0)) { if ((bdxtail != 0.0) || (bdytail != 0.0) || (cdxtail != 0.0) || (cdytail != 0.0)) { Two_Product(bdxtail, cdy, ti1, ti0); Two_Product(bdx, cdytail, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); u[3] = u3; negate = -bdy; Two_Product(cdxtail, negate, ti1, ti0); negate = -bdytail; Two_Product(cdx, negate, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); v[3] = v3; bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct); Two_Product(bdxtail, cdytail, ti1, ti0); Two_Product(cdxtail, bdytail, tj1, tj0); Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]); bctt[3] = bctt3; bcttlen = 4; } else { bct[0] = 0.0; bctlen = 1; bctt[0] = 0.0; bcttlen = 1; } if (adxtail != 0.0) { temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a); axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct); temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; if (bdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail, temp32a); axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt); temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx, temp16a); temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adytail != 0.0) { temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a); aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct); temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail, temp32a); aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt); temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady, temp16a); temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } } if ((bdxtail != 0.0) || (bdytail != 0.0)) { if ((cdxtail != 0.0) || (cdytail != 0.0) || (adxtail != 0.0) || (adytail != 0.0)) { Two_Product(cdxtail, ady, ti1, ti0); Two_Product(cdx, adytail, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); u[3] = u3; negate = -cdy; Two_Product(adxtail, negate, ti1, ti0); negate = -cdytail; Two_Product(adx, negate, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); v[3] = v3; catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat); Two_Product(cdxtail, adytail, ti1, ti0); Two_Product(adxtail, cdytail, tj1, tj0); Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]); catt[3] = catt3; cattlen = 4; } else { cat[0] = 0.0; catlen = 1; catt[0] = 0.0; cattlen = 1; } if (bdxtail != 0.0) { temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a); bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat); temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; if (cdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adytail != 0.0) { temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail, temp32a); bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt); temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx, temp16a); temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdytail != 0.0) { temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a); bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat); temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail, temp32a); bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt); temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy, temp16a); temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } } if ((cdxtail != 0.0) || (cdytail != 0.0)) { if ((adxtail != 0.0) || (adytail != 0.0) || (bdxtail != 0.0) || (bdytail != 0.0)) { Two_Product(adxtail, bdy, ti1, ti0); Two_Product(adx, bdytail, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]); u[3] = u3; negate = -ady; Two_Product(bdxtail, negate, ti1, ti0); negate = -adytail; Two_Product(bdx, negate, tj1, tj0); Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]); v[3] = v3; abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt); Two_Product(adxtail, bdytail, ti1, ti0); Two_Product(bdxtail, adytail, tj1, tj0); Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]); abtt[3] = abtt3; abttlen = 4; } else { abt[0] = 0.0; abtlen = 1; abtt[0] = 0.0; abttlen = 1; } if (cdxtail != 0.0) { temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a); cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt); temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; if (adytail != 0.0) { temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdytail != 0.0) { temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8); temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail, temp16a); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen, temp16a, finother); finswap = finnow; finnow = finother; finother = finswap; } temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail, temp32a); cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt); temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx, temp16a); temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdytail != 0.0) { temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a); cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt); temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy, temp32a); temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp32alen, temp32a, temp48); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len, temp48, finother); finswap = finnow; finnow = finother; finother = finswap; temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail, temp32a); cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt); temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy, temp16a); temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail, temp16b); temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a, temp16blen, temp16b, temp32b); temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a, temp32blen, temp32b, temp64); finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len, temp64, finother); finswap = finnow; finnow = finother; finother = finswap; } } return finnow[finlength - 1];}#ifdef ANSI_DECLARATORSREAL incircle(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd)#else /* not ANSI_DECLARATORS */REAL incircle(m, b, pa, pb, pc, pd)struct mesh *m;struct behavior *b;vertex pa;vertex pb;vertex pc;vertex pd;#endif /* not ANSI_DECLARATORS */{ REAL adx, bdx, cdx, ady, bdy, cdy; REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; REAL alift, blift, clift; REAL det; REAL permanent, errbound; m->incirclecount++; adx = pa[0] - pd[0]; bdx = pb[0] - pd[0]; cdx = pc[0] - pd[0]; ady = pa[1] - pd[1]; bdy = pb[1] - pd[1]; cdy = pc[1] - pd[1]; bdxcdy = bdx * cdy; cdxbdy = cdx * bdy; alift = adx * adx + ady * ady; cdxady = cdx * ady; adxcdy = adx * cdy; blift = bdx * bdx + bdy * bdy; adxbdy = adx * bdy; bdxady = bdx * ady; clift = cdx * cdx + cdy * cdy; det = alift * (bdxcdy - cdxbdy) + blift * (cdxady - adxcdy) + clift * (adxbdy - bdxady); if (b->noexact) { return det; } permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift + (Absolute(cdxady) + Absolute(adxcdy)) * blift + (Absolute(adxbdy) + Absolute(bdxady)) * clift; errbound = iccerrboundA * permanent; if ((det > errbound) || (-det > errbound)) { return det; } return incircleadapt(pa, pb, pc, pd, permanent);}/*****************************************************************************//* *//* orient3d() Return a positive value if the point pd lies below the *//* plane passing through pa, pb, and pc; "below" is defined so *//* that pa, pb, and pc appear in counterclockwise order when *//* viewed from above the plane. Returns a negative value if *//* pd lies above the plane. Returns zero if the points are *//* coplanar. The result is also a rough approximation of six *//* times the signed volume of the tetrahedron defined by the *//* four points. *//* *//* Uses exact arithmetic if necessary to ensure a correct answer. The *//* result returned is the determinant of a matrix. This determinant is *//* computed adaptively, in the sense that exact arithmetic is used only to *//* the degree it is needed to ensure that the returned value has the *//* correct sign. Hence, this function is usually quite fast, but will run *//* more slowly when the input points are coplanar or nearly so. *//* *//* See my Robust Predicates paper for details. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSREAL orient3dadapt(vertex pa, vertex pb, vertex pc, vertex pd, REAL aheight, REAL bheight, REAL cheight, REAL dheight, REAL permanent)#else /* not ANSI_DECLARATORS */REAL orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight, permanent)vertex pa;vertex pb;vertex pc;vertex pd;REAL aheight;REAL bheight;REAL cheight;REAL dheight;REAL permanent;#endif /* not ANSI_DECLARATORS */{ INEXACT REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; REAL det, errbound; INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1; REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0; REAL bc[4], ca[4], ab[4]; INEXACT REAL bc3, ca3, ab3; REAL adet[8], bdet[8], cdet[8]; int alen, blen, clen; REAL abdet[16]; int ablen; REAL *finnow, *finother, *finswap; REAL fin1[192], fin2[192]; int finlength; REAL adxtail, bdxtail, cdxtail; REAL adytail, bdytail, cdytail; REAL adheighttail, bdheighttail, cdheighttail; INEXACT REAL at_blarge, at_clarge; INEXACT REAL bt_clarge, bt_alarge; INEXACT REAL ct_alarge, ct_blarge; REAL at_b[4], at_c[4], bt_c[4], bt_a[4], ct_a[4], ct_b[4]; int at_blen, at_clen, bt_clen, bt_alen, ct_alen, ct_blen; INEXACT REAL bdxt_cdy1, cdxt_bdy1, cdxt_ady1; INEXACT REAL adxt_cdy1, adxt_bdy1, bdxt_ady1; REAL bdxt_cdy0, cdxt_bdy0, cdxt_ady0; REAL adxt_cdy0, adxt_bdy0, bdxt_ady0; INEXACT REAL bdyt_cdx1, cdyt_bdx1, cdyt_adx1; INEXACT REAL adyt_cdx1, adyt_bdx1, bdyt_adx1; REAL bdyt_cdx0, cdyt_bdx0, cdyt_adx0; REAL adyt_cdx0, adyt_bdx0, bdyt_adx0; REAL bct[8], cat[8], abt[8]; int bctlen, catlen, abtlen; INEXACT REAL bdxt_cdyt1, cdxt_bdyt1, cdxt_adyt1; INEXACT REAL adxt_cdyt1, adxt_bdyt1, bdxt_adyt1; REAL bdxt_cdyt0, cdxt_bdyt0, cdxt_adyt0; REAL adxt_cdyt0, adxt_bdyt0, bdxt_adyt0; REAL u[4], v[12], w[16]; INEXACT REAL u3; int vlength, wlength; REAL negate; INEXACT REAL bvirt; REAL avirt, bround, around; INEXACT REAL c; INEXACT REAL abig; REAL ahi, alo, bhi, blo; REAL err1, err2, err3; INEXACT REAL _i, _j, _k; REAL _0; adx = (REAL) (pa[0] - pd[0]); bdx = (REAL) (pb[0] - pd[0]); cdx = (REAL) (pc[0] - pd[0]); ady = (REAL) (pa[1] - pd[1]); bdy = (REAL) (pb[1] - pd[1]); cdy = (REAL) (pc[1] - pd[1]); adheight = (REAL) (aheight - dheight); bdheight = (REAL) (bheight - dheight); cdheight = (REAL) (cheight - dheight); Two_Product(bdx, cdy, bdxcdy1, bdxcdy0); Two_Product(cdx, bdy, cdxbdy1, cdxbdy0); Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]); bc[3] = bc3; alen = scale_expansion_zeroelim(4, bc, adheight, adet); Two_Product(cdx, ady, cdxady1, cdxady0); Two_Product(adx, cdy, adxcdy1, adxcdy0); Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]); ca[3] = ca3; blen = scale_expansion_zeroelim(4, ca, bdheight, bdet); Two_Product(adx, bdy, adxbdy1, adxbdy0); Two_Product(bdx, ady, bdxady1, bdxady0); Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]); ab[3] = ab3; clen = scale_expansion_zeroelim(4, ab, cdheight, cdet); ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet); finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1); det = estimate(finlength, fin1); errbound = o3derrboundB * permanent; if ((det >= errbound) || (-det >= errbound)) { return det; } Two_Diff_Tail(pa[0], pd[0], adx, adxtail); Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail); Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail); Two_Diff_Tail(pa[1], pd[1], ady, adytail); Two_Diff_Tail(pb[1], pd[1], bdy, bdytail); Two_Diff_Tail(pc[1], pd[1], cdy, cdytail); Two_Diff_Tail(aheight, dheight, adheight, adheighttail); Two_Diff_Tail(bheight, dheight, bdheight, bdheighttail); Two_Diff_Tail(cheight, dheight, cdheight, cdheighttail); if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0) && (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0) && (adheighttail == 0.0) && (bdheighttail == 0.0) && (cdheighttail == 0.0)) { return det; } errbound = o3derrboundC * permanent + resulterrbound * Absolute(det); det += (adheight * ((bdx * cdytail + cdy * bdxtail) - (bdy * cdxtail + cdx * bdytail)) + adheighttail * (bdx * cdy - bdy * cdx)) + (bdheight * ((cdx * adytail + ady * cdxtail) - (cdy * adxtail + adx * cdytail)) + bdheighttail * (cdx * ady - cdy * adx)) + (cdheight * ((adx * bdytail + bdy * adxtail) - (ady * bdxtail + bdx * adytail)) + cdheighttail * (adx * bdy - ady * bdx)); if ((det >= errbound) || (-det >= errbound)) { return det; } finnow = fin1; finother = fin2; if (adxtail == 0.0) { if (adytail == 0.0) { at_b[0] = 0.0; at_blen = 1; at_c[0] = 0.0; at_clen = 1; } else { negate = -adytail; Two_Product(negate, bdx, at_blarge, at_b[0]); at_b[1] = at_blarge; at_blen = 2; Two_Product(adytail, cdx, at_clarge, at_c[0]); at_c[1] = at_clarge; at_clen = 2; } } else { if (adytail == 0.0) { Two_Product(adxtail, bdy, at_blarge, at_b[0]); at_b[1] = at_blarge; at_blen = 2; negate = -adxtail; Two_Product(negate, cdy, at_clarge, at_c[0]); at_c[1] = at_clarge; at_clen = 2; } else { Two_Product(adxtail, bdy, adxt_bdy1, adxt_bdy0); Two_Product(adytail, bdx, adyt_bdx1, adyt_bdx0); Two_Two_Diff(adxt_bdy1, adxt_bdy0, adyt_bdx1, adyt_bdx0, at_blarge, at_b[2], at_b[1], at_b[0]); at_b[3] = at_blarge; at_blen = 4; Two_Product(adytail, cdx, adyt_cdx1, adyt_cdx0); Two_Product(adxtail, cdy, adxt_cdy1, adxt_cdy0); Two_Two_Diff(adyt_cdx1, adyt_cdx0, adxt_cdy1, adxt_cdy0, at_clarge, at_c[2], at_c[1], at_c[0]); at_c[3] = at_clarge; at_clen = 4; } } if (bdxtail == 0.0) { if (bdytail == 0.0) { bt_c[0] = 0.0; bt_clen = 1; bt_a[0] = 0.0; bt_alen = 1; } else { negate = -bdytail; Two_Product(negate, cdx, bt_clarge, bt_c[0]); bt_c[1] = bt_clarge; bt_clen = 2; Two_Product(bdytail, adx, bt_alarge, bt_a[0]); bt_a[1] = bt_alarge; bt_alen = 2; } } else { if (bdytail == 0.0) { Two_Product(bdxtail, cdy, bt_clarge, bt_c[0]); bt_c[1] = bt_clarge; bt_clen = 2; negate = -bdxtail; Two_Product(negate, ady, bt_alarge, bt_a[0]); bt_a[1] = bt_alarge; bt_alen = 2; } else { Two_Product(bdxtail, cdy, bdxt_cdy1, bdxt_cdy0); Two_Product(bdytail, cdx, bdyt_cdx1, bdyt_cdx0); Two_Two_Diff(bdxt_cdy1, bdxt_cdy0, bdyt_cdx1, bdyt_cdx0, bt_clarge, bt_c[2], bt_c[1], bt_c[0]); bt_c[3] = bt_clarge; bt_clen = 4; Two_Product(bdytail, adx, bdyt_adx1, bdyt_adx0); Two_Product(bdxtail, ady, bdxt_ady1, bdxt_ady0); Two_Two_Diff(bdyt_adx1, bdyt_adx0, bdxt_ady1, bdxt_ady0, bt_alarge, bt_a[2], bt_a[1], bt_a[0]); bt_a[3] = bt_alarge; bt_alen = 4; } } if (cdxtail == 0.0) { if (cdytail == 0.0) { ct_a[0] = 0.0; ct_alen = 1; ct_b[0] = 0.0; ct_blen = 1; } else { negate = -cdytail; Two_Product(negate, adx, ct_alarge, ct_a[0]); ct_a[1] = ct_alarge; ct_alen = 2; Two_Product(cdytail, bdx, ct_blarge, ct_b[0]); ct_b[1] = ct_blarge; ct_blen = 2; } } else { if (cdytail == 0.0) { Two_Product(cdxtail, ady, ct_alarge, ct_a[0]); ct_a[1] = ct_alarge; ct_alen = 2; negate = -cdxtail; Two_Product(negate, bdy, ct_blarge, ct_b[0]); ct_b[1] = ct_blarge; ct_blen = 2; } else { Two_Product(cdxtail, ady, cdxt_ady1, cdxt_ady0); Two_Product(cdytail, adx, cdyt_adx1, cdyt_adx0); Two_Two_Diff(cdxt_ady1, cdxt_ady0, cdyt_adx1, cdyt_adx0, ct_alarge, ct_a[2], ct_a[1], ct_a[0]); ct_a[3] = ct_alarge; ct_alen = 4; Two_Product(cdytail, bdx, cdyt_bdx1, cdyt_bdx0); Two_Product(cdxtail, bdy, cdxt_bdy1, cdxt_bdy0); Two_Two_Diff(cdyt_bdx1, cdyt_bdx0, cdxt_bdy1, cdxt_bdy0, ct_blarge, ct_b[2], ct_b[1], ct_b[0]); ct_b[3] = ct_blarge; ct_blen = 4; } } bctlen = fast_expansion_sum_zeroelim(bt_clen, bt_c, ct_blen, ct_b, bct); wlength = scale_expansion_zeroelim(bctlen, bct, adheight, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; catlen = fast_expansion_sum_zeroelim(ct_alen, ct_a, at_clen, at_c, cat); wlength = scale_expansion_zeroelim(catlen, cat, bdheight, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; abtlen = fast_expansion_sum_zeroelim(at_blen, at_b, bt_alen, bt_a, abt); wlength = scale_expansion_zeroelim(abtlen, abt, cdheight, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; if (adheighttail != 0.0) { vlength = scale_expansion_zeroelim(4, bc, adheighttail, v); finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdheighttail != 0.0) { vlength = scale_expansion_zeroelim(4, ca, bdheighttail, v); finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdheighttail != 0.0) { vlength = scale_expansion_zeroelim(4, ab, cdheighttail, v); finlength = fast_expansion_sum_zeroelim(finlength, finnow, vlength, v, finother); finswap = finnow; finnow = finother; finother = finswap; } if (adxtail != 0.0) { if (bdytail != 0.0) { Two_Product(adxtail, bdytail, adxt_bdyt1, adxt_bdyt0); Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (cdheighttail != 0.0) { Two_One_Product(adxt_bdyt1, adxt_bdyt0, cdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } if (cdytail != 0.0) { negate = -adxtail; Two_Product(negate, cdytail, adxt_cdyt1, adxt_cdyt0); Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (bdheighttail != 0.0) { Two_One_Product(adxt_cdyt1, adxt_cdyt0, bdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } } if (bdxtail != 0.0) { if (cdytail != 0.0) { Two_Product(bdxtail, cdytail, bdxt_cdyt1, bdxt_cdyt0); Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (adheighttail != 0.0) { Two_One_Product(bdxt_cdyt1, bdxt_cdyt0, adheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } if (adytail != 0.0) { negate = -bdxtail; Two_Product(negate, adytail, bdxt_adyt1, bdxt_adyt0); Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (cdheighttail != 0.0) { Two_One_Product(bdxt_adyt1, bdxt_adyt0, cdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } } if (cdxtail != 0.0) { if (adytail != 0.0) { Two_Product(cdxtail, adytail, cdxt_adyt1, cdxt_adyt0); Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (bdheighttail != 0.0) { Two_One_Product(cdxt_adyt1, cdxt_adyt0, bdheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } if (bdytail != 0.0) { negate = -cdxtail; Two_Product(negate, bdytail, cdxt_bdyt1, cdxt_bdyt0); Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheight, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; if (adheighttail != 0.0) { Two_One_Product(cdxt_bdyt1, cdxt_bdyt0, adheighttail, u3, u[2], u[1], u[0]); u[3] = u3; finlength = fast_expansion_sum_zeroelim(finlength, finnow, 4, u, finother); finswap = finnow; finnow = finother; finother = finswap; } } } if (adheighttail != 0.0) { wlength = scale_expansion_zeroelim(bctlen, bct, adheighttail, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; } if (bdheighttail != 0.0) { wlength = scale_expansion_zeroelim(catlen, cat, bdheighttail, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; } if (cdheighttail != 0.0) { wlength = scale_expansion_zeroelim(abtlen, abt, cdheighttail, w); finlength = fast_expansion_sum_zeroelim(finlength, finnow, wlength, w, finother); finswap = finnow; finnow = finother; finother = finswap; } return finnow[finlength - 1];}#ifdef ANSI_DECLARATORSREAL orient3d(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd, REAL aheight, REAL bheight, REAL cheight, REAL dheight)#else /* not ANSI_DECLARATORS */REAL orient3d(m, b, pa, pb, pc, pd, aheight, bheight, cheight, dheight)struct mesh *m;struct behavior *b;vertex pa;vertex pb;vertex pc;vertex pd;REAL aheight;REAL bheight;REAL cheight;REAL dheight;#endif /* not ANSI_DECLARATORS */{ REAL adx, bdx, cdx, ady, bdy, cdy, adheight, bdheight, cdheight; REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady; REAL det; REAL permanent, errbound; m->orient3dcount++; adx = pa[0] - pd[0]; bdx = pb[0] - pd[0]; cdx = pc[0] - pd[0]; ady = pa[1] - pd[1]; bdy = pb[1] - pd[1]; cdy = pc[1] - pd[1]; adheight = aheight - dheight; bdheight = bheight - dheight; cdheight = cheight - dheight; bdxcdy = bdx * cdy; cdxbdy = cdx * bdy; cdxady = cdx * ady; adxcdy = adx * cdy; adxbdy = adx * bdy; bdxady = bdx * ady; det = adheight * (bdxcdy - cdxbdy) + bdheight * (cdxady - adxcdy) + cdheight * (adxbdy - bdxady); if (b->noexact) { return det; } permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * Absolute(adheight) + (Absolute(cdxady) + Absolute(adxcdy)) * Absolute(bdheight) + (Absolute(adxbdy) + Absolute(bdxady)) * Absolute(cdheight); errbound = o3derrboundA * permanent; if ((det > errbound) || (-det > errbound)) { return det; } return orient3dadapt(pa, pb, pc, pd, aheight, bheight, cheight, dheight, permanent);}/*****************************************************************************//* *//* nonregular() Return a positive value if the point pd is incompatible *//* with the circle or plane passing through pa, pb, and pc *//* (meaning that pd is inside the circle or below the *//* plane); a negative value if it is compatible; and zero if *//* the four points are cocircular/coplanar. The points pa, *//* pb, and pc must be in counterclockwise order, or the sign *//* of the result will be reversed. *//* *//* If the -w switch is used, the points are lifted onto the parabolic *//* lifting map, then they are dropped according to their weights, then the *//* 3D orientation test is applied. If the -W switch is used, the points' *//* heights are already provided, so the 3D orientation test is applied *//* directly. If neither switch is used, the incircle test is applied. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSREAL nonregular(struct mesh *m, struct behavior *b, vertex pa, vertex pb, vertex pc, vertex pd)#else /* not ANSI_DECLARATORS */REAL nonregular(m, b, pa, pb, pc, pd)struct mesh *m;struct behavior *b;vertex pa;vertex pb;vertex pc;vertex pd;#endif /* not ANSI_DECLARATORS */{ if (b->weighted == 0) { return incircle(m, b, pa, pb, pc, pd); } else if (b->weighted == 1) { return orient3d(m, b, pa, pb, pc, pd, pa[0] * pa[0] + pa[1] * pa[1] - pa[2], pb[0] * pb[0] + pb[1] * pb[1] - pb[2], pc[0] * pc[0] + pc[1] * pc[1] - pc[2], pd[0] * pd[0] + pd[1] * pd[1] - pd[2]); } else { return orient3d(m, b, pa, pb, pc, pd, pa[2], pb[2], pc[2], pd[2]); }}/*****************************************************************************//* *//* findcircumcenter() Find the circumcenter of a triangle. *//* *//* The result is returned both in terms of x-y coordinates and xi-eta *//* (barycentric) coordinates. The xi-eta coordinate system is defined in *//* terms of the triangle: the origin of the triangle is the origin of the *//* coordinate system; the destination of the triangle is one unit along the *//* xi axis; and the apex of the triangle is one unit along the eta axis. *//* This procedure also returns the square of the length of the triangle's *//* shortest edge. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid findcircumcenter(struct mesh *m, struct behavior *b, vertex torg, vertex tdest, vertex tapex, vertex circumcenter, REAL *xi, REAL *eta, int offcenter)#else /* not ANSI_DECLARATORS */void findcircumcenter(m, b, torg, tdest, tapex, circumcenter, xi, eta, offcenter)struct mesh *m;struct behavior *b;vertex torg;vertex tdest;vertex tapex;vertex circumcenter;REAL *xi;REAL *eta;int offcenter;#endif /* not ANSI_DECLARATORS */{ REAL xdo, ydo, xao, yao; REAL dodist, aodist, dadist; REAL denominator; REAL dx, dy, dxoff, dyoff; m->circumcentercount++; /* Compute the circumcenter of the triangle. */ xdo = tdest[0] - torg[0]; ydo = tdest[1] - torg[1]; xao = tapex[0] - torg[0]; yao = tapex[1] - torg[1]; dodist = xdo * xdo + ydo * ydo; aodist = xao * xao + yao * yao; dadist = (tdest[0] - tapex[0]) * (tdest[0] - tapex[0]) + (tdest[1] - tapex[1]) * (tdest[1] - tapex[1]); if (b->noexact) { denominator = 0.5 / (xdo * yao - xao * ydo); } else { /* Use the counterclockwise() routine to ensure a positive (and */ /* reasonably accurate) result, avoiding any possibility of */ /* division by zero. */ denominator = 0.5 / counterclockwise(m, b, tdest, tapex, torg); /* Don't count the above as an orientation test. */ m->counterclockcount--; } dx = (yao * dodist - ydo * aodist) * denominator; dy = (xdo * aodist - xao * dodist) * denominator; /* Find the (squared) length of the triangle's shortest edge. This */ /* serves as a conservative estimate of the insertion radius of the */ /* circumcenter's parent. The estimate is used to ensure that */ /* the algorithm terminates even if very small angles appear in */ /* the input PSLG. */ if ((dodist < aodist) && (dodist < dadist)) { if (offcenter && (b->offconstant > 0.0)) { /* Find the position of the off-center, as described by Alper Ungor. */ dxoff = 0.5 * xdo - b->offconstant * ydo; dyoff = 0.5 * ydo + b->offconstant * xdo; /* If the off-center is closer to the origin than the */ /* circumcenter, use the off-center instead. */ if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { dx = dxoff; dy = dyoff; } } } else if (aodist < dadist) { if (offcenter && (b->offconstant > 0.0)) { dxoff = 0.5 * xao + b->offconstant * yao; dyoff = 0.5 * yao - b->offconstant * xao; /* If the off-center is closer to the origin than the */ /* circumcenter, use the off-center instead. */ if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy) { dx = dxoff; dy = dyoff; } } } else { if (offcenter && (b->offconstant > 0.0)) { dxoff = 0.5 * (tapex[0] - tdest[0]) - b->offconstant * (tapex[1] - tdest[1]); dyoff = 0.5 * (tapex[1] - tdest[1]) + b->offconstant * (tapex[0] - tdest[0]); /* If the off-center is closer to the destination than the */ /* circumcenter, use the off-center instead. */ if (dxoff * dxoff + dyoff * dyoff < (dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo)) { dx = xdo + dxoff; dy = ydo + dyoff; } } } circumcenter[0] = torg[0] + dx; circumcenter[1] = torg[1] + dy; /* To interpolate vertex attributes for the new vertex inserted at */ /* the circumcenter, define a coordinate system with a xi-axis, */ /* directed from the triangle's origin to its destination, and */ /* an eta-axis, directed from its origin to its apex. */ /* Calculate the xi and eta coordinates of the circumcenter. */ *xi = (yao * dx - xao * dy) * (2.0 * denominator); *eta = (xdo * dy - ydo * dx) * (2.0 * denominator);}/** **//** **//********* Geometric primitives end here *********//*****************************************************************************//* *//* triangleinit() Initialize some variables. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid triangleinit(struct mesh *m)#else /* not ANSI_DECLARATORS */void triangleinit(m)struct mesh *m;#endif /* not ANSI_DECLARATORS */{ poolzero(&m->vertices); poolzero(&m->triangles); poolzero(&m->subsegs); poolzero(&m->viri); poolzero(&m->badsubsegs); poolzero(&m->badtriangles); poolzero(&m->flipstackers); poolzero(&m->splaynodes); m->recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */ m->undeads = 0; /* No eliminated input vertices yet. */ m->samples = 1; /* Point location should take at least one sample. */ m->checksegments = 0; /* There are no segments in the triangulation yet. */ m->checkquality = 0; /* The quality triangulation stage has not begun. */ m->incirclecount = m->counterclockcount = m->orient3dcount = 0; m->hyperbolacount = m->circletopcount = m->circumcentercount = 0; randomseed = 1; exactinit(); /* Initialize exact arithmetic constants. */}/*****************************************************************************//* *//* randomnation() Generate a random number between 0 and `choices' - 1. *//* *//* This is a simple linear congruential random number generator. Hence, it *//* is a bad random number generator, but good enough for most randomized *//* geometric algorithms. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSunsigned long randomnation(unsigned int choices)#else /* not ANSI_DECLARATORS */unsigned long randomnation(choices)unsigned int choices;#endif /* not ANSI_DECLARATORS */{ randomseed = (randomseed * 1366l + 150889l) % 714025l; return randomseed / (714025l / choices + 1);}/********* Mesh quality testing routines begin here *********//** **//** **//*****************************************************************************//* *//* checkmesh() Test the mesh for topological consistency. *//* *//*****************************************************************************/#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid checkmesh(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void checkmesh(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri triangleloop; struct otri oppotri, oppooppotri; vertex triorg, tridest, triapex; vertex oppoorg, oppodest; int horrors; int saveexact; triangle ptr; /* Temporary variable used by sym(). */ /* Temporarily turn on exact arithmetic if it's off. */ saveexact = b->noexact; b->noexact = 0; if (!b->quiet) { printf(" Checking consistency of mesh...\n"); } horrors = 0; /* Run through the list of triangles, checking each one. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* Check all three edges of the triangle. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { org(triangleloop, triorg); dest(triangleloop, tridest); if (triangleloop.orient == 0) { /* Only test for inversion once. */ /* Test if the triangle is flat or inverted. */ apex(triangleloop, triapex); if (counterclockwise(m, b, triorg, tridest, triapex) <= 0.0) { printf(" !! !! Inverted "); printtriangle(m, b, &triangleloop); horrors++; } } /* Find the neighboring triangle on this edge. */ sym(triangleloop, oppotri); if (oppotri.tri != m->dummytri) { /* Check that the triangle's neighbor knows it's a neighbor. */ sym(oppotri, oppooppotri); if ((triangleloop.tri != oppooppotri.tri) || (triangleloop.orient != oppooppotri.orient)) { printf(" !! !! Asymmetric triangle-triangle bond:\n"); if (triangleloop.tri == oppooppotri.tri) { printf(" (Right triangle, wrong orientation)\n"); } printf(" First "); printtriangle(m, b, &triangleloop); printf(" Second (nonreciprocating) "); printtriangle(m, b, &oppotri); horrors++; } /* Check that both triangles agree on the identities */ /* of their shared vertices. */ org(oppotri, oppoorg); dest(oppotri, oppodest); if ((triorg != oppodest) || (tridest != oppoorg)) { printf(" !! !! Mismatched edge coordinates between two triangles:\n" ); printf(" First mismatched "); printtriangle(m, b, &triangleloop); printf(" Second mismatched "); printtriangle(m, b, &oppotri); horrors++; } } } triangleloop.tri = triangletraverse(m); } if (horrors == 0) { if (!b->quiet) { printf(" In my studied opinion, the mesh appears to be consistent.\n"); } } else if (horrors == 1) { printf(" !! !! !! !! Precisely one festering wound discovered.\n"); } else { printf(" !! !! !! !! %d abominations witnessed.\n", horrors); } /* Restore the status of exact arithmetic. */ b->noexact = saveexact;}#endif /* not REDUCED *//*****************************************************************************//* *//* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. *//* *//*****************************************************************************/#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid checkdelaunay(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void checkdelaunay(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri triangleloop; struct otri oppotri; struct osub opposubseg; vertex triorg, tridest, triapex; vertex oppoapex; int shouldbedelaunay; int horrors; int saveexact; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Temporarily turn on exact arithmetic if it's off. */ saveexact = b->noexact; b->noexact = 0; if (!b->quiet) { printf(" Checking Delaunay property of mesh...\n"); } horrors = 0; /* Run through the list of triangles, checking each one. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* Check all three edges of the triangle. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { org(triangleloop, triorg); dest(triangleloop, tridest); apex(triangleloop, triapex); sym(triangleloop, oppotri); apex(oppotri, oppoapex); /* Only test that the edge is locally Delaunay if there is an */ /* adjoining triangle whose pointer is larger (to ensure that */ /* each pair isn't tested twice). */ shouldbedelaunay = (oppotri.tri != m->dummytri) && !deadtri(oppotri.tri) && (triangleloop.tri < oppotri.tri) && (triorg != m->infvertex1) && (triorg != m->infvertex2) && (triorg != m->infvertex3) && (tridest != m->infvertex1) && (tridest != m->infvertex2) && (tridest != m->infvertex3) && (triapex != m->infvertex1) && (triapex != m->infvertex2) && (triapex != m->infvertex3) && (oppoapex != m->infvertex1) && (oppoapex != m->infvertex2) && (oppoapex != m->infvertex3); if (m->checksegments && shouldbedelaunay) { /* If a subsegment separates the triangles, then the edge is */ /* constrained, so no local Delaunay test should be done. */ tspivot(triangleloop, opposubseg); if (opposubseg.ss != m->dummysub){ shouldbedelaunay = 0; } } if (shouldbedelaunay) { if (nonregular(m, b, triorg, tridest, triapex, oppoapex) > 0.0) { if (!b->weighted) { printf(" !! !! Non-Delaunay pair of triangles:\n"); printf(" First non-Delaunay "); printtriangle(m, b, &triangleloop); printf(" Second non-Delaunay "); } else { printf(" !! !! Non-regular pair of triangles:\n"); printf(" First non-regular "); printtriangle(m, b, &triangleloop); printf(" Second non-regular "); } printtriangle(m, b, &oppotri); horrors++; } } } triangleloop.tri = triangletraverse(m); } if (horrors == 0) { if (!b->quiet) { printf( " By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n"); } } else if (horrors == 1) { printf( " !! !! !! !! Precisely one terrifying transgression identified.\n"); } else { printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors); } /* Restore the status of exact arithmetic. */ b->noexact = saveexact;}#endif /* not REDUCED *//*****************************************************************************//* *//* enqueuebadtriang() Add a bad triangle data structure to the end of a *//* queue. *//* *//* The queue is actually a set of 4096 queues. I use multiple queues to *//* give priority to smaller angles. I originally implemented a heap, but *//* the queues are faster by a larger margin than I'd suspected. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid enqueuebadtriang(struct mesh *m, struct behavior *b, struct badtriang *badtri)#else /* not ANSI_DECLARATORS */void enqueuebadtriang(m, b, badtri)struct mesh *m;struct behavior *b;struct badtriang *badtri;#endif /* not ANSI_DECLARATORS */{ REAL length, multiplier; int exponent, expincrement; int queuenumber; int posexponent; int i; if (b->verbose > 2) { printf(" Queueing bad triangle:\n"); printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", badtri->triangorg[0], badtri->triangorg[1], badtri->triangdest[0], badtri->triangdest[1], badtri->triangapex[0], badtri->triangapex[1]); } /* Determine the appropriate queue to put the bad triangle into. */ /* Recall that the key is the square of its shortest edge length. */ if (badtri->key >= 1.0) { length = badtri->key; posexponent = 1; } else { /* `badtri->key' is 2.0 to a negative exponent, so we'll record that */ /* fact and use the reciprocal of `badtri->key', which is > 1.0. */ length = 1.0 / badtri->key; posexponent = 0; } /* `length' is approximately 2.0 to what exponent? The following code */ /* determines the answer in time logarithmic in the exponent. */ exponent = 0; while (length > 2.0) { /* Find an approximation by repeated squaring of two. */ expincrement = 1; multiplier = 0.5; while (length * multiplier * multiplier > 1.0) { expincrement *= 2; multiplier *= multiplier; } /* Reduce the value of `length', then iterate if necessary. */ exponent += expincrement; length *= multiplier; } /* `length' is approximately squareroot(2.0) to what exponent? */ exponent = 2.0 * exponent + (length > SQUAREROOTTWO); /* `exponent' is now in the range 0...2047 for IEEE double precision. */ /* Choose a queue in the range 0...4095. The shortest edges have the */ /* highest priority (queue 4095). */ if (posexponent) { queuenumber = 2047 - exponent; } else { queuenumber = 2048 + exponent; } /* Are we inserting into an empty queue? */ if (m->queuefront[queuenumber] == (struct badtriang *) NULL) { /* Yes, we are inserting into an empty queue. */ /* Will this become the highest-priority queue? */ if (queuenumber > m->firstnonemptyq) { /* Yes, this is the highest-priority queue. */ m->nextnonemptyq[queuenumber] = m->firstnonemptyq; m->firstnonemptyq = queuenumber; } else { /* No, this is not the highest-priority queue. */ /* Find the queue with next higher priority. */ i = queuenumber + 1; while (m->queuefront[i] == (struct badtriang *) NULL) { i++; } /* Mark the newly nonempty queue as following a higher-priority queue. */ m->nextnonemptyq[queuenumber] = m->nextnonemptyq[i]; m->nextnonemptyq[i] = queuenumber; } /* Put the bad triangle at the beginning of the (empty) queue. */ m->queuefront[queuenumber] = badtri; } else { /* Add the bad triangle to the end of an already nonempty queue. */ m->queuetail[queuenumber]->nexttriang = badtri; } /* Maintain a pointer to the last triangle of the queue. */ m->queuetail[queuenumber] = badtri; /* Newly enqueued bad triangle has no successor in the queue. */ badtri->nexttriang = (struct badtriang *) NULL;}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* enqueuebadtri() Add a bad triangle to the end of a queue. *//* *//* Allocates a badtriang data structure for the triangle, then passes it to *//* enqueuebadtriang(). *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid enqueuebadtri(struct mesh *m, struct behavior *b, struct otri *enqtri, REAL minedge, vertex enqapex, vertex enqorg, vertex enqdest)#else /* not ANSI_DECLARATORS */void enqueuebadtri(m, b, enqtri, minedge, enqapex, enqorg, enqdest)struct mesh *m;struct behavior *b;struct otri *enqtri;REAL minedge;vertex enqapex;vertex enqorg;vertex enqdest;#endif /* not ANSI_DECLARATORS */{ struct badtriang *newbad; /* Allocate space for the bad triangle. */ newbad = (struct badtriang *) poolalloc(&m->badtriangles); newbad->poortri = encode(*enqtri); newbad->key = minedge; newbad->triangapex = enqapex; newbad->triangorg = enqorg; newbad->triangdest = enqdest; enqueuebadtriang(m, b, newbad);}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* dequeuebadtriang() Remove a triangle from the front of the queue. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSstruct badtriang *dequeuebadtriang(struct mesh *m)#else /* not ANSI_DECLARATORS */struct badtriang *dequeuebadtriang(m)struct mesh *m;#endif /* not ANSI_DECLARATORS */{ struct badtriang *result; /* If no queues are nonempty, return NULL. */ if (m->firstnonemptyq < 0) { return (struct badtriang *) NULL; } /* Find the first triangle of the highest-priority queue. */ result = m->queuefront[m->firstnonemptyq]; /* Remove the triangle from the queue. */ m->queuefront[m->firstnonemptyq] = result->nexttriang; /* If this queue is now empty, note the new highest-priority */ /* nonempty queue. */ if (result == m->queuetail[m->firstnonemptyq]) { m->firstnonemptyq = m->nextnonemptyq[m->firstnonemptyq]; } return result;}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* checkseg4encroach() Check a subsegment to see if it is encroached; add *//* it to the list if it is. *//* *//* A subsegment is encroached if there is a vertex in its diametral lens. *//* For Ruppert's algorithm (-D switch), the "diametral lens" is the *//* diametral circle. For Chew's algorithm (default), the diametral lens is *//* just big enough to enclose two isosceles triangles whose bases are the *//* subsegment. Each of the two isosceles triangles has two angles equal *//* to `b->minangle'. *//* *//* Chew's algorithm does not require diametral lenses at all--but they save *//* time. Any vertex inside a subsegment's diametral lens implies that the *//* triangle adjoining the subsegment will be too skinny, so it's only a *//* matter of time before the encroaching vertex is deleted by Chew's *//* algorithm. It's faster to simply not insert the doomed vertex in the *//* first place, which is why I use diametral lenses with Chew's algorithm. *//* *//* Returns a nonzero value if the subsegment is encroached. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSint checkseg4encroach(struct mesh *m, struct behavior *b, struct osub *testsubseg)#else /* not ANSI_DECLARATORS */int checkseg4encroach(m, b, testsubseg)struct mesh *m;struct behavior *b;struct osub *testsubseg;#endif /* not ANSI_DECLARATORS */{ struct otri neighbortri; struct osub testsym; struct badsubseg *encroachedseg; REAL dotproduct; int encroached; int sides; vertex eorg, edest, eapex; triangle ptr; /* Temporary variable used by stpivot(). */ encroached = 0; sides = 0; sorg(*testsubseg, eorg); sdest(*testsubseg, edest); /* Check one neighbor of the subsegment. */ stpivot(*testsubseg, neighbortri); /* Does the neighbor exist, or is this a boundary edge? */ if (neighbortri.tri != m->dummytri) { sides++; /* Find a vertex opposite this subsegment. */ apex(neighbortri, eapex); /* Check whether the apex is in the diametral lens of the subsegment */ /* (the diametral circle if `conformdel' is set). A dot product */ /* of two sides of the triangle is used to check whether the angle */ /* at the apex is greater than (180 - 2 `minangle') degrees (for */ /* lenses; 90 degrees for diametral circles). */ dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); if (dotproduct < 0.0) { if (b->conformdel || (dotproduct * dotproduct >= (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) * ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { encroached = 1; } } } /* Check the other neighbor of the subsegment. */ ssym(*testsubseg, testsym); stpivot(testsym, neighbortri); /* Does the neighbor exist, or is this a boundary edge? */ if (neighbortri.tri != m->dummytri) { sides++; /* Find the other vertex opposite this subsegment. */ apex(neighbortri, eapex); /* Check whether the apex is in the diametral lens of the subsegment */ /* (or the diametral circle, if `conformdel' is set). */ dotproduct = (eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]); if (dotproduct < 0.0) { if (b->conformdel || (dotproduct * dotproduct >= (2.0 * b->goodangle - 1.0) * (2.0 * b->goodangle - 1.0) * ((eorg[0] - eapex[0]) * (eorg[0] - eapex[0]) + (eorg[1] - eapex[1]) * (eorg[1] - eapex[1])) * ((edest[0] - eapex[0]) * (edest[0] - eapex[0]) + (edest[1] - eapex[1]) * (edest[1] - eapex[1])))) { encroached += 2; } } } if (encroached && (!b->nobisect || ((b->nobisect == 1) && (sides == 2)))) { if (b->verbose > 2) { printf( " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", eorg[0], eorg[1], edest[0], edest[1]); } /* Add the subsegment to the list of encroached subsegments. */ /* Be sure to get the orientation right. */ encroachedseg = (struct badsubseg *) poolalloc(&m->badsubsegs); if (encroached == 1) { encroachedseg->encsubseg = sencode(*testsubseg); encroachedseg->subsegorg = eorg; encroachedseg->subsegdest = edest; } else { encroachedseg->encsubseg = sencode(testsym); encroachedseg->subsegorg = edest; encroachedseg->subsegdest = eorg; } } return encroached;}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* testtriangle() Test a triangle for quality and size. *//* *//* Tests a triangle to see if it satisfies the minimum angle condition and *//* the maximum area condition. Triangles that aren't up to spec are added *//* to the bad triangle queue. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid testtriangle(struct mesh *m, struct behavior *b, struct otri *testtri)#else /* not ANSI_DECLARATORS */void testtriangle(m, b, testtri)struct mesh *m;struct behavior *b;struct otri *testtri;#endif /* not ANSI_DECLARATORS */{ struct otri tri1, tri2; struct osub testsub; vertex torg, tdest, tapex; vertex base1, base2; vertex org1, dest1, org2, dest2; vertex joinvertex; REAL dxod, dyod, dxda, dyda, dxao, dyao; REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2; REAL apexlen, orglen, destlen, minedge; REAL angle; REAL area; REAL dist1, dist2; subseg sptr; /* Temporary variable used by tspivot(). */ triangle ptr; /* Temporary variable used by oprev() and dnext(). */ org(*testtri, torg); dest(*testtri, tdest); apex(*testtri, tapex); dxod = torg[0] - tdest[0]; dyod = torg[1] - tdest[1]; dxda = tdest[0] - tapex[0]; dyda = tdest[1] - tapex[1]; dxao = tapex[0] - torg[0]; dyao = tapex[1] - torg[1]; dxod2 = dxod * dxod; dyod2 = dyod * dyod; dxda2 = dxda * dxda; dyda2 = dyda * dyda; dxao2 = dxao * dxao; dyao2 = dyao * dyao; /* Find the lengths of the triangle's three edges. */ apexlen = dxod2 + dyod2; orglen = dxda2 + dyda2; destlen = dxao2 + dyao2; if ((apexlen < orglen) && (apexlen < destlen)) { /* The edge opposite the apex is shortest. */ minedge = apexlen; /* Find the square of the cosine of the angle at the apex. */ angle = dxda * dxao + dyda * dyao; angle = angle * angle / (orglen * destlen); base1 = torg; base2 = tdest; otricopy(*testtri, tri1); } else if (orglen < destlen) { /* The edge opposite the origin is shortest. */ minedge = orglen; /* Find the square of the cosine of the angle at the origin. */ angle = dxod * dxao + dyod * dyao; angle = angle * angle / (apexlen * destlen); base1 = tdest; base2 = tapex; lnext(*testtri, tri1); } else { /* The edge opposite the destination is shortest. */ minedge = destlen; /* Find the square of the cosine of the angle at the destination. */ angle = dxod * dxda + dyod * dyda; angle = angle * angle / (apexlen * orglen); base1 = tapex; base2 = torg; lprev(*testtri, tri1); } if (b->vararea || b->fixedarea || b->usertest) { /* Check whether the area is larger than permitted. */ area = 0.5 * (dxod * dyda - dyod * dxda); if (b->fixedarea && (area > b->maxarea)) { /* Add this triangle to the list of bad triangles. */ enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); return; } /* Nonpositive area constraints are treated as unconstrained. */ if ((b->vararea) && (area > areabound(*testtri)) && (areabound(*testtri) > 0.0)) { /* Add this triangle to the list of bad triangles. */ enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); return; } if (b->usertest) { /* Check whether the user thinks this triangle is too large. */ if (triunsuitable(torg, tdest, tapex, area)) { enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); return; } } } /* Check whether the angle is smaller than permitted. */ if (angle > b->goodangle) { /* Use the rules of Miller, Pav, and Walkington to decide that certain */ /* triangles should not be split, even if they have bad angles. */ /* A skinny triangle is not split if its shortest edge subtends a */ /* small input angle, and both endpoints of the edge lie on a */ /* concentric circular shell. For convenience, I make a small */ /* adjustment to that rule: I check if the endpoints of the edge */ /* both lie in segment interiors, equidistant from the apex where */ /* the two segments meet. */ /* First, check if both points lie in segment interiors. */ if ((vertextype(base1) == SEGMENTVERTEX) && (vertextype(base2) == SEGMENTVERTEX)) { /* Check if both points lie in a common segment. If they do, the */ /* skinny triangle is enqueued to be split as usual. */ tspivot(tri1, testsub); if (testsub.ss == m->dummysub) { /* No common segment. Find a subsegment that contains `torg'. */ otricopy(tri1, tri2); do { oprevself(tri1); tspivot(tri1, testsub); } while (testsub.ss == m->dummysub); /* Find the endpoints of the containing segment. */ segorg(testsub, org1); segdest(testsub, dest1); /* Find a subsegment that contains `tdest'. */ do { dnextself(tri2); tspivot(tri2, testsub); } while (testsub.ss == m->dummysub); /* Find the endpoints of the containing segment. */ segorg(testsub, org2); segdest(testsub, dest2); /* Check if the two containing segments have an endpoint in common. */ joinvertex = (vertex) NULL; if ((dest1[0] == org2[0]) && (dest1[1] == org2[1])) { joinvertex = dest1; } else if ((org1[0] == dest2[0]) && (org1[1] == dest2[1])) { joinvertex = org1; } if (joinvertex != (vertex) NULL) { /* Compute the distance from the common endpoint (of the two */ /* segments) to each of the endpoints of the shortest edge. */ dist1 = ((base1[0] - joinvertex[0]) * (base1[0] - joinvertex[0]) + (base1[1] - joinvertex[1]) * (base1[1] - joinvertex[1])); dist2 = ((base2[0] - joinvertex[0]) * (base2[0] - joinvertex[0]) + (base2[1] - joinvertex[1]) * (base2[1] - joinvertex[1])); /* If the two distances are equal, don't split the triangle. */ if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2)) { /* Return now to avoid enqueueing the bad triangle. */ return; } } } } /* Add this triangle to the list of bad triangles. */ enqueuebadtri(m, b, testtri, minedge, tapex, torg, tdest); }}#endif /* not CDT_ONLY *//** **//** **//********* Mesh quality testing routines end here *********//********* Point location routines begin here *********//** **//** **//*****************************************************************************//* *//* makevertexmap() Construct a mapping from vertices to triangles to *//* improve the speed of point location for segment *//* insertion. *//* *//* Traverses all the triangles, and provides each corner of each triangle *//* with a pointer to that triangle. Of course, pointers will be *//* overwritten by other pointers because (almost) each vertex is a corner *//* of several triangles, but in the end every vertex will point to some *//* triangle that contains it. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid makevertexmap(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void makevertexmap(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri triangleloop; vertex triorg; if (b->verbose) { printf(" Constructing mapping from vertices to triangles.\n"); } traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* Check all three vertices of the triangle. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { org(triangleloop, triorg); setvertex2tri(triorg, encode(triangleloop)); } triangleloop.tri = triangletraverse(m); }}/*****************************************************************************//* *//* preciselocate() Find a triangle or edge containing a given point. *//* *//* Begins its search from `searchtri'. It is important that `searchtri' *//* be a handle with the property that `searchpoint' is strictly to the left *//* of the edge denoted by `searchtri', or is collinear with that edge and *//* does not intersect that edge. (In particular, `searchpoint' should not *//* be the origin or destination of that edge.) *//* *//* These conditions are imposed because preciselocate() is normally used in *//* one of two situations: *//* *//* (1) To try to find the location to insert a new point. Normally, we *//* know an edge that the point is strictly to the left of. In the *//* incremental Delaunay algorithm, that edge is a bounding box edge. *//* In Ruppert's Delaunay refinement algorithm for quality meshing, *//* that edge is the shortest edge of the triangle whose circumcenter *//* is being inserted. *//* *//* (2) To try to find an existing point. In this case, any edge on the *//* convex hull is a good starting edge. You must screen out the *//* possibility that the vertex sought is an endpoint of the starting *//* edge before you call preciselocate(). *//* *//* On completion, `searchtri' is a triangle that contains `searchpoint'. *//* *//* This implementation differs from that given by Guibas and Stolfi. It *//* walks from triangle to triangle, crossing an edge only if `searchpoint' *//* is on the other side of the line containing that edge. After entering *//* a triangle, there are two edges by which one can leave that triangle. *//* If both edges are valid (`searchpoint' is on the other side of both *//* edges), one of the two is chosen by drawing a line perpendicular to *//* the entry edge (whose endpoints are `forg' and `fdest') passing through *//* `fapex'. Depending on which side of this perpendicular `searchpoint' *//* falls on, an exit edge is chosen. *//* *//* This implementation is empirically faster than the Guibas and Stolfi *//* point location routine (which I originally used), which tends to spiral *//* in toward its target. *//* *//* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' *//* is a handle whose origin is the existing vertex. *//* *//* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a *//* handle whose primary edge is the edge on which the point lies. *//* *//* Returns INTRIANGLE if the point lies strictly within a triangle. *//* `searchtri' is a handle on the triangle that contains the point. *//* *//* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a *//* handle whose primary edge the point is to the right of. This might *//* occur when the circumcenter of a triangle falls just slightly outside *//* the mesh due to floating-point roundoff error. It also occurs when *//* seeking a hole or region point that a foolish user has placed outside *//* the mesh. *//* *//* If `stopatsubsegment' is nonzero, the search will stop if it tries to *//* walk through a subsegment, and will return OUTSIDE. *//* *//* WARNING: This routine is designed for convex triangulations, and will *//* not generally work after the holes and concavities have been carved. *//* However, it can still be used to find the circumcenter of a triangle, as *//* long as the search is begun from the triangle in question. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSenum locateresult preciselocate(struct mesh *m, struct behavior *b, vertex searchpoint, struct otri *searchtri, int stopatsubsegment)#else /* not ANSI_DECLARATORS */enum locateresult preciselocate(m, b, searchpoint, searchtri, stopatsubsegment)struct mesh *m;struct behavior *b;vertex searchpoint;struct otri *searchtri;int stopatsubsegment;#endif /* not ANSI_DECLARATORS */{ struct otri backtracktri; struct osub checkedge; vertex forg, fdest, fapex; REAL orgorient, destorient; int moveleft; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose > 2) { printf(" Searching for point (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); } /* Where are we? */ org(*searchtri, forg); dest(*searchtri, fdest); apex(*searchtri, fapex); while (1) { if (b->verbose > 2) { printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]); } /* Check whether the apex is the point we seek. */ if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) { lprevself(*searchtri); return ONVERTEX; } /* Does the point lie on the other side of the line defined by the */ /* triangle edge opposite the triangle's destination? */ destorient = counterclockwise(m, b, forg, fapex, searchpoint); /* Does the point lie on the other side of the line defined by the */ /* triangle edge opposite the triangle's origin? */ orgorient = counterclockwise(m, b, fapex, fdest, searchpoint); if (destorient > 0.0) { if (orgorient > 0.0) { /* Move left if the inner product of (fapex - searchpoint) and */ /* (fdest - forg) is positive. This is equivalent to drawing */ /* a line perpendicular to the line (forg, fdest) and passing */ /* through `fapex', and determining which side of this line */ /* `searchpoint' falls on. */ moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) + (fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0; } else { moveleft = 1; } } else { if (orgorient > 0.0) { moveleft = 0; } else { /* The point we seek must be on the boundary of or inside this */ /* triangle. */ if (destorient == 0.0) { lprevself(*searchtri); return ONEDGE; } if (orgorient == 0.0) { lnextself(*searchtri); return ONEDGE; } return INTRIANGLE; } } /* Move to another triangle. Leave a trace `backtracktri' in case */ /* floating-point roundoff or some such bogey causes us to walk */ /* off a boundary of the triangulation. */ if (moveleft) { lprev(*searchtri, backtracktri); fdest = fapex; } else { lnext(*searchtri, backtracktri); forg = fapex; } sym(backtracktri, *searchtri); if (m->checksegments && stopatsubsegment) { /* Check for walking through a subsegment. */ tspivot(backtracktri, checkedge); if (checkedge.ss != m->dummysub) { /* Go back to the last triangle. */ otricopy(backtracktri, *searchtri); return OUTSIDE; } } /* Check for walking right out of the triangulation. */ if (searchtri->tri == m->dummytri) { /* Go back to the last triangle. */ otricopy(backtracktri, *searchtri); return OUTSIDE; } apex(*searchtri, fapex); }}/*****************************************************************************//* *//* locate() Find a triangle or edge containing a given point. *//* *//* Searching begins from one of: the input `searchtri', a recently *//* encountered triangle `recenttri', or from a triangle chosen from a *//* random sample. The choice is made by determining which triangle's *//* origin is closest to the point we are searching for. Normally, *//* `searchtri' should be a handle on the convex hull of the triangulation. *//* *//* Details on the random sampling method can be found in the Mucke, Saias, *//* and Zhu paper cited in the header of this code. *//* *//* On completion, `searchtri' is a triangle that contains `searchpoint'. *//* *//* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' *//* is a handle whose origin is the existing vertex. *//* *//* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a *//* handle whose primary edge is the edge on which the point lies. *//* *//* Returns INTRIANGLE if the point lies strictly within a triangle. *//* `searchtri' is a handle on the triangle that contains the point. *//* *//* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a *//* handle whose primary edge the point is to the right of. This might *//* occur when the circumcenter of a triangle falls just slightly outside *//* the mesh due to floating-point roundoff error. It also occurs when *//* seeking a hole or region point that a foolish user has placed outside *//* the mesh. *//* *//* WARNING: This routine is designed for convex triangulations, and will *//* not generally work after the holes and concavities have been carved. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSenum locateresult locate(struct mesh *m, struct behavior *b, vertex searchpoint, struct otri *searchtri)#else /* not ANSI_DECLARATORS */enum locateresult locate(m, b, searchpoint, searchtri)struct mesh *m;struct behavior *b;vertex searchpoint;struct otri *searchtri;#endif /* not ANSI_DECLARATORS */{ VOID **sampleblock; char *firsttri; struct otri sampletri; vertex torg, tdest; unsigned long alignptr; REAL searchdist, dist; REAL ahead; long samplesperblock, totalsamplesleft, samplesleft; long population, totalpopulation; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose > 2) { printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); } /* Record the distance from the suggested starting triangle to the */ /* point we seek. */ org(*searchtri, torg); searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); if (b->verbose > 2) { printf(" Boundary triangle has origin (%.12g, %.12g).\n", torg[0], torg[1]); } /* If a recently encountered triangle has been recorded and has not been */ /* deallocated, test it as a good starting point. */ if (m->recenttri.tri != (triangle *) NULL) { if (!deadtri(m->recenttri.tri)) { org(m->recenttri, torg); if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { otricopy(m->recenttri, *searchtri); return ONVERTEX; } dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); if (dist < searchdist) { otricopy(m->recenttri, *searchtri); searchdist = dist; if (b->verbose > 2) { printf(" Choosing recent triangle with origin (%.12g, %.12g).\n", torg[0], torg[1]); } } } } /* The number of random samples taken is proportional to the cube root of */ /* the number of triangles in the mesh. The next bit of code assumes */ /* that the number of triangles increases monotonically (or at least */ /* doesn't decrease enough to matter). */ while (SAMPLEFACTOR * m->samples * m->samples * m->samples < m->triangles.items) { m->samples++; } /* We'll draw ceiling(samples * TRIPERBLOCK / maxitems) random samples */ /* from each block of triangles (except the first)--until we meet the */ /* sample quota. The ceiling means that blocks at the end might be */ /* neglected, but I don't care. */ samplesperblock = (m->samples * TRIPERBLOCK - 1) / m->triangles.maxitems + 1; /* We'll draw ceiling(samples * itemsfirstblock / maxitems) random samples */ /* from the first block of triangles. */ samplesleft = (m->samples * m->triangles.itemsfirstblock - 1) / m->triangles.maxitems + 1; totalsamplesleft = m->samples; population = m->triangles.itemsfirstblock; totalpopulation = m->triangles.maxitems; sampleblock = m->triangles.firstblock; sampletri.orient = 0; while (totalsamplesleft > 0) { /* If we're in the last block, `population' needs to be corrected. */ if (population > totalpopulation) { population = totalpopulation; } /* Find a pointer to the first triangle in the block. */ alignptr = (unsigned long) (sampleblock + 1); firsttri = (char *) (alignptr + (unsigned long) m->triangles.alignbytes - (alignptr % (unsigned long) m->triangles.alignbytes)); /* Choose `samplesleft' randomly sampled triangles in this block. */ do { sampletri.tri = (triangle *) (firsttri + (randomnation((unsigned int) population) * m->triangles.itembytes)); if (!deadtri(sampletri.tri)) { org(sampletri, torg); dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0]) + (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]); if (dist < searchdist) { otricopy(sampletri, *searchtri); searchdist = dist; if (b->verbose > 2) { printf(" Choosing triangle with origin (%.12g, %.12g).\n", torg[0], torg[1]); } } } samplesleft--; totalsamplesleft--; } while ((samplesleft > 0) && (totalsamplesleft > 0)); if (totalsamplesleft > 0) { sampleblock = (VOID **) *sampleblock; samplesleft = samplesperblock; totalpopulation -= population; population = TRIPERBLOCK; } } /* Where are we? */ org(*searchtri, torg); dest(*searchtri, tdest); /* Check the starting triangle's vertices. */ if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) { return ONVERTEX; } if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) { lnextself(*searchtri); return ONVERTEX; } /* Orient `searchtri' to fit the preconditions of calling preciselocate(). */ ahead = counterclockwise(m, b, torg, tdest, searchpoint); if (ahead < 0.0) { /* Turn around so that `searchpoint' is to the left of the */ /* edge specified by `searchtri'. */ symself(*searchtri); } else if (ahead == 0.0) { /* Check if `searchpoint' is between `torg' and `tdest'. */ if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0])) && ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) { return ONEDGE; } } return preciselocate(m, b, searchpoint, searchtri, 0);}/** **//** **//********* Point location routines end here *********//********* Mesh transformation routines begin here *********//** **//** **//*****************************************************************************//* *//* insertsubseg() Create a new subsegment and insert it between two *//* triangles. *//* *//* The new subsegment is inserted at the edge described by the handle *//* `tri'. Its vertices are properly initialized. The marker `subsegmark' *//* is applied to the subsegment and, if appropriate, its vertices. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid insertsubseg(struct mesh *m, struct behavior *b, struct otri *tri, int subsegmark)#else /* not ANSI_DECLARATORS */void insertsubseg(m, b, tri, subsegmark)struct mesh *m;struct behavior *b;struct otri *tri; /* Edge at which to insert the new subsegment. */int subsegmark; /* Marker for the new subsegment. */#endif /* not ANSI_DECLARATORS */{ struct otri oppotri; struct osub newsubseg; vertex triorg, tridest; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ org(*tri, triorg); dest(*tri, tridest); /* Mark vertices if possible. */ if (vertexmark(triorg) == 0) { setvertexmark(triorg, subsegmark); } if (vertexmark(tridest) == 0) { setvertexmark(tridest, subsegmark); } /* Check if there's already a subsegment here. */ tspivot(*tri, newsubseg); if (newsubseg.ss == m->dummysub) { /* Make new subsegment and initialize its vertices. */ makesubseg(m, &newsubseg); setsorg(newsubseg, tridest); setsdest(newsubseg, triorg); setsegorg(newsubseg, tridest); setsegdest(newsubseg, triorg); /* Bond new subsegment to the two triangles it is sandwiched between. */ /* Note that the facing triangle `oppotri' might be equal to */ /* `dummytri' (outer space), but the new subsegment is bonded to it */ /* all the same. */ tsbond(*tri, newsubseg); sym(*tri, oppotri); ssymself(newsubseg); tsbond(oppotri, newsubseg); setmark(newsubseg, subsegmark); if (b->verbose > 2) { printf(" Inserting new "); printsubseg(m, b, &newsubseg); } } else { if (mark(newsubseg) == 0) { setmark(newsubseg, subsegmark); } }}/*****************************************************************************//* *//* Terminology *//* *//* A "local transformation" replaces a small set of triangles with another *//* set of triangles. This may or may not involve inserting or deleting a *//* vertex. *//* *//* The term "casing" is used to describe the set of triangles that are *//* attached to the triangles being transformed, but are not transformed *//* themselves. Think of the casing as a fixed hollow structure inside *//* which all the action happens. A "casing" is only defined relative to *//* a single transformation; each occurrence of a transformation will *//* involve a different casing. *//* *//*****************************************************************************//*****************************************************************************//* *//* flip() Transform two triangles to two different triangles by flipping *//* an edge counterclockwise within a quadrilateral. *//* *//* Imagine the original triangles, abc and bad, oriented so that the *//* shared edge ab lies in a horizontal plane, with the vertex b on the left *//* and the vertex a on the right. The vertex c lies below the edge, and *//* the vertex d lies above the edge. The `flipedge' handle holds the edge *//* ab of triangle abc, and is directed left, from vertex a to vertex b. *//* *//* The triangles abc and bad are deleted and replaced by the triangles cdb *//* and dca. The triangles that represent abc and bad are NOT deallocated; *//* they are reused for dca and cdb, respectively. Hence, any handles that *//* may have held the original triangles are still valid, although not *//* directed as they were before. *//* *//* Upon completion of this routine, the `flipedge' handle holds the edge *//* dc of triangle dca, and is directed down, from vertex d to vertex c. *//* (Hence, the two triangles have rotated counterclockwise.) *//* *//* WARNING: This transformation is geometrically valid only if the *//* quadrilateral adbc is convex. Furthermore, this transformation is *//* valid only if there is not a subsegment between the triangles abc and *//* bad. This routine does not check either of these preconditions, and *//* it is the responsibility of the calling routine to ensure that they are *//* met. If they are not, the streets shall be filled with wailing and *//* gnashing of teeth. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid flip(struct mesh *m, struct behavior *b, struct otri *flipedge)#else /* not ANSI_DECLARATORS */void flip(m, b, flipedge)struct mesh *m;struct behavior *b;struct otri *flipedge; /* Handle for the triangle abc. */#endif /* not ANSI_DECLARATORS */{ struct otri botleft, botright; struct otri topleft, topright; struct otri top; struct otri botlcasing, botrcasing; struct otri toplcasing, toprcasing; struct osub botlsubseg, botrsubseg; struct osub toplsubseg, toprsubseg; vertex leftvertex, rightvertex, botvertex; vertex farvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Identify the vertices of the quadrilateral. */ org(*flipedge, rightvertex); dest(*flipedge, leftvertex); apex(*flipedge, botvertex); sym(*flipedge, top);#ifdef SELF_CHECK if (top.tri == m->dummytri) { printf("Internal error in flip(): Attempt to flip on boundary.\n"); lnextself(*flipedge); return; } if (m->checksegments) { tspivot(*flipedge, toplsubseg); if (toplsubseg.ss != m->dummysub) { printf("Internal error in flip(): Attempt to flip a segment.\n"); lnextself(*flipedge); return; } }#endif /* SELF_CHECK */ apex(top, farvertex); /* Identify the casing of the quadrilateral. */ lprev(top, topleft); sym(topleft, toplcasing); lnext(top, topright); sym(topright, toprcasing); lnext(*flipedge, botleft); sym(botleft, botlcasing); lprev(*flipedge, botright); sym(botright, botrcasing); /* Rotate the quadrilateral one-quarter turn counterclockwise. */ bond(topleft, botlcasing); bond(botleft, botrcasing); bond(botright, toprcasing); bond(topright, toplcasing); if (m->checksegments) { /* Check for subsegments and rebond them to the quadrilateral. */ tspivot(topleft, toplsubseg); tspivot(botleft, botlsubseg); tspivot(botright, botrsubseg); tspivot(topright, toprsubseg); if (toplsubseg.ss == m->dummysub) { tsdissolve(topright); } else { tsbond(topright, toplsubseg); } if (botlsubseg.ss == m->dummysub) { tsdissolve(topleft); } else { tsbond(topleft, botlsubseg); } if (botrsubseg.ss == m->dummysub) { tsdissolve(botleft); } else { tsbond(botleft, botrsubseg); } if (toprsubseg.ss == m->dummysub) { tsdissolve(botright); } else { tsbond(botright, toprsubseg); } } /* New vertex assignments for the rotated quadrilateral. */ setorg(*flipedge, farvertex); setdest(*flipedge, botvertex); setapex(*flipedge, rightvertex); setorg(top, botvertex); setdest(top, farvertex); setapex(top, leftvertex); if (b->verbose > 2) { printf(" Edge flip results in left "); printtriangle(m, b, &top); printf(" and right "); printtriangle(m, b, flipedge); }}/*****************************************************************************//* *//* unflip() Transform two triangles to two different triangles by *//* flipping an edge clockwise within a quadrilateral. Reverses *//* the flip() operation so that the data structures representing *//* the triangles are back where they were before the flip(). *//* *//* Imagine the original triangles, abc and bad, oriented so that the *//* shared edge ab lies in a horizontal plane, with the vertex b on the left *//* and the vertex a on the right. The vertex c lies below the edge, and *//* the vertex d lies above the edge. The `flipedge' handle holds the edge *//* ab of triangle abc, and is directed left, from vertex a to vertex b. *//* *//* The triangles abc and bad are deleted and replaced by the triangles cdb *//* and dca. The triangles that represent abc and bad are NOT deallocated; *//* they are reused for cdb and dca, respectively. Hence, any handles that *//* may have held the original triangles are still valid, although not *//* directed as they were before. *//* *//* Upon completion of this routine, the `flipedge' handle holds the edge *//* cd of triangle cdb, and is directed up, from vertex c to vertex d. *//* (Hence, the two triangles have rotated clockwise.) *//* *//* WARNING: This transformation is geometrically valid only if the *//* quadrilateral adbc is convex. Furthermore, this transformation is *//* valid only if there is not a subsegment between the triangles abc and *//* bad. This routine does not check either of these preconditions, and *//* it is the responsibility of the calling routine to ensure that they are *//* met. If they are not, the streets shall be filled with wailing and *//* gnashing of teeth. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid unflip(struct mesh *m, struct behavior *b, struct otri *flipedge)#else /* not ANSI_DECLARATORS */void unflip(m, b, flipedge)struct mesh *m;struct behavior *b;struct otri *flipedge; /* Handle for the triangle abc. */#endif /* not ANSI_DECLARATORS */{ struct otri botleft, botright; struct otri topleft, topright; struct otri top; struct otri botlcasing, botrcasing; struct otri toplcasing, toprcasing; struct osub botlsubseg, botrsubseg; struct osub toplsubseg, toprsubseg; vertex leftvertex, rightvertex, botvertex; vertex farvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Identify the vertices of the quadrilateral. */ org(*flipedge, rightvertex); dest(*flipedge, leftvertex); apex(*flipedge, botvertex); sym(*flipedge, top);#ifdef SELF_CHECK if (top.tri == m->dummytri) { printf("Internal error in unflip(): Attempt to flip on boundary.\n"); lnextself(*flipedge); return; } if (m->checksegments) { tspivot(*flipedge, toplsubseg); if (toplsubseg.ss != m->dummysub) { printf("Internal error in unflip(): Attempt to flip a subsegment.\n"); lnextself(*flipedge); return; } }#endif /* SELF_CHECK */ apex(top, farvertex); /* Identify the casing of the quadrilateral. */ lprev(top, topleft); sym(topleft, toplcasing); lnext(top, topright); sym(topright, toprcasing); lnext(*flipedge, botleft); sym(botleft, botlcasing); lprev(*flipedge, botright); sym(botright, botrcasing); /* Rotate the quadrilateral one-quarter turn clockwise. */ bond(topleft, toprcasing); bond(botleft, toplcasing); bond(botright, botlcasing); bond(topright, botrcasing); if (m->checksegments) { /* Check for subsegments and rebond them to the quadrilateral. */ tspivot(topleft, toplsubseg); tspivot(botleft, botlsubseg); tspivot(botright, botrsubseg); tspivot(topright, toprsubseg); if (toplsubseg.ss == m->dummysub) { tsdissolve(botleft); } else { tsbond(botleft, toplsubseg); } if (botlsubseg.ss == m->dummysub) { tsdissolve(botright); } else { tsbond(botright, botlsubseg); } if (botrsubseg.ss == m->dummysub) { tsdissolve(topright); } else { tsbond(topright, botrsubseg); } if (toprsubseg.ss == m->dummysub) { tsdissolve(topleft); } else { tsbond(topleft, toprsubseg); } } /* New vertex assignments for the rotated quadrilateral. */ setorg(*flipedge, botvertex); setdest(*flipedge, farvertex); setapex(*flipedge, leftvertex); setorg(top, farvertex); setdest(top, botvertex); setapex(top, rightvertex); if (b->verbose > 2) { printf(" Edge unflip results in left "); printtriangle(m, b, flipedge); printf(" and right "); printtriangle(m, b, &top); }}/*****************************************************************************//* *//* insertvertex() Insert a vertex into a Delaunay triangulation, *//* performing flips as necessary to maintain the Delaunay *//* property. *//* *//* The point `insertvertex' is located. If `searchtri.tri' is not NULL, *//* the search for the containing triangle begins from `searchtri'. If *//* `searchtri.tri' is NULL, a full point location procedure is called. *//* If `insertvertex' is found inside a triangle, the triangle is split into *//* three; if `insertvertex' lies on an edge, the edge is split in two, *//* thereby splitting the two adjacent triangles into four. Edge flips are *//* used to restore the Delaunay property. If `insertvertex' lies on an *//* existing vertex, no action is taken, and the value DUPLICATEVERTEX is *//* returned. On return, `searchtri' is set to a handle whose origin is the *//* existing vertex. *//* *//* Normally, the parameter `splitseg' is set to NULL, implying that no *//* subsegment should be split. In this case, if `insertvertex' is found to *//* lie on a segment, no action is taken, and the value VIOLATINGVERTEX is *//* returned. On return, `searchtri' is set to a handle whose primary edge *//* is the violated subsegment. *//* *//* If the calling routine wishes to split a subsegment by inserting a *//* vertex in it, the parameter `splitseg' should be that subsegment. In *//* this case, `searchtri' MUST be the triangle handle reached by pivoting *//* from that subsegment; no point location is done. *//* *//* `segmentflaws' and `triflaws' are flags that indicate whether or not *//* there should be checks for the creation of encroached subsegments or bad *//* quality triangles. If a newly inserted vertex encroaches upon *//* subsegments, these subsegments are added to the list of subsegments to *//* be split if `segmentflaws' is set. If bad triangles are created, these *//* are added to the queue if `triflaws' is set. *//* *//* If a duplicate vertex or violated segment does not prevent the vertex *//* from being inserted, the return value will be ENCROACHINGVERTEX if the *//* vertex encroaches upon a subsegment (and checking is enabled), or *//* SUCCESSFULVERTEX otherwise. In either case, `searchtri' is set to a *//* handle whose origin is the newly inserted vertex. *//* *//* insertvertex() does not use flip() for reasons of speed; some *//* information can be reused from edge flip to edge flip, like the *//* locations of subsegments. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSenum insertvertexresult insertvertex(struct mesh *m, struct behavior *b, vertex newvertex, struct otri *searchtri, struct osub *splitseg, int segmentflaws, int triflaws)#else /* not ANSI_DECLARATORS */enum insertvertexresult insertvertex(m, b, newvertex, searchtri, splitseg, segmentflaws, triflaws)struct mesh *m;struct behavior *b;vertex newvertex;struct otri *searchtri;struct osub *splitseg;int segmentflaws;int triflaws;#endif /* not ANSI_DECLARATORS */{ struct otri horiz; struct otri top; struct otri botleft, botright; struct otri topleft, topright; struct otri newbotleft, newbotright; struct otri newtopright; struct otri botlcasing, botrcasing; struct otri toplcasing, toprcasing; struct otri testtri; struct osub botlsubseg, botrsubseg; struct osub toplsubseg, toprsubseg; struct osub brokensubseg; struct osub checksubseg; struct osub rightsubseg; struct osub newsubseg; struct badsubseg *encroached; struct flipstacker *newflip; vertex first; vertex leftvertex, rightvertex, botvertex, topvertex, farvertex; vertex segmentorg, segmentdest; REAL attrib; REAL area; enum insertvertexresult success; enum locateresult intersect; int doflip; int mirrorflag; int enq; int i; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by spivot() and tspivot(). */ if (b->verbose > 1) { printf(" Inserting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } if (splitseg == (struct osub *) NULL) { /* Find the location of the vertex to be inserted. Check if a good */ /* starting triangle has already been provided by the caller. */ if (searchtri->tri == m->dummytri) { /* Find a boundary triangle. */ horiz.tri = m->dummytri; horiz.orient = 0; symself(horiz); /* Search for a triangle containing `newvertex'. */ intersect = locate(m, b, newvertex, &horiz); } else { /* Start searching from the triangle provided by the caller. */ otricopy(*searchtri, horiz); intersect = preciselocate(m, b, newvertex, &horiz, 1); } } else { /* The calling routine provides the subsegment in which */ /* the vertex is inserted. */ otricopy(*searchtri, horiz); intersect = ONEDGE; } if (intersect == ONVERTEX) { /* There's already a vertex there. Return in `searchtri' a triangle */ /* whose origin is the existing vertex. */ otricopy(horiz, *searchtri); otricopy(horiz, m->recenttri); return DUPLICATEVERTEX; } if ((intersect == ONEDGE) || (intersect == OUTSIDE)) { /* The vertex falls on an edge or boundary. */ if (m->checksegments && (splitseg == (struct osub *) NULL)) { /* Check whether the vertex falls on a subsegment. */ tspivot(horiz, brokensubseg); if (brokensubseg.ss != m->dummysub) { /* The vertex falls on a subsegment, and hence will not be inserted. */ if (segmentflaws) { enq = b->nobisect != 2; if (enq && (b->nobisect == 1)) { /* This subsegment may be split only if it is an */ /* internal boundary. */ sym(horiz, testtri); enq = testtri.tri != m->dummytri; } if (enq) { /* Add the subsegment to the list of encroached subsegments. */ encroached = (struct badsubseg *) poolalloc(&m->badsubsegs); encroached->encsubseg = sencode(brokensubseg); sorg(brokensubseg, encroached->subsegorg); sdest(brokensubseg, encroached->subsegdest); if (b->verbose > 2) { printf( " Queueing encroached subsegment (%.12g, %.12g) (%.12g, %.12g).\n", encroached->subsegorg[0], encroached->subsegorg[1], encroached->subsegdest[0], encroached->subsegdest[1]); } } } /* Return a handle whose primary edge contains the vertex, */ /* which has not been inserted. */ otricopy(horiz, *searchtri); otricopy(horiz, m->recenttri); return VIOLATINGVERTEX; } } /* Insert the vertex on an edge, dividing one triangle into two (if */ /* the edge lies on a boundary) or two triangles into four. */ lprev(horiz, botright); sym(botright, botrcasing); sym(horiz, topright); /* Is there a second triangle? (Or does this edge lie on a boundary?) */ mirrorflag = topright.tri != m->dummytri; if (mirrorflag) { lnextself(topright); sym(topright, toprcasing); maketriangle(m, b, &newtopright); } else { /* Splitting a boundary edge increases the number of boundary edges. */ m->hullsize++; } maketriangle(m, b, &newbotright); /* Set the vertices of changed and new triangles. */ org(horiz, rightvertex); dest(horiz, leftvertex); apex(horiz, botvertex); setorg(newbotright, botvertex); setdest(newbotright, rightvertex); setapex(newbotright, newvertex); setorg(horiz, newvertex); for (i = 0; i < m->eextras; i++) { /* Set the element attributes of a new triangle. */ setelemattribute(newbotright, i, elemattribute(botright, i)); } if (b->vararea) { /* Set the area constraint of a new triangle. */ setareabound(newbotright, areabound(botright)); } if (mirrorflag) { dest(topright, topvertex); setorg(newtopright, rightvertex); setdest(newtopright, topvertex); setapex(newtopright, newvertex); setorg(topright, newvertex); for (i = 0; i < m->eextras; i++) { /* Set the element attributes of another new triangle. */ setelemattribute(newtopright, i, elemattribute(topright, i)); } if (b->vararea) { /* Set the area constraint of another new triangle. */ setareabound(newtopright, areabound(topright)); } } /* There may be subsegments that need to be bonded */ /* to the new triangle(s). */ if (m->checksegments) { tspivot(botright, botrsubseg); if (botrsubseg.ss != m->dummysub) { tsdissolve(botright); tsbond(newbotright, botrsubseg); } if (mirrorflag) { tspivot(topright, toprsubseg); if (toprsubseg.ss != m->dummysub) { tsdissolve(topright); tsbond(newtopright, toprsubseg); } } } /* Bond the new triangle(s) to the surrounding triangles. */ bond(newbotright, botrcasing); lprevself(newbotright); bond(newbotright, botright); lprevself(newbotright); if (mirrorflag) { bond(newtopright, toprcasing); lnextself(newtopright); bond(newtopright, topright); lnextself(newtopright); bond(newtopright, newbotright); } if (splitseg != (struct osub *) NULL) { /* Split the subsegment into two. */ setsdest(*splitseg, newvertex); segorg(*splitseg, segmentorg); segdest(*splitseg, segmentdest); ssymself(*splitseg); spivot(*splitseg, rightsubseg); insertsubseg(m, b, &newbotright, mark(*splitseg)); tspivot(newbotright, newsubseg); setsegorg(newsubseg, segmentorg); setsegdest(newsubseg, segmentdest); sbond(*splitseg, newsubseg); ssymself(newsubseg); sbond(newsubseg, rightsubseg); ssymself(*splitseg); /* Transfer the subsegment's boundary marker to the vertex */ /* if required. */ if (vertexmark(newvertex) == 0) { setvertexmark(newvertex, mark(*splitseg)); } } if (m->checkquality) { poolrestart(&m->flipstackers); m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); m->lastflip->flippedtri = encode(horiz); m->lastflip->prevflip = (struct flipstacker *) &insertvertex; }#ifdef SELF_CHECK if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle prior to edge vertex insertion (bottom).\n"); } if (mirrorflag) { if (counterclockwise(m, b, leftvertex, rightvertex, topvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to edge vertex insertion (top).\n"); } if (counterclockwise(m, b, rightvertex, topvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (top right).\n"); } if (counterclockwise(m, b, topvertex, leftvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (top left).\n"); } } if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (bottom left).\n"); } if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf( " Clockwise triangle after edge vertex insertion (bottom right).\n"); }#endif /* SELF_CHECK */ if (b->verbose > 2) { printf(" Updating bottom left "); printtriangle(m, b, &botright); if (mirrorflag) { printf(" Updating top left "); printtriangle(m, b, &topright); printf(" Creating top right "); printtriangle(m, b, &newtopright); } printf(" Creating bottom right "); printtriangle(m, b, &newbotright); } /* Position `horiz' on the first edge to check for */ /* the Delaunay property. */ lnextself(horiz); } else { /* Insert the vertex in a triangle, splitting it into three. */ lnext(horiz, botleft); lprev(horiz, botright); sym(botleft, botlcasing); sym(botright, botrcasing); maketriangle(m, b, &newbotleft); maketriangle(m, b, &newbotright); /* Set the vertices of changed and new triangles. */ org(horiz, rightvertex); dest(horiz, leftvertex); apex(horiz, botvertex); setorg(newbotleft, leftvertex); setdest(newbotleft, botvertex); setapex(newbotleft, newvertex); setorg(newbotright, botvertex); setdest(newbotright, rightvertex); setapex(newbotright, newvertex); setapex(horiz, newvertex); for (i = 0; i < m->eextras; i++) { /* Set the element attributes of the new triangles. */ attrib = elemattribute(horiz, i); setelemattribute(newbotleft, i, attrib); setelemattribute(newbotright, i, attrib); } if (b->vararea) { /* Set the area constraint of the new triangles. */ area = areabound(horiz); setareabound(newbotleft, area); setareabound(newbotright, area); } /* There may be subsegments that need to be bonded */ /* to the new triangles. */ if (m->checksegments) { tspivot(botleft, botlsubseg); if (botlsubseg.ss != m->dummysub) { tsdissolve(botleft); tsbond(newbotleft, botlsubseg); } tspivot(botright, botrsubseg); if (botrsubseg.ss != m->dummysub) { tsdissolve(botright); tsbond(newbotright, botrsubseg); } } /* Bond the new triangles to the surrounding triangles. */ bond(newbotleft, botlcasing); bond(newbotright, botrcasing); lnextself(newbotleft); lprevself(newbotright); bond(newbotleft, newbotright); lnextself(newbotleft); bond(botleft, newbotleft); lprevself(newbotright); bond(botright, newbotright); if (m->checkquality) { poolrestart(&m->flipstackers); m->lastflip = (struct flipstacker *) poolalloc(&m->flipstackers); m->lastflip->flippedtri = encode(horiz); m->lastflip->prevflip = (struct flipstacker *) NULL; }#ifdef SELF_CHECK if (counterclockwise(m, b, rightvertex, leftvertex, botvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to vertex insertion.\n"); } if (counterclockwise(m, b, rightvertex, leftvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after vertex insertion (top).\n"); } if (counterclockwise(m, b, leftvertex, botvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after vertex insertion (left).\n"); } if (counterclockwise(m, b, botvertex, rightvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after vertex insertion (right).\n"); }#endif /* SELF_CHECK */ if (b->verbose > 2) { printf(" Updating top "); printtriangle(m, b, &horiz); printf(" Creating left "); printtriangle(m, b, &newbotleft); printf(" Creating right "); printtriangle(m, b, &newbotright); } } /* The insertion is successful by default, unless an encroached */ /* subsegment is found. */ success = SUCCESSFULVERTEX; /* Circle around the newly inserted vertex, checking each edge opposite */ /* it for the Delaunay property. Non-Delaunay edges are flipped. */ /* `horiz' is always the edge being checked. `first' marks where to */ /* stop circling. */ org(horiz, first); rightvertex = first; dest(horiz, leftvertex); /* Circle until finished. */ while (1) { /* By default, the edge will be flipped. */ doflip = 1; if (m->checksegments) { /* Check for a subsegment, which cannot be flipped. */ tspivot(horiz, checksubseg); if (checksubseg.ss != m->dummysub) { /* The edge is a subsegment and cannot be flipped. */ doflip = 0;#ifndef CDT_ONLY if (segmentflaws) { /* Does the new vertex encroach upon this subsegment? */ if (checkseg4encroach(m, b, &checksubseg)) { success = ENCROACHINGVERTEX; } }#endif /* not CDT_ONLY */ } } if (doflip) { /* Check if the edge is a boundary edge. */ sym(horiz, top); if (top.tri == m->dummytri) { /* The edge is a boundary edge and cannot be flipped. */ doflip = 0; } else { /* Find the vertex on the other side of the edge. */ apex(top, farvertex); /* In the incremental Delaunay triangulation algorithm, any of */ /* `leftvertex', `rightvertex', and `farvertex' could be vertices */ /* of the triangular bounding box. These vertices must be */ /* treated as if they are infinitely distant, even though their */ /* "coordinates" are not. */ if ((leftvertex == m->infvertex1) || (leftvertex == m->infvertex2) || (leftvertex == m->infvertex3)) { /* `leftvertex' is infinitely distant. Check the convexity of */ /* the boundary of the triangulation. 'farvertex' might be */ /* infinite as well, but trust me, this same condition should */ /* be applied. */ doflip = counterclockwise(m, b, newvertex, rightvertex, farvertex) > 0.0; } else if ((rightvertex == m->infvertex1) || (rightvertex == m->infvertex2) || (rightvertex == m->infvertex3)) { /* `rightvertex' is infinitely distant. Check the convexity of */ /* the boundary of the triangulation. 'farvertex' might be */ /* infinite as well, but trust me, this same condition should */ /* be applied. */ doflip = counterclockwise(m, b, farvertex, leftvertex, newvertex) > 0.0; } else if ((farvertex == m->infvertex1) || (farvertex == m->infvertex2) || (farvertex == m->infvertex3)) { /* `farvertex' is infinitely distant and cannot be inside */ /* the circumcircle of the triangle `horiz'. */ doflip = 0; } else { /* Test whether the edge is locally Delaunay. */ doflip = incircle(m, b, leftvertex, newvertex, rightvertex, farvertex) > 0.0; } if (doflip) { /* We made it! Flip the edge `horiz' by rotating its containing */ /* quadrilateral (the two triangles adjacent to `horiz'). */ /* Identify the casing of the quadrilateral. */ lprev(top, topleft); sym(topleft, toplcasing); lnext(top, topright); sym(topright, toprcasing); lnext(horiz, botleft); sym(botleft, botlcasing); lprev(horiz, botright); sym(botright, botrcasing); /* Rotate the quadrilateral one-quarter turn counterclockwise. */ bond(topleft, botlcasing); bond(botleft, botrcasing); bond(botright, toprcasing); bond(topright, toplcasing); if (m->checksegments) { /* Check for subsegments and rebond them to the quadrilateral. */ tspivot(topleft, toplsubseg); tspivot(botleft, botlsubseg); tspivot(botright, botrsubseg); tspivot(topright, toprsubseg); if (toplsubseg.ss == m->dummysub) { tsdissolve(topright); } else { tsbond(topright, toplsubseg); } if (botlsubseg.ss == m->dummysub) { tsdissolve(topleft); } else { tsbond(topleft, botlsubseg); } if (botrsubseg.ss == m->dummysub) { tsdissolve(botleft); } else { tsbond(botleft, botrsubseg); } if (toprsubseg.ss == m->dummysub) { tsdissolve(botright); } else { tsbond(botright, toprsubseg); } } /* New vertex assignments for the rotated quadrilateral. */ setorg(horiz, farvertex); setdest(horiz, newvertex); setapex(horiz, rightvertex); setorg(top, newvertex); setdest(top, farvertex); setapex(top, leftvertex); for (i = 0; i < m->eextras; i++) { /* Take the average of the two triangles' attributes. */ attrib = 0.5 * (elemattribute(top, i) + elemattribute(horiz, i)); setelemattribute(top, i, attrib); setelemattribute(horiz, i, attrib); } if (b->vararea) { if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) { area = -1.0; } else { /* Take the average of the two triangles' area constraints. */ /* This prevents small area constraints from migrating a */ /* long, long way from their original location due to flips. */ area = 0.5 * (areabound(top) + areabound(horiz)); } setareabound(top, area); setareabound(horiz, area); } if (m->checkquality) { newflip = (struct flipstacker *) poolalloc(&m->flipstackers); newflip->flippedtri = encode(horiz); newflip->prevflip = m->lastflip; m->lastflip = newflip; }#ifdef SELF_CHECK if (newvertex != (vertex) NULL) { if (counterclockwise(m, b, leftvertex, newvertex, rightvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to edge flip (bottom).\n"); } /* The following test has been removed because constrainededge() */ /* sometimes generates inverted triangles that insertvertex() */ /* removes. *//* if (counterclockwise(m, b, rightvertex, farvertex, leftvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle prior to edge flip (top).\n"); }*/ if (counterclockwise(m, b, farvertex, leftvertex, newvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after edge flip (left).\n"); } if (counterclockwise(m, b, newvertex, rightvertex, farvertex) < 0.0) { printf("Internal error in insertvertex():\n"); printf(" Clockwise triangle after edge flip (right).\n"); } }#endif /* SELF_CHECK */ if (b->verbose > 2) { printf(" Edge flip results in left "); lnextself(topleft); printtriangle(m, b, &topleft); printf(" and right "); printtriangle(m, b, &horiz); } /* On the next iterations, consider the two edges that were */ /* exposed (this is, are now visible to the newly inserted */ /* vertex) by the edge flip. */ lprevself(horiz); leftvertex = farvertex; } } } if (!doflip) { /* The handle `horiz' is accepted as locally Delaunay. */#ifndef CDT_ONLY if (triflaws) { /* Check the triangle `horiz' for quality. */ testtriangle(m, b, &horiz); }#endif /* not CDT_ONLY */ /* Look for the next edge around the newly inserted vertex. */ lnextself(horiz); sym(horiz, testtri); /* Check for finishing a complete revolution about the new vertex, or */ /* falling outside of the triangulation. The latter will happen */ /* when a vertex is inserted at a boundary. */ if ((leftvertex == first) || (testtri.tri == m->dummytri)) { /* We're done. Return a triangle whose origin is the new vertex. */ lnext(horiz, *searchtri); lnext(horiz, m->recenttri); return success; } /* Finish finding the next edge around the newly inserted vertex. */ lnext(testtri, horiz); rightvertex = leftvertex; dest(horiz, leftvertex); } }}/*****************************************************************************//* *//* triangulatepolygon() Find the Delaunay triangulation of a polygon that *//* has a certain "nice" shape. This includes the *//* polygons that result from deletion of a vertex or *//* insertion of a segment. *//* *//* This is a conceptually difficult routine. The starting assumption is *//* that we have a polygon with n sides. n - 1 of these sides are currently *//* represented as edges in the mesh. One side, called the "base", need not *//* be. *//* *//* Inside the polygon is a structure I call a "fan", consisting of n - 1 *//* triangles that share a common origin. For each of these triangles, the *//* edge opposite the origin is one of the sides of the polygon. The *//* primary edge of each triangle is the edge directed from the origin to *//* the destination; note that this is not the same edge that is a side of *//* the polygon. `firstedge' is the primary edge of the first triangle. *//* From there, the triangles follow in counterclockwise order about the *//* polygon, until `lastedge', the primary edge of the last triangle. *//* `firstedge' and `lastedge' are probably connected to other triangles *//* beyond the extremes of the fan, but their identity is not important, as *//* long as the fan remains connected to them. *//* *//* Imagine the polygon oriented so that its base is at the bottom. This *//* puts `firstedge' on the far right, and `lastedge' on the far left. *//* The right vertex of the base is the destination of `firstedge', and the *//* left vertex of the base is the apex of `lastedge'. *//* *//* The challenge now is to find the right sequence of edge flips to *//* transform the fan into a Delaunay triangulation of the polygon. Each *//* edge flip effectively removes one triangle from the fan, committing it *//* to the polygon. The resulting polygon has one fewer edge. If `doflip' *//* is set, the final flip will be performed, resulting in a fan of one *//* (useless?) triangle. If `doflip' is not set, the final flip is not *//* performed, resulting in a fan of two triangles, and an unfinished *//* triangular polygon that is not yet filled out with a single triangle. *//* On completion of the routine, `lastedge' is the last remaining triangle, *//* or the leftmost of the last two. *//* *//* Although the flips are performed in the order described above, the *//* decisions about what flips to perform are made in precisely the reverse *//* order. The recursive triangulatepolygon() procedure makes a decision, *//* uses up to two recursive calls to triangulate the "subproblems" *//* (polygons with fewer edges), and then performs an edge flip. *//* *//* The "decision" it makes is which vertex of the polygon should be *//* connected to the base. This decision is made by testing every possible *//* vertex. Once the best vertex is found, the two edges that connect this *//* vertex to the base become the bases for two smaller polygons. These *//* are triangulated recursively. Unfortunately, this approach can take *//* O(n^2) time not only in the worst case, but in many common cases. It's *//* rarely a big deal for vertex deletion, where n is rarely larger than *//* ten, but it could be a big deal for segment insertion, especially if *//* there's a lot of long segments that each cut many triangles. I ought to *//* code a faster algorithm some day. *//* *//* The `edgecount' parameter is the number of sides of the polygon, *//* including its base. `triflaws' is a flag that determines whether the *//* new triangles should be tested for quality, and enqueued if they are *//* bad. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid triangulatepolygon(struct mesh *m, struct behavior *b, struct otri *firstedge, struct otri *lastedge, int edgecount, int doflip, int triflaws)#else /* not ANSI_DECLARATORS */void triangulatepolygon(m, b, firstedge, lastedge, edgecount, doflip, triflaws)struct mesh *m;struct behavior *b;struct otri *firstedge;struct otri *lastedge;int edgecount;int doflip;int triflaws;#endif /* not ANSI_DECLARATORS */{ struct otri testtri; struct otri besttri; struct otri tempedge; vertex leftbasevertex, rightbasevertex; vertex testvertex; vertex bestvertex; int bestnumber; int i; triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ /* Identify the base vertices. */ apex(*lastedge, leftbasevertex); dest(*firstedge, rightbasevertex); if (b->verbose > 2) { printf(" Triangulating interior polygon at edge\n"); printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasevertex[0], leftbasevertex[1], rightbasevertex[0], rightbasevertex[1]); } /* Find the best vertex to connect the base to. */ onext(*firstedge, besttri); dest(besttri, bestvertex); otricopy(besttri, testtri); bestnumber = 1; for (i = 2; i <= edgecount - 2; i++) { onextself(testtri); dest(testtri, testvertex); /* Is this a better vertex? */ if (incircle(m, b, leftbasevertex, rightbasevertex, bestvertex, testvertex) > 0.0) { otricopy(testtri, besttri); bestvertex = testvertex; bestnumber = i; } } if (b->verbose > 2) { printf(" Connecting edge to (%.12g, %.12g)\n", bestvertex[0], bestvertex[1]); } if (bestnumber > 1) { /* Recursively triangulate the smaller polygon on the right. */ oprev(besttri, tempedge); triangulatepolygon(m, b, firstedge, &tempedge, bestnumber + 1, 1, triflaws); } if (bestnumber < edgecount - 2) { /* Recursively triangulate the smaller polygon on the left. */ sym(besttri, tempedge); triangulatepolygon(m, b, &besttri, lastedge, edgecount - bestnumber, 1, triflaws); /* Find `besttri' again; it may have been lost to edge flips. */ sym(tempedge, besttri); } if (doflip) { /* Do one final edge flip. */ flip(m, b, &besttri);#ifndef CDT_ONLY if (triflaws) { /* Check the quality of the newly committed triangle. */ sym(besttri, testtri); testtriangle(m, b, &testtri); }#endif /* not CDT_ONLY */ } /* Return the base triangle. */ otricopy(besttri, *lastedge);}/*****************************************************************************//* *//* deletevertex() Delete a vertex from a Delaunay triangulation, ensuring *//* that the triangulation remains Delaunay. *//* *//* The origin of `deltri' is deleted. The union of the triangles adjacent *//* to this vertex is a polygon, for which the Delaunay triangulation is *//* found. Two triangles are removed from the mesh. *//* *//* Only interior vertices that do not lie on segments or boundaries may be *//* deleted. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid deletevertex(struct mesh *m, struct behavior *b, struct otri *deltri)#else /* not ANSI_DECLARATORS */void deletevertex(m, b, deltri)struct mesh *m;struct behavior *b;struct otri *deltri;#endif /* not ANSI_DECLARATORS */{ struct otri countingtri; struct otri firstedge, lastedge; struct otri deltriright; struct otri lefttri, righttri; struct otri leftcasing, rightcasing; struct osub leftsubseg, rightsubseg; vertex delvertex; vertex neworg; int edgecount; triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ subseg sptr; /* Temporary variable used by tspivot(). */ org(*deltri, delvertex); if (b->verbose > 1) { printf(" Deleting (%.12g, %.12g).\n", delvertex[0], delvertex[1]); } vertexdealloc(m, delvertex); /* Count the degree of the vertex being deleted. */ onext(*deltri, countingtri); edgecount = 1; while (!otriequal(*deltri, countingtri)) {#ifdef SELF_CHECK if (countingtri.tri == m->dummytri) { printf("Internal error in deletevertex():\n"); printf(" Attempt to delete boundary vertex.\n"); internalerror(); }#endif /* SELF_CHECK */ edgecount++; onextself(countingtri); }#ifdef SELF_CHECK if (edgecount < 3) { printf("Internal error in deletevertex():\n Vertex has degree %d.\n", edgecount); internalerror(); }#endif /* SELF_CHECK */ if (edgecount > 3) { /* Triangulate the polygon defined by the union of all triangles */ /* adjacent to the vertex being deleted. Check the quality of */ /* the resulting triangles. */ onext(*deltri, firstedge); oprev(*deltri, lastedge); triangulatepolygon(m, b, &firstedge, &lastedge, edgecount, 0, !b->nobisect); } /* Splice out two triangles. */ lprev(*deltri, deltriright); dnext(*deltri, lefttri); sym(lefttri, leftcasing); oprev(deltriright, righttri); sym(righttri, rightcasing); bond(*deltri, leftcasing); bond(deltriright, rightcasing); tspivot(lefttri, leftsubseg); if (leftsubseg.ss != m->dummysub) { tsbond(*deltri, leftsubseg); } tspivot(righttri, rightsubseg); if (rightsubseg.ss != m->dummysub) { tsbond(deltriright, rightsubseg); } /* Set the new origin of `deltri' and check its quality. */ org(lefttri, neworg); setorg(*deltri, neworg); if (!b->nobisect) { testtriangle(m, b, deltri); } /* Delete the two spliced-out triangles. */ triangledealloc(m, lefttri.tri); triangledealloc(m, righttri.tri);}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* undovertex() Undo the most recent vertex insertion. *//* *//* Walks through the list of transformations (flips and a vertex insertion) *//* in the reverse of the order in which they were done, and undoes them. *//* The inserted vertex is removed from the triangulation and deallocated. *//* Two triangles (possibly just one) are also deallocated. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid undovertex(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void undovertex(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri fliptri; struct otri botleft, botright, topright; struct otri botlcasing, botrcasing, toprcasing; struct otri gluetri; struct osub botlsubseg, botrsubseg, toprsubseg; vertex botvertex, rightvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ /* Walk through the list of transformations (flips and a vertex insertion) */ /* in the reverse of the order in which they were done, and undo them. */ while (m->lastflip != (struct flipstacker *) NULL) { /* Find a triangle involved in the last unreversed transformation. */ decode(m->lastflip->flippedtri, fliptri); /* We are reversing one of three transformations: a trisection of one */ /* triangle into three (by inserting a vertex in the triangle), a */ /* bisection of two triangles into four (by inserting a vertex in an */ /* edge), or an edge flip. */ if (m->lastflip->prevflip == (struct flipstacker *) NULL) { /* Restore a triangle that was split into three triangles, */ /* so it is again one triangle. */ dprev(fliptri, botleft); lnextself(botleft); onext(fliptri, botright); lprevself(botright); sym(botleft, botlcasing); sym(botright, botrcasing); dest(botleft, botvertex); setapex(fliptri, botvertex); lnextself(fliptri); bond(fliptri, botlcasing); tspivot(botleft, botlsubseg); tsbond(fliptri, botlsubseg); lnextself(fliptri); bond(fliptri, botrcasing); tspivot(botright, botrsubseg); tsbond(fliptri, botrsubseg); /* Delete the two spliced-out triangles. */ triangledealloc(m, botleft.tri); triangledealloc(m, botright.tri); } else if (m->lastflip->prevflip == (struct flipstacker *) &insertvertex) { /* Restore two triangles that were split into four triangles, */ /* so they are again two triangles. */ lprev(fliptri, gluetri); sym(gluetri, botright); lnextself(botright); sym(botright, botrcasing); dest(botright, rightvertex); setorg(fliptri, rightvertex); bond(gluetri, botrcasing); tspivot(botright, botrsubseg); tsbond(gluetri, botrsubseg); /* Delete the spliced-out triangle. */ triangledealloc(m, botright.tri); sym(fliptri, gluetri); if (gluetri.tri != m->dummytri) { lnextself(gluetri); dnext(gluetri, topright); sym(topright, toprcasing); setorg(gluetri, rightvertex); bond(gluetri, toprcasing); tspivot(topright, toprsubseg); tsbond(gluetri, toprsubseg); /* Delete the spliced-out triangle. */ triangledealloc(m, topright.tri); } /* This is the end of the list, sneakily encoded. */ m->lastflip->prevflip = (struct flipstacker *) NULL; } else { /* Undo an edge flip. */ unflip(m, b, &fliptri); } /* Go on and process the next transformation. */ m->lastflip = m->lastflip->prevflip; }}#endif /* not CDT_ONLY *//** **//** **//********* Mesh transformation routines end here *********//********* Divide-and-conquer Delaunay triangulation begins here *********//** **//** **//*****************************************************************************//* *//* The divide-and-conquer bounding box *//* *//* I originally implemented the divide-and-conquer and incremental Delaunay *//* triangulations using the edge-based data structure presented by Guibas *//* and Stolfi. Switching to a triangle-based data structure doubled the *//* speed. However, I had to think of a few extra tricks to maintain the *//* elegance of the original algorithms. *//* *//* The "bounding box" used by my variant of the divide-and-conquer *//* algorithm uses one triangle for each edge of the convex hull of the *//* triangulation. These bounding triangles all share a common apical *//* vertex, which is represented by NULL and which represents nothing. *//* The bounding triangles are linked in a circular fan about this NULL *//* vertex, and the edges on the convex hull of the triangulation appear *//* opposite the NULL vertex. You might find it easiest to imagine that *//* the NULL vertex is a point in 3D space behind the center of the *//* triangulation, and that the bounding triangles form a sort of cone. *//* *//* This bounding box makes it easy to represent degenerate cases. For *//* instance, the triangulation of two vertices is a single edge. This edge *//* is represented by two bounding box triangles, one on each "side" of the *//* edge. These triangles are also linked together in a fan about the NULL *//* vertex. *//* *//* The bounding box also makes it easy to traverse the convex hull, as the *//* divide-and-conquer algorithm needs to do. *//* *//*****************************************************************************//*****************************************************************************//* *//* vertexsort() Sort an array of vertices by x-coordinate, using the *//* y-coordinate as a secondary key. *//* *//* Uses quicksort. Randomized O(n log n) time. No, I did not make any of *//* the usual quicksort mistakes. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid vertexsort(vertex *sortarray, int arraysize)#else /* not ANSI_DECLARATORS */void vertexsort(sortarray, arraysize)vertex *sortarray;int arraysize;#endif /* not ANSI_DECLARATORS */{ int left, right; int pivot; REAL pivotx, pivoty; vertex temp; if (arraysize == 2) { /* Recursive base case. */ if ((sortarray[0][0] > sortarray[1][0]) || ((sortarray[0][0] == sortarray[1][0]) && (sortarray[0][1] > sortarray[1][1]))) { temp = sortarray[1]; sortarray[1] = sortarray[0]; sortarray[0] = temp; } return; } /* Choose a random pivot to split the array. */ pivot = (int) randomnation((unsigned int) arraysize); pivotx = sortarray[pivot][0]; pivoty = sortarray[pivot][1]; /* Split the array. */ left = -1; right = arraysize; while (left < right) { /* Search for a vertex whose x-coordinate is too large for the left. */ do { left++; } while ((left <= right) && ((sortarray[left][0] < pivotx) || ((sortarray[left][0] == pivotx) && (sortarray[left][1] < pivoty)))); /* Search for a vertex whose x-coordinate is too small for the right. */ do { right--; } while ((left <= right) && ((sortarray[right][0] > pivotx) || ((sortarray[right][0] == pivotx) && (sortarray[right][1] > pivoty)))); if (left < right) { /* Swap the left and right vertices. */ temp = sortarray[left]; sortarray[left] = sortarray[right]; sortarray[right] = temp; } } if (left > 1) { /* Recursively sort the left subset. */ vertexsort(sortarray, left); } if (right < arraysize - 2) { /* Recursively sort the right subset. */ vertexsort(&sortarray[right + 1], arraysize - right - 1); }}/*****************************************************************************//* *//* vertexmedian() An order statistic algorithm, almost. Shuffles an *//* array of vertices so that the first `median' vertices *//* occur lexicographically before the remaining vertices. *//* *//* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate *//* if axis == 1. Very similar to the vertexsort() procedure, but runs in *//* randomized linear time. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid vertexmedian(vertex *sortarray, int arraysize, int median, int axis)#else /* not ANSI_DECLARATORS */void vertexmedian(sortarray, arraysize, median, axis)vertex *sortarray;int arraysize;int median;int axis;#endif /* not ANSI_DECLARATORS */{ int left, right; int pivot; REAL pivot1, pivot2; vertex temp; if (arraysize == 2) { /* Recursive base case. */ if ((sortarray[0][axis] > sortarray[1][axis]) || ((sortarray[0][axis] == sortarray[1][axis]) && (sortarray[0][1 - axis] > sortarray[1][1 - axis]))) { temp = sortarray[1]; sortarray[1] = sortarray[0]; sortarray[0] = temp; } return; } /* Choose a random pivot to split the array. */ pivot = (int) randomnation((unsigned int) arraysize); pivot1 = sortarray[pivot][axis]; pivot2 = sortarray[pivot][1 - axis]; /* Split the array. */ left = -1; right = arraysize; while (left < right) { /* Search for a vertex whose x-coordinate is too large for the left. */ do { left++; } while ((left <= right) && ((sortarray[left][axis] < pivot1) || ((sortarray[left][axis] == pivot1) && (sortarray[left][1 - axis] < pivot2)))); /* Search for a vertex whose x-coordinate is too small for the right. */ do { right--; } while ((left <= right) && ((sortarray[right][axis] > pivot1) || ((sortarray[right][axis] == pivot1) && (sortarray[right][1 - axis] > pivot2)))); if (left < right) { /* Swap the left and right vertices. */ temp = sortarray[left]; sortarray[left] = sortarray[right]; sortarray[right] = temp; } } /* Unlike in vertexsort(), at most one of the following */ /* conditionals is true. */ if (left > median) { /* Recursively shuffle the left subset. */ vertexmedian(sortarray, left, median, axis); } if (right < median - 1) { /* Recursively shuffle the right subset. */ vertexmedian(&sortarray[right + 1], arraysize - right - 1, median - right - 1, axis); }}/*****************************************************************************//* *//* alternateaxes() Sorts the vertices as appropriate for the divide-and- *//* conquer algorithm with alternating cuts. *//* *//* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. *//* For the base case, subsets containing only two or three vertices are *//* always sorted by x-coordinate. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid alternateaxes(vertex *sortarray, int arraysize, int axis)#else /* not ANSI_DECLARATORS */void alternateaxes(sortarray, arraysize, axis)vertex *sortarray;int arraysize;int axis;#endif /* not ANSI_DECLARATORS */{ int divider; divider = arraysize >> 1; if (arraysize <= 3) { /* Recursive base case: subsets of two or three vertices will be */ /* handled specially, and should always be sorted by x-coordinate. */ axis = 0; } /* Partition with a horizontal or vertical cut. */ vertexmedian(sortarray, arraysize, divider, axis); /* Recursively partition the subsets with a cross cut. */ if (arraysize - divider >= 2) { if (divider >= 2) { alternateaxes(sortarray, divider, 1 - axis); } alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis); }}/*****************************************************************************//* *//* mergehulls() Merge two adjacent Delaunay triangulations into a *//* single Delaunay triangulation. *//* *//* This is similar to the algorithm given by Guibas and Stolfi, but uses *//* a triangle-based, rather than edge-based, data structure. *//* *//* The algorithm walks up the gap between the two triangulations, knitting *//* them together. As they are merged, some of their bounding triangles *//* are converted into real triangles of the triangulation. The procedure *//* pulls each hull's bounding triangles apart, then knits them together *//* like the teeth of two gears. The Delaunay property determines, at each *//* step, whether the next "tooth" is a bounding triangle of the left hull *//* or the right. When a bounding triangle becomes real, its apex is *//* changed from NULL to a real vertex. *//* *//* Only two new triangles need to be allocated. These become new bounding *//* triangles at the top and bottom of the seam. They are used to connect *//* the remaining bounding triangles (those that have not been converted *//* into real triangles) into a single fan. *//* *//* On entry, `farleft' and `innerleft' are bounding triangles of the left *//* triangulation. The origin of `farleft' is the leftmost vertex, and *//* the destination of `innerleft' is the rightmost vertex of the *//* triangulation. Similarly, `innerright' and `farright' are bounding *//* triangles of the right triangulation. The origin of `innerright' and *//* destination of `farright' are the leftmost and rightmost vertices. *//* *//* On completion, the origin of `farleft' is the leftmost vertex of the *//* merged triangulation, and the destination of `farright' is the rightmost *//* vertex. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid mergehulls(struct mesh *m, struct behavior *b, struct otri *farleft, struct otri *innerleft, struct otri *innerright, struct otri *farright, int axis)#else /* not ANSI_DECLARATORS */void mergehulls(m, b, farleft, innerleft, innerright, farright, axis)struct mesh *m;struct behavior *b;struct otri *farleft;struct otri *innerleft;struct otri *innerright;struct otri *farright;int axis;#endif /* not ANSI_DECLARATORS */{ struct otri leftcand, rightcand; struct otri baseedge; struct otri nextedge; struct otri sidecasing, topcasing, outercasing; struct otri checkedge; vertex innerleftdest; vertex innerrightorg; vertex innerleftapex, innerrightapex; vertex farleftpt, farrightpt; vertex farleftapex, farrightapex; vertex lowerleft, lowerright; vertex upperleft, upperright; vertex nextapex; vertex checkvertex; int changemade; int badedge; int leftfinished, rightfinished; triangle ptr; /* Temporary variable used by sym(). */ dest(*innerleft, innerleftdest); apex(*innerleft, innerleftapex); org(*innerright, innerrightorg); apex(*innerright, innerrightapex); /* Special treatment for horizontal cuts. */ if (b->dwyer && (axis == 1)) { org(*farleft, farleftpt); apex(*farleft, farleftapex); dest(*farright, farrightpt); apex(*farright, farrightapex); /* The pointers to the extremal vertices are shifted to point to the */ /* topmost and bottommost vertex of each hull, rather than the */ /* leftmost and rightmost vertices. */ while (farleftapex[1] < farleftpt[1]) { lnextself(*farleft); symself(*farleft); farleftpt = farleftapex; apex(*farleft, farleftapex); } sym(*innerleft, checkedge); apex(checkedge, checkvertex); while (checkvertex[1] > innerleftdest[1]) { lnext(checkedge, *innerleft); innerleftapex = innerleftdest; innerleftdest = checkvertex; sym(*innerleft, checkedge); apex(checkedge, checkvertex); } while (innerrightapex[1] < innerrightorg[1]) { lnextself(*innerright); symself(*innerright); innerrightorg = innerrightapex; apex(*innerright, innerrightapex); } sym(*farright, checkedge); apex(checkedge, checkvertex); while (checkvertex[1] > farrightpt[1]) { lnext(checkedge, *farright); farrightapex = farrightpt; farrightpt = checkvertex; sym(*farright, checkedge); apex(checkedge, checkvertex); } } /* Find a line tangent to and below both hulls. */ do { changemade = 0; /* Make innerleftdest the "bottommost" vertex of the left hull. */ if (counterclockwise(m, b, innerleftdest, innerleftapex, innerrightorg) > 0.0) { lprevself(*innerleft); symself(*innerleft); innerleftdest = innerleftapex; apex(*innerleft, innerleftapex); changemade = 1; } /* Make innerrightorg the "bottommost" vertex of the right hull. */ if (counterclockwise(m, b, innerrightapex, innerrightorg, innerleftdest) > 0.0) { lnextself(*innerright); symself(*innerright); innerrightorg = innerrightapex; apex(*innerright, innerrightapex); changemade = 1; } } while (changemade); /* Find the two candidates to be the next "gear tooth." */ sym(*innerleft, leftcand); sym(*innerright, rightcand); /* Create the bottom new bounding triangle. */ maketriangle(m, b, &baseedge); /* Connect it to the bounding boxes of the left and right triangulations. */ bond(baseedge, *innerleft); lnextself(baseedge); bond(baseedge, *innerright); lnextself(baseedge); setorg(baseedge, innerrightorg); setdest(baseedge, innerleftdest); /* Apex is intentionally left NULL. */ if (b->verbose > 2) { printf(" Creating base bounding "); printtriangle(m, b, &baseedge); } /* Fix the extreme triangles if necessary. */ org(*farleft, farleftpt); if (innerleftdest == farleftpt) { lnext(baseedge, *farleft); } dest(*farright, farrightpt); if (innerrightorg == farrightpt) { lprev(baseedge, *farright); } /* The vertices of the current knitting edge. */ lowerleft = innerleftdest; lowerright = innerrightorg; /* The candidate vertices for knitting. */ apex(leftcand, upperleft); apex(rightcand, upperright); /* Walk up the gap between the two triangulations, knitting them together. */ while (1) { /* Have we reached the top? (This isn't quite the right question, */ /* because even though the left triangulation might seem finished now, */ /* moving up on the right triangulation might reveal a new vertex of */ /* the left triangulation. And vice-versa.) */ leftfinished = counterclockwise(m, b, upperleft, lowerleft, lowerright) <= 0.0; rightfinished = counterclockwise(m, b, upperright, lowerleft, lowerright) <= 0.0; if (leftfinished && rightfinished) { /* Create the top new bounding triangle. */ maketriangle(m, b, &nextedge); setorg(nextedge, lowerleft); setdest(nextedge, lowerright); /* Apex is intentionally left NULL. */ /* Connect it to the bounding boxes of the two triangulations. */ bond(nextedge, baseedge); lnextself(nextedge); bond(nextedge, rightcand); lnextself(nextedge); bond(nextedge, leftcand); if (b->verbose > 2) { printf(" Creating top bounding "); printtriangle(m, b, &nextedge); } /* Special treatment for horizontal cuts. */ if (b->dwyer && (axis == 1)) { org(*farleft, farleftpt); apex(*farleft, farleftapex); dest(*farright, farrightpt); apex(*farright, farrightapex); sym(*farleft, checkedge); apex(checkedge, checkvertex); /* The pointers to the extremal vertices are restored to the */ /* leftmost and rightmost vertices (rather than topmost and */ /* bottommost). */ while (checkvertex[0] < farleftpt[0]) { lprev(checkedge, *farleft); farleftapex = farleftpt; farleftpt = checkvertex; sym(*farleft, checkedge); apex(checkedge, checkvertex); } while (farrightapex[0] > farrightpt[0]) { lprevself(*farright); symself(*farright); farrightpt = farrightapex; apex(*farright, farrightapex); } } return; } /* Consider eliminating edges from the left triangulation. */ if (!leftfinished) { /* What vertex would be exposed if an edge were deleted? */ lprev(leftcand, nextedge); symself(nextedge); apex(nextedge, nextapex); /* If nextapex is NULL, then no vertex would be exposed; the */ /* triangulation would have been eaten right through. */ if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) > 0.0; while (badedge) { /* Eliminate the edge with an edge flip. As a result, the */ /* left triangulation will have one more boundary triangle. */ lnextself(nextedge); sym(nextedge, topcasing); lnextself(nextedge); sym(nextedge, sidecasing); bond(nextedge, topcasing); bond(leftcand, sidecasing); lnextself(leftcand); sym(leftcand, outercasing); lprevself(nextedge); bond(nextedge, outercasing); /* Correct the vertices to reflect the edge flip. */ setorg(leftcand, lowerleft); setdest(leftcand, NULL); setapex(leftcand, nextapex); setorg(nextedge, NULL); setdest(nextedge, upperleft); setapex(nextedge, nextapex); /* Consider the newly exposed vertex. */ upperleft = nextapex; /* What vertex would be exposed if another edge were deleted? */ otricopy(sidecasing, nextedge); apex(nextedge, nextapex); if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperleft, nextapex) > 0.0; } else { /* Avoid eating right through the triangulation. */ badedge = 0; } } } } /* Consider eliminating edges from the right triangulation. */ if (!rightfinished) { /* What vertex would be exposed if an edge were deleted? */ lnext(rightcand, nextedge); symself(nextedge); apex(nextedge, nextapex); /* If nextapex is NULL, then no vertex would be exposed; the */ /* triangulation would have been eaten right through. */ if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) > 0.0; while (badedge) { /* Eliminate the edge with an edge flip. As a result, the */ /* right triangulation will have one more boundary triangle. */ lprevself(nextedge); sym(nextedge, topcasing); lprevself(nextedge); sym(nextedge, sidecasing); bond(nextedge, topcasing); bond(rightcand, sidecasing); lprevself(rightcand); sym(rightcand, outercasing); lnextself(nextedge); bond(nextedge, outercasing); /* Correct the vertices to reflect the edge flip. */ setorg(rightcand, NULL); setdest(rightcand, lowerright); setapex(rightcand, nextapex); setorg(nextedge, upperright); setdest(nextedge, NULL); setapex(nextedge, nextapex); /* Consider the newly exposed vertex. */ upperright = nextapex; /* What vertex would be exposed if another edge were deleted? */ otricopy(sidecasing, nextedge); apex(nextedge, nextapex); if (nextapex != (vertex) NULL) { /* Check whether the edge is Delaunay. */ badedge = incircle(m, b, lowerleft, lowerright, upperright, nextapex) > 0.0; } else { /* Avoid eating right through the triangulation. */ badedge = 0; } } } } if (leftfinished || (!rightfinished && (incircle(m, b, upperleft, lowerleft, lowerright, upperright) > 0.0))) { /* Knit the triangulations, adding an edge from `lowerleft' */ /* to `upperright'. */ bond(baseedge, rightcand); lprev(rightcand, baseedge); setdest(baseedge, lowerleft); lowerright = upperright; sym(baseedge, rightcand); apex(rightcand, upperright); } else { /* Knit the triangulations, adding an edge from `upperleft' */ /* to `lowerright'. */ bond(baseedge, leftcand); lnext(leftcand, baseedge); setorg(baseedge, lowerright); lowerleft = upperleft; sym(baseedge, leftcand); apex(leftcand, upperleft); } if (b->verbose > 2) { printf(" Connecting "); printtriangle(m, b, &baseedge); } }}/*****************************************************************************//* *//* divconqrecurse() Recursively form a Delaunay triangulation by the *//* divide-and-conquer method. *//* *//* Recursively breaks down the problem into smaller pieces, which are *//* knitted together by mergehulls(). The base cases (problems of two or *//* three vertices) are handled specially here. *//* *//* On completion, `farleft' and `farright' are bounding triangles such that *//* the origin of `farleft' is the leftmost vertex (breaking ties by *//* choosing the highest leftmost vertex), and the destination of *//* `farright' is the rightmost vertex (breaking ties by choosing the *//* lowest rightmost vertex). *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid divconqrecurse(struct mesh *m, struct behavior *b, vertex *sortarray, int vertices, int axis, struct otri *farleft, struct otri *farright)#else /* not ANSI_DECLARATORS */void divconqrecurse(m, b, sortarray, vertices, axis, farleft, farright)struct mesh *m;struct behavior *b;vertex *sortarray;int vertices;int axis;struct otri *farleft;struct otri *farright;#endif /* not ANSI_DECLARATORS */{ struct otri midtri, tri1, tri2, tri3; struct otri innerleft, innerright; REAL area; int divider; if (b->verbose > 2) { printf(" Triangulating %d vertices.\n", vertices); } if (vertices == 2) { /* The triangulation of two vertices is an edge. An edge is */ /* represented by two bounding triangles. */ maketriangle(m, b, farleft); setorg(*farleft, sortarray[0]); setdest(*farleft, sortarray[1]); /* The apex is intentionally left NULL. */ maketriangle(m, b, farright); setorg(*farright, sortarray[1]); setdest(*farright, sortarray[0]); /* The apex is intentionally left NULL. */ bond(*farleft, *farright); lprevself(*farleft); lnextself(*farright); bond(*farleft, *farright); lprevself(*farleft); lnextself(*farright); bond(*farleft, *farright); if (b->verbose > 2) { printf(" Creating "); printtriangle(m, b, farleft); printf(" Creating "); printtriangle(m, b, farright); } /* Ensure that the origin of `farleft' is sortarray[0]. */ lprev(*farright, *farleft); return; } else if (vertices == 3) { /* The triangulation of three vertices is either a triangle (with */ /* three bounding triangles) or two edges (with four bounding */ /* triangles). In either case, four triangles are created. */ maketriangle(m, b, &midtri); maketriangle(m, b, &tri1); maketriangle(m, b, &tri2); maketriangle(m, b, &tri3); area = counterclockwise(m, b, sortarray[0], sortarray[1], sortarray[2]); if (area == 0.0) { /* Three collinear vertices; the triangulation is two edges. */ setorg(midtri, sortarray[0]); setdest(midtri, sortarray[1]); setorg(tri1, sortarray[1]); setdest(tri1, sortarray[0]); setorg(tri2, sortarray[2]); setdest(tri2, sortarray[1]); setorg(tri3, sortarray[1]); setdest(tri3, sortarray[2]); /* All apices are intentionally left NULL. */ bond(midtri, tri1); bond(tri2, tri3); lnextself(midtri); lprevself(tri1); lnextself(tri2); lprevself(tri3); bond(midtri, tri3); bond(tri1, tri2); lnextself(midtri); lprevself(tri1); lnextself(tri2); lprevself(tri3); bond(midtri, tri1); bond(tri2, tri3); /* Ensure that the origin of `farleft' is sortarray[0]. */ otricopy(tri1, *farleft); /* Ensure that the destination of `farright' is sortarray[2]. */ otricopy(tri2, *farright); } else { /* The three vertices are not collinear; the triangulation is one */ /* triangle, namely `midtri'. */ setorg(midtri, sortarray[0]); setdest(tri1, sortarray[0]); setorg(tri3, sortarray[0]); /* Apices of tri1, tri2, and tri3 are left NULL. */ if (area > 0.0) { /* The vertices are in counterclockwise order. */ setdest(midtri, sortarray[1]); setorg(tri1, sortarray[1]); setdest(tri2, sortarray[1]); setapex(midtri, sortarray[2]); setorg(tri2, sortarray[2]); setdest(tri3, sortarray[2]); } else { /* The vertices are in clockwise order. */ setdest(midtri, sortarray[2]); setorg(tri1, sortarray[2]); setdest(tri2, sortarray[2]); setapex(midtri, sortarray[1]); setorg(tri2, sortarray[1]); setdest(tri3, sortarray[1]); } /* The topology does not depend on how the vertices are ordered. */ bond(midtri, tri1); lnextself(midtri); bond(midtri, tri2); lnextself(midtri); bond(midtri, tri3); lprevself(tri1); lnextself(tri2); bond(tri1, tri2); lprevself(tri1); lprevself(tri3); bond(tri1, tri3); lnextself(tri2); lprevself(tri3); bond(tri2, tri3); /* Ensure that the origin of `farleft' is sortarray[0]. */ otricopy(tri1, *farleft); /* Ensure that the destination of `farright' is sortarray[2]. */ if (area > 0.0) { otricopy(tri2, *farright); } else { lnext(*farleft, *farright); } } if (b->verbose > 2) { printf(" Creating "); printtriangle(m, b, &midtri); printf(" Creating "); printtriangle(m, b, &tri1); printf(" Creating "); printtriangle(m, b, &tri2); printf(" Creating "); printtriangle(m, b, &tri3); } return; } else { /* Split the vertices in half. */ divider = vertices >> 1; /* Recursively triangulate each half. */ divconqrecurse(m, b, sortarray, divider, 1 - axis, farleft, &innerleft); divconqrecurse(m, b, &sortarray[divider], vertices - divider, 1 - axis, &innerright, farright); if (b->verbose > 1) { printf(" Joining triangulations with %d and %d vertices.\n", divider, vertices - divider); } /* Merge the two triangulations into one. */ mergehulls(m, b, farleft, &innerleft, &innerright, farright, axis); }}#ifdef ANSI_DECLARATORSlong removeghosts(struct mesh *m, struct behavior *b, struct otri *startghost)#else /* not ANSI_DECLARATORS */long removeghosts(m, b, startghost)struct mesh *m;struct behavior *b;struct otri *startghost;#endif /* not ANSI_DECLARATORS */{ struct otri searchedge; struct otri dissolveedge; struct otri deadtriangle; vertex markorg; long hullsize; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose) { printf(" Removing ghost triangles.\n"); } /* Find an edge on the convex hull to start point location from. */ lprev(*startghost, searchedge); symself(searchedge); m->dummytri[0] = encode(searchedge); /* Remove the bounding box and count the convex hull edges. */ otricopy(*startghost, dissolveedge); hullsize = 0; do { hullsize++; lnext(dissolveedge, deadtriangle); lprevself(dissolveedge); symself(dissolveedge); /* If no PSLG is involved, set the boundary markers of all the vertices */ /* on the convex hull. If a PSLG is used, this step is done later. */ if (!b->poly) { /* Watch out for the case where all the input vertices are collinear. */ if (dissolveedge.tri != m->dummytri) { org(dissolveedge, markorg); if (vertexmark(markorg) == 0) { setvertexmark(markorg, 1); } } } /* Remove a bounding triangle from a convex hull triangle. */ dissolve(dissolveedge); /* Find the next bounding triangle. */ sym(deadtriangle, dissolveedge); /* Delete the bounding triangle. */ triangledealloc(m, deadtriangle.tri); } while (!otriequal(dissolveedge, *startghost)); return hullsize;}/*****************************************************************************//* *//* divconqdelaunay() Form a Delaunay triangulation by the divide-and- *//* conquer method. *//* *//* Sorts the vertices, calls a recursive procedure to triangulate them, and *//* removes the bounding box, setting boundary markers as appropriate. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSlong divconqdelaunay(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */long divconqdelaunay(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ vertex *sortarray; struct otri hullleft, hullright; int divider; int i, j; if (b->verbose) { printf(" Sorting vertices.\n"); } /* Allocate an array of pointers to vertices for sorting. */ sortarray = (vertex *) trimalloc(m->invertices * (int) sizeof(vertex)); traversalinit(&m->vertices); for (i = 0; i < m->invertices; i++) { sortarray[i] = vertextraverse(m); } /* Sort the vertices. */ vertexsort(sortarray, m->invertices); /* Discard duplicate vertices, which can really mess up the algorithm. */ i = 0; for (j = 1; j < m->invertices; j++) { if ((sortarray[i][0] == sortarray[j][0]) && (sortarray[i][1] == sortarray[j][1])) { if (!b->quiet) { printf("Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", sortarray[j][0], sortarray[j][1]); } setvertextype(sortarray[j], UNDEADVERTEX); m->undeads++; } else { i++; sortarray[i] = sortarray[j]; } } i++; if (b->dwyer) { /* Re-sort the array of vertices to accommodate alternating cuts. */ divider = i >> 1; if (i - divider >= 2) { if (divider >= 2) { alternateaxes(sortarray, divider, 1); } alternateaxes(&sortarray[divider], i - divider, 1); } } if (b->verbose) { printf(" Forming triangulation.\n"); } /* Form the Delaunay triangulation. */ divconqrecurse(m, b, sortarray, i, 0, &hullleft, &hullright); trifree((VOID *) sortarray); return removeghosts(m, b, &hullleft);}/** **//** **//********* Divide-and-conquer Delaunay triangulation ends here *********//********* Incremental Delaunay triangulation begins here *********//** **//** **//*****************************************************************************//* *//* boundingbox() Form an "infinite" bounding triangle to insert vertices *//* into. *//* *//* The vertices at "infinity" are assigned finite coordinates, which are *//* used by the point location routines, but (mostly) ignored by the *//* Delaunay edge flip routines. *//* *//*****************************************************************************/#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid boundingbox(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void boundingbox(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri inftri; /* Handle for the triangular bounding box. */ REAL width; if (b->verbose) { printf(" Creating triangular bounding box.\n"); } /* Find the width (or height, whichever is larger) of the triangulation. */ width = m->xmax - m->xmin; if (m->ymax - m->ymin > width) { width = m->ymax - m->ymin; } if (width == 0.0) { width = 1.0; } /* Create the vertices of the bounding box. */ m->infvertex1 = (vertex) trimalloc(m->vertices.itembytes); m->infvertex2 = (vertex) trimalloc(m->vertices.itembytes); m->infvertex3 = (vertex) trimalloc(m->vertices.itembytes); m->infvertex1[0] = m->xmin - 50.0 * width; m->infvertex1[1] = m->ymin - 40.0 * width; m->infvertex2[0] = m->xmax + 50.0 * width; m->infvertex2[1] = m->ymin - 40.0 * width; m->infvertex3[0] = 0.5 * (m->xmin + m->xmax); m->infvertex3[1] = m->ymax + 60.0 * width; /* Create the bounding box. */ maketriangle(m, b, &inftri); setorg(inftri, m->infvertex1); setdest(inftri, m->infvertex2); setapex(inftri, m->infvertex3); /* Link dummytri to the bounding box so we can always find an */ /* edge to begin searching (point location) from. */ m->dummytri[0] = (triangle) inftri.tri; if (b->verbose > 2) { printf(" Creating "); printtriangle(m, b, &inftri); }}#endif /* not REDUCED *//*****************************************************************************//* *//* removebox() Remove the "infinite" bounding triangle, setting boundary *//* markers as appropriate. *//* *//* The triangular bounding box has three boundary triangles (one for each *//* side of the bounding box), and a bunch of triangles fanning out from *//* the three bounding box vertices (one triangle for each edge of the *//* convex hull of the inner mesh). This routine removes these triangles. *//* *//* Returns the number of edges on the convex hull of the triangulation. *//* *//*****************************************************************************/#ifndef REDUCED#ifdef ANSI_DECLARATORSlong removebox(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */long removebox(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri deadtriangle; struct otri searchedge; struct otri checkedge; struct otri nextedge, finaledge, dissolveedge; vertex markorg; long hullsize; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose) { printf(" Removing triangular bounding box.\n"); } /* Find a boundary triangle. */ nextedge.tri = m->dummytri; nextedge.orient = 0; symself(nextedge); /* Mark a place to stop. */ lprev(nextedge, finaledge); lnextself(nextedge); symself(nextedge); /* Find a triangle (on the boundary of the vertex set) that isn't */ /* a bounding box triangle. */ lprev(nextedge, searchedge); symself(searchedge); /* Check whether nextedge is another boundary triangle */ /* adjacent to the first one. */ lnext(nextedge, checkedge); symself(checkedge); if (checkedge.tri == m->dummytri) { /* Go on to the next triangle. There are only three boundary */ /* triangles, and this next triangle cannot be the third one, */ /* so it's safe to stop here. */ lprevself(searchedge); symself(searchedge); } /* Find a new boundary edge to search from, as the current search */ /* edge lies on a bounding box triangle and will be deleted. */ m->dummytri[0] = encode(searchedge); hullsize = -2l; while (!otriequal(nextedge, finaledge)) { hullsize++; lprev(nextedge, dissolveedge); symself(dissolveedge); /* If not using a PSLG, the vertices should be marked now. */ /* (If using a PSLG, markhull() will do the job.) */ if (!b->poly) { /* Be careful! One must check for the case where all the input */ /* vertices are collinear, and thus all the triangles are part of */ /* the bounding box. Otherwise, the setvertexmark() call below */ /* will cause a bad pointer reference. */ if (dissolveedge.tri != m->dummytri) { org(dissolveedge, markorg); if (vertexmark(markorg) == 0) { setvertexmark(markorg, 1); } } } /* Disconnect the bounding box triangle from the mesh triangle. */ dissolve(dissolveedge); lnext(nextedge, deadtriangle); sym(deadtriangle, nextedge); /* Get rid of the bounding box triangle. */ triangledealloc(m, deadtriangle.tri); /* Do we need to turn the corner? */ if (nextedge.tri == m->dummytri) { /* Turn the corner. */ otricopy(dissolveedge, nextedge); } } triangledealloc(m, finaledge.tri); trifree((VOID *) m->infvertex1); /* Deallocate the bounding box vertices. */ trifree((VOID *) m->infvertex2); trifree((VOID *) m->infvertex3); return hullsize;}#endif /* not REDUCED *//*****************************************************************************//* *//* incrementaldelaunay() Form a Delaunay triangulation by incrementally *//* inserting vertices. *//* *//* Returns the number of edges on the convex hull of the triangulation. *//* *//*****************************************************************************/#ifndef REDUCED#ifdef ANSI_DECLARATORSlong incrementaldelaunay(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */long incrementaldelaunay(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri starttri; vertex vertexloop; /* Create a triangular bounding box. */ boundingbox(m, b); if (b->verbose) { printf(" Incrementally inserting vertices.\n"); } traversalinit(&m->vertices); vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { starttri.tri = m->dummytri; if (insertvertex(m, b, vertexloop, &starttri, (struct osub *) NULL, 0, 0) == DUPLICATEVERTEX) { if (!b->quiet) { printf("Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", vertexloop[0], vertexloop[1]); } setvertextype(vertexloop, UNDEADVERTEX); m->undeads++; } vertexloop = vertextraverse(m); } /* Remove the bounding box. */ return removebox(m, b);}#endif /* not REDUCED *//** **//** **//********* Incremental Delaunay triangulation ends here *********//********* Sweepline Delaunay triangulation begins here *********//** **//** **/#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid eventheapinsert(struct event **heap, int heapsize, struct event *newevent)#else /* not ANSI_DECLARATORS */void eventheapinsert(heap, heapsize, newevent)struct event **heap;int heapsize;struct event *newevent;#endif /* not ANSI_DECLARATORS */{ REAL eventx, eventy; int eventnum; int parent; int notdone; eventx = newevent->xkey; eventy = newevent->ykey; eventnum = heapsize; notdone = eventnum > 0; while (notdone) { parent = (eventnum - 1) >> 1; if ((heap[parent]->ykey < eventy) || ((heap[parent]->ykey == eventy) && (heap[parent]->xkey <= eventx))) { notdone = 0; } else { heap[eventnum] = heap[parent]; heap[eventnum]->heapposition = eventnum; eventnum = parent; notdone = eventnum > 0; } } heap[eventnum] = newevent; newevent->heapposition = eventnum;}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid eventheapify(struct event **heap, int heapsize, int eventnum)#else /* not ANSI_DECLARATORS */void eventheapify(heap, heapsize, eventnum)struct event **heap;int heapsize;int eventnum;#endif /* not ANSI_DECLARATORS */{ struct event *thisevent; REAL eventx, eventy; int leftchild, rightchild; int smallest; int notdone; thisevent = heap[eventnum]; eventx = thisevent->xkey; eventy = thisevent->ykey; leftchild = 2 * eventnum + 1; notdone = leftchild < heapsize; while (notdone) { if ((heap[leftchild]->ykey < eventy) || ((heap[leftchild]->ykey == eventy) && (heap[leftchild]->xkey < eventx))) { smallest = leftchild; } else { smallest = eventnum; } rightchild = leftchild + 1; if (rightchild < heapsize) { if ((heap[rightchild]->ykey < heap[smallest]->ykey) || ((heap[rightchild]->ykey == heap[smallest]->ykey) && (heap[rightchild]->xkey < heap[smallest]->xkey))) { smallest = rightchild; } } if (smallest == eventnum) { notdone = 0; } else { heap[eventnum] = heap[smallest]; heap[eventnum]->heapposition = eventnum; heap[smallest] = thisevent; thisevent->heapposition = smallest; eventnum = smallest; leftchild = 2 * eventnum + 1; notdone = leftchild < heapsize; } }}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid eventheapdelete(struct event **heap, int heapsize, int eventnum)#else /* not ANSI_DECLARATORS */void eventheapdelete(heap, heapsize, eventnum)struct event **heap;int heapsize;int eventnum;#endif /* not ANSI_DECLARATORS */{ struct event *moveevent; REAL eventx, eventy; int parent; int notdone; moveevent = heap[heapsize - 1]; if (eventnum > 0) { eventx = moveevent->xkey; eventy = moveevent->ykey; do { parent = (eventnum - 1) >> 1; if ((heap[parent]->ykey < eventy) || ((heap[parent]->ykey == eventy) && (heap[parent]->xkey <= eventx))) { notdone = 0; } else { heap[eventnum] = heap[parent]; heap[eventnum]->heapposition = eventnum; eventnum = parent; notdone = eventnum > 0; } } while (notdone); } heap[eventnum] = moveevent; moveevent->heapposition = eventnum; eventheapify(heap, heapsize - 1, eventnum);}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid createeventheap(struct mesh *m, struct event ***eventheap, struct event **events, struct event **freeevents)#else /* not ANSI_DECLARATORS */void createeventheap(m, eventheap, events, freeevents)struct mesh *m;struct event ***eventheap;struct event **events;struct event **freeevents;#endif /* not ANSI_DECLARATORS */{ vertex thisvertex; int maxevents; int i; maxevents = (3 * m->invertices) / 2; *eventheap = (struct event **) trimalloc(maxevents * (int) sizeof(struct event *)); *events = (struct event *) trimalloc(maxevents * (int) sizeof(struct event)); traversalinit(&m->vertices); for (i = 0; i < m->invertices; i++) { thisvertex = vertextraverse(m); (*events)[i].eventptr = (VOID *) thisvertex; (*events)[i].xkey = thisvertex[0]; (*events)[i].ykey = thisvertex[1]; eventheapinsert(*eventheap, i, *events + i); } *freeevents = (struct event *) NULL; for (i = maxevents - 1; i >= m->invertices; i--) { (*events)[i].eventptr = (VOID *) *freeevents; *freeevents = *events + i; }}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSint rightofhyperbola(struct mesh *m, struct otri *fronttri, vertex newsite)#else /* not ANSI_DECLARATORS */int rightofhyperbola(m, fronttri, newsite)struct mesh *m;struct otri *fronttri;vertex newsite;#endif /* not ANSI_DECLARATORS */{ vertex leftvertex, rightvertex; REAL dxa, dya, dxb, dyb; m->hyperbolacount++; dest(*fronttri, leftvertex); apex(*fronttri, rightvertex); if ((leftvertex[1] < rightvertex[1]) || ((leftvertex[1] == rightvertex[1]) && (leftvertex[0] < rightvertex[0]))) { if (newsite[0] >= rightvertex[0]) { return 1; } } else { if (newsite[0] <= leftvertex[0]) { return 0; } } dxa = leftvertex[0] - newsite[0]; dya = leftvertex[1] - newsite[1]; dxb = rightvertex[0] - newsite[0]; dyb = rightvertex[1] - newsite[1]; return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSREAL circletop(struct mesh *m, vertex pa, vertex pb, vertex pc, REAL ccwabc)#else /* not ANSI_DECLARATORS */REAL circletop(m, pa, pb, pc, ccwabc)struct mesh *m;vertex pa;vertex pb;vertex pc;REAL ccwabc;#endif /* not ANSI_DECLARATORS */{ REAL xac, yac, xbc, ybc, xab, yab; REAL aclen2, bclen2, ablen2; m->circletopcount++; xac = pa[0] - pc[0]; yac = pa[1] - pc[1]; xbc = pb[0] - pc[0]; ybc = pb[1] - pc[1]; xab = pa[0] - pb[0]; yab = pa[1] - pb[1]; aclen2 = xac * xac + yac * yac; bclen2 = xbc * xbc + ybc * ybc; ablen2 = xab * xab + yab * yab; return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2)) / (2.0 * ccwabc);}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSvoid check4deadevent(struct otri *checktri, struct event **freeevents, struct event **eventheap, int *heapsize)#else /* not ANSI_DECLARATORS */void check4deadevent(checktri, freeevents, eventheap, heapsize)struct otri *checktri;struct event **freeevents;struct event **eventheap;int *heapsize;#endif /* not ANSI_DECLARATORS */{ struct event *deadevent; vertex eventvertex; int eventnum; org(*checktri, eventvertex); if (eventvertex != (vertex) NULL) { deadevent = (struct event *) eventvertex; eventnum = deadevent->heapposition; deadevent->eventptr = (VOID *) *freeevents; *freeevents = deadevent; eventheapdelete(eventheap, *heapsize, eventnum); (*heapsize)--; setorg(*checktri, NULL); }}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSstruct splaynode *splay(struct mesh *m, struct splaynode *splaytree, vertex searchpoint, struct otri *searchtri)#else /* not ANSI_DECLARATORS */struct splaynode *splay(m, splaytree, searchpoint, searchtri)struct mesh *m;struct splaynode *splaytree;vertex searchpoint;struct otri *searchtri;#endif /* not ANSI_DECLARATORS */{ struct splaynode *child, *grandchild; struct splaynode *lefttree, *righttree; struct splaynode *leftright; vertex checkvertex; int rightofroot, rightofchild; if (splaytree == (struct splaynode *) NULL) { return (struct splaynode *) NULL; } dest(splaytree->keyedge, checkvertex); if (checkvertex == splaytree->keydest) { rightofroot = rightofhyperbola(m, &splaytree->keyedge, searchpoint); if (rightofroot) { otricopy(splaytree->keyedge, *searchtri); child = splaytree->rchild; } else { child = splaytree->lchild; } if (child == (struct splaynode *) NULL) { return splaytree; } dest(child->keyedge, checkvertex); if (checkvertex != child->keydest) { child = splay(m, child, searchpoint, searchtri); if (child == (struct splaynode *) NULL) { if (rightofroot) { splaytree->rchild = (struct splaynode *) NULL; } else { splaytree->lchild = (struct splaynode *) NULL; } return splaytree; } } rightofchild = rightofhyperbola(m, &child->keyedge, searchpoint); if (rightofchild) { otricopy(child->keyedge, *searchtri); grandchild = splay(m, child->rchild, searchpoint, searchtri); child->rchild = grandchild; } else { grandchild = splay(m, child->lchild, searchpoint, searchtri); child->lchild = grandchild; } if (grandchild == (struct splaynode *) NULL) { if (rightofroot) { splaytree->rchild = child->lchild; child->lchild = splaytree; } else { splaytree->lchild = child->rchild; child->rchild = splaytree; } return child; } if (rightofchild) { if (rightofroot) { splaytree->rchild = child->lchild; child->lchild = splaytree; } else { splaytree->lchild = grandchild->rchild; grandchild->rchild = splaytree; } child->rchild = grandchild->lchild; grandchild->lchild = child; } else { if (rightofroot) { splaytree->rchild = grandchild->lchild; grandchild->lchild = splaytree; } else { splaytree->lchild = child->rchild; child->rchild = splaytree; } child->lchild = grandchild->rchild; grandchild->rchild = child; } return grandchild; } else { lefttree = splay(m, splaytree->lchild, searchpoint, searchtri); righttree = splay(m, splaytree->rchild, searchpoint, searchtri); pooldealloc(&m->splaynodes, (VOID *) splaytree); if (lefttree == (struct splaynode *) NULL) { return righttree; } else if (righttree == (struct splaynode *) NULL) { return lefttree; } else if (lefttree->rchild == (struct splaynode *) NULL) { lefttree->rchild = righttree->lchild; righttree->lchild = lefttree; return righttree; } else if (righttree->lchild == (struct splaynode *) NULL) { righttree->lchild = lefttree->rchild; lefttree->rchild = righttree; return lefttree; } else {/* printf("Holy Toledo!!!\n"); */ leftright = lefttree->rchild; while (leftright->rchild != (struct splaynode *) NULL) { leftright = leftright->rchild; } leftright->rchild = righttree; return lefttree; } }}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSstruct splaynode *splayinsert(struct mesh *m, struct splaynode *splayroot, struct otri *newkey, vertex searchpoint)#else /* not ANSI_DECLARATORS */struct splaynode *splayinsert(m, splayroot, newkey, searchpoint)struct mesh *m;struct splaynode *splayroot;struct otri *newkey;vertex searchpoint;#endif /* not ANSI_DECLARATORS */{ struct splaynode *newsplaynode; newsplaynode = (struct splaynode *) poolalloc(&m->splaynodes); otricopy(*newkey, newsplaynode->keyedge); dest(*newkey, newsplaynode->keydest); if (splayroot == (struct splaynode *) NULL) { newsplaynode->lchild = (struct splaynode *) NULL; newsplaynode->rchild = (struct splaynode *) NULL; } else if (rightofhyperbola(m, &splayroot->keyedge, searchpoint)) { newsplaynode->lchild = splayroot; newsplaynode->rchild = splayroot->rchild; splayroot->rchild = (struct splaynode *) NULL; } else { newsplaynode->lchild = splayroot->lchild; newsplaynode->rchild = splayroot; splayroot->lchild = (struct splaynode *) NULL; } return newsplaynode;}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSstruct splaynode *circletopinsert(struct mesh *m, struct behavior *b, struct splaynode *splayroot, struct otri *newkey, vertex pa, vertex pb, vertex pc, REAL topy)#else /* not ANSI_DECLARATORS */struct splaynode *circletopinsert(m, b, splayroot, newkey, pa, pb, pc, topy)struct mesh *m;struct behavior *b;struct splaynode *splayroot;struct otri *newkey;vertex pa;vertex pb;vertex pc;REAL topy;#endif /* not ANSI_DECLARATORS */{ REAL ccwabc; REAL xac, yac, xbc, ybc; REAL aclen2, bclen2; REAL searchpoint[2]; struct otri dummytri; ccwabc = counterclockwise(m, b, pa, pb, pc); xac = pa[0] - pc[0]; yac = pa[1] - pc[1]; xbc = pb[0] - pc[0]; ybc = pb[1] - pc[1]; aclen2 = xac * xac + yac * yac; bclen2 = xbc * xbc + ybc * ybc; searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc); searchpoint[1] = topy; return splayinsert(m, splay(m, splayroot, (vertex) searchpoint, &dummytri), newkey, (vertex) searchpoint);}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSstruct splaynode *frontlocate(struct mesh *m, struct splaynode *splayroot, struct otri *bottommost, vertex searchvertex, struct otri *searchtri, int *farright)#else /* not ANSI_DECLARATORS */struct splaynode *frontlocate(m, splayroot, bottommost, searchvertex, searchtri, farright)struct mesh *m;struct splaynode *splayroot;struct otri *bottommost;vertex searchvertex;struct otri *searchtri;int *farright;#endif /* not ANSI_DECLARATORS */{ int farrightflag; triangle ptr; /* Temporary variable used by onext(). */ otricopy(*bottommost, *searchtri); splayroot = splay(m, splayroot, searchvertex, searchtri); farrightflag = 0; while (!farrightflag && rightofhyperbola(m, searchtri, searchvertex)) { onextself(*searchtri); farrightflag = otriequal(*searchtri, *bottommost); } *farright = farrightflag; return splayroot;}#endif /* not REDUCED */#ifndef REDUCED#ifdef ANSI_DECLARATORSlong sweeplinedelaunay(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */long sweeplinedelaunay(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct event **eventheap; struct event *events; struct event *freeevents; struct event *nextevent; struct event *newevent; struct splaynode *splayroot; struct otri bottommost; struct otri searchtri; struct otri fliptri; struct otri lefttri, righttri, farlefttri, farrighttri; struct otri inserttri; vertex firstvertex, secondvertex; vertex nextvertex, lastvertex; vertex connectvertex; vertex leftvertex, midvertex, rightvertex; REAL lefttest, righttest; int heapsize; int check4events, farrightflag; triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */ poolinit(&m->splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, SPLAYNODEPERBLOCK, 0); splayroot = (struct splaynode *) NULL; if (b->verbose) { printf(" Placing vertices in event heap.\n"); } createeventheap(m, &eventheap, &events, &freeevents); heapsize = m->invertices; if (b->verbose) { printf(" Forming triangulation.\n"); } maketriangle(m, b, &lefttri); maketriangle(m, b, &righttri); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, righttri); firstvertex = (vertex) eventheap[0]->eventptr; eventheap[0]->eventptr = (VOID *) freeevents; freeevents = eventheap[0]; eventheapdelete(eventheap, heapsize, 0); heapsize--; do { if (heapsize == 0) { printf("Error: Input vertices are all identical.\n"); triexit(1); } secondvertex = (vertex) eventheap[0]->eventptr; eventheap[0]->eventptr = (VOID *) freeevents; freeevents = eventheap[0]; eventheapdelete(eventheap, heapsize, 0); heapsize--; if ((firstvertex[0] == secondvertex[0]) && (firstvertex[1] == secondvertex[1])) { if (!b->quiet) { printf("Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", secondvertex[0], secondvertex[1]); } setvertextype(secondvertex, UNDEADVERTEX); m->undeads++; } } while ((firstvertex[0] == secondvertex[0]) && (firstvertex[1] == secondvertex[1])); setorg(lefttri, firstvertex); setdest(lefttri, secondvertex); setorg(righttri, secondvertex); setdest(righttri, firstvertex); lprev(lefttri, bottommost); lastvertex = secondvertex; while (heapsize > 0) { nextevent = eventheap[0]; eventheapdelete(eventheap, heapsize, 0); heapsize--; check4events = 1; if (nextevent->xkey < m->xmin) { decode(nextevent->eventptr, fliptri); oprev(fliptri, farlefttri); check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize); onext(fliptri, farrighttri); check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize); if (otriequal(farlefttri, bottommost)) { lprev(fliptri, bottommost); } flip(m, b, &fliptri); setapex(fliptri, NULL); lprev(fliptri, lefttri); lnext(fliptri, righttri); sym(lefttri, farlefttri); if (randomnation(SAMPLERATE) == 0) { symself(fliptri); dest(fliptri, leftvertex); apex(fliptri, midvertex); org(fliptri, rightvertex); splayroot = circletopinsert(m, b, splayroot, &lefttri, leftvertex, midvertex, rightvertex, nextevent->ykey); } } else { nextvertex = (vertex) nextevent->eventptr; if ((nextvertex[0] == lastvertex[0]) && (nextvertex[1] == lastvertex[1])) { if (!b->quiet) { printf("Warning: A duplicate vertex at (%.12g, %.12g) appeared and was ignored.\n", nextvertex[0], nextvertex[1]); } setvertextype(nextvertex, UNDEADVERTEX); m->undeads++; check4events = 0; } else { lastvertex = nextvertex; splayroot = frontlocate(m, splayroot, &bottommost, nextvertex, &searchtri, &farrightflag);/* otricopy(bottommost, searchtri); farrightflag = 0; while (!farrightflag && rightofhyperbola(m, &searchtri, nextvertex)) { onextself(searchtri); farrightflag = otriequal(searchtri, bottommost); }*/ check4deadevent(&searchtri, &freeevents, eventheap, &heapsize); otricopy(searchtri, farrighttri); sym(searchtri, farlefttri); maketriangle(m, b, &lefttri); maketriangle(m, b, &righttri); dest(farrighttri, connectvertex); setorg(lefttri, connectvertex); setdest(lefttri, nextvertex); setorg(righttri, nextvertex); setdest(righttri, connectvertex); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, righttri); lnextself(lefttri); lprevself(righttri); bond(lefttri, farlefttri); bond(righttri, farrighttri); if (!farrightflag && otriequal(farrighttri, bottommost)) { otricopy(lefttri, bottommost); } if (randomnation(SAMPLERATE) == 0) { splayroot = splayinsert(m, splayroot, &lefttri, nextvertex); } else if (randomnation(SAMPLERATE) == 0) { lnext(righttri, inserttri); splayroot = splayinsert(m, splayroot, &inserttri, nextvertex); } } } nextevent->eventptr = (VOID *) freeevents; freeevents = nextevent; if (check4events) { apex(farlefttri, leftvertex); dest(lefttri, midvertex); apex(lefttri, rightvertex); lefttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); if (lefttest > 0.0) { newevent = freeevents; freeevents = (struct event *) freeevents->eventptr; newevent->xkey = m->xminextreme; newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, lefttest); newevent->eventptr = (VOID *) encode(lefttri); eventheapinsert(eventheap, heapsize, newevent); heapsize++; setorg(lefttri, newevent); } apex(righttri, leftvertex); org(righttri, midvertex); apex(farrighttri, rightvertex); righttest = counterclockwise(m, b, leftvertex, midvertex, rightvertex); if (righttest > 0.0) { newevent = freeevents; freeevents = (struct event *) freeevents->eventptr; newevent->xkey = m->xminextreme; newevent->ykey = circletop(m, leftvertex, midvertex, rightvertex, righttest); newevent->eventptr = (VOID *) encode(farrighttri); eventheapinsert(eventheap, heapsize, newevent); heapsize++; setorg(farrighttri, newevent); } } } pooldeinit(&m->splaynodes); lprevself(bottommost); return removeghosts(m, b, &bottommost);}#endif /* not REDUCED *//** **//** **//********* Sweepline Delaunay triangulation ends here *********//********* General mesh construction routines begin here *********//** **//** **//*****************************************************************************//* *//* delaunay() Form a Delaunay triangulation. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSlong delaunay(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */long delaunay(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ long hulledges; m->eextras = 0; initializetrisubpools(m, b);#ifdef REDUCED if (!b->quiet) { printf( "Constructing Delaunay triangulation by divide-and-conquer method.\n"); } hulledges = divconqdelaunay(m, b);#else /* not REDUCED */ if (!b->quiet) { printf("Constructing Delaunay triangulation "); if (b->incremental) { printf("by incremental method.\n"); } else if (b->sweepline) { printf("by sweepline method.\n"); } else { printf("by divide-and-conquer method.\n"); } } if (b->incremental) { hulledges = incrementaldelaunay(m, b); } else if (b->sweepline) { hulledges = sweeplinedelaunay(m, b); } else { hulledges = divconqdelaunay(m, b); }#endif /* not REDUCED */ if (m->triangles.items == 0) { /* The input vertices were all collinear, so there are no triangles. */ return 0l; } else { return hulledges; }}/*****************************************************************************//* *//* reconstruct() Reconstruct a triangulation from its .ele (and possibly *//* .poly) file. Used when the -r switch is used. *//* *//* Reads an .ele file and reconstructs the original mesh. If the -p switch *//* is used, this procedure will also read a .poly file and reconstruct the *//* subsegments of the original mesh. If the -a switch is used, this *//* procedure will also read an .area file and set a maximum area constraint *//* on each triangle. *//* *//* Vertices that are not corners of triangles, such as nodes on edges of *//* subparametric elements, are discarded. *//* *//* This routine finds the adjacencies between triangles (and subsegments) *//* by forming one stack of triangles for each vertex. Each triangle is on *//* three different stacks simultaneously. Each triangle's subsegment *//* pointers are used to link the items in each stack. This memory-saving *//* feature makes the code harder to read. The most important thing to keep *//* in mind is that each triangle is removed from a stack precisely when *//* the corresponding pointer is adjusted to refer to a subsegment rather *//* than the next triangle of the stack. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSint reconstruct(struct mesh *m, struct behavior *b, int *trianglelist, REAL *triangleattriblist, REAL *trianglearealist, int elements, int corners, int attribs, int *segmentlist,int *segmentmarkerlist, int numberofsegments)#else /* not ANSI_DECLARATORS */int reconstruct(m, b, trianglelist, triangleattriblist, trianglearealist, elements, corners, attribs, segmentlist, segmentmarkerlist, numberofsegments)struct mesh *m;struct behavior *b;int *trianglelist;REAL *triangleattriblist;REAL *trianglearealist;int elements;int corners;int attribs;int *segmentlist;int *segmentmarkerlist;int numberofsegments;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSlong reconstruct(struct mesh *m, struct behavior *b, char *elefilename, char *areafilename, char *polyfilename, FILE *polyfile)#else /* not ANSI_DECLARATORS */long reconstruct(m, b, elefilename, areafilename, polyfilename, polyfile)struct mesh *m;struct behavior *b;char *elefilename;char *areafilename;char *polyfilename;FILE *polyfile;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY int vertexindex; int attribindex;#else /* not TRILIBRARY */ FILE *elefile; FILE *areafile; char inputline[INPUTLINESIZE]; char *stringptr; int areaelements;#endif /* not TRILIBRARY */ struct otri triangleloop; struct otri triangleleft; struct otri checktri; struct otri checkleft; struct otri checkneighbor; struct osub subsegloop; triangle *vertexarray; triangle *prevlink; triangle nexttri; vertex tdest, tapex; vertex checkdest, checkapex; vertex shorg; vertex killvertex; vertex segmentorg, segmentdest; REAL area; int corner[3]; int end[2]; int killvertexindex; int incorners; int segmentmarkers; int boundmarker; int aroundvertex; long hullsize; int notfound; long elementnumber, segmentnumber; int i, j; triangle ptr; /* Temporary variable used by sym(). */#ifdef TRILIBRARY m->inelements = elements; incorners = corners; if (incorners < 3) { printf("Error: Triangles must have at least 3 vertices.\n"); triexit(1); } m->eextras = attribs;#else /* not TRILIBRARY */ /* Read the triangles from an .ele file. */ if (!b->quiet) { printf("Opening %s.\n", elefilename); } elefile = fopen(elefilename, "r"); if (elefile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", elefilename); triexit(1); } /* Read number of triangles, number of vertices per triangle, and */ /* number of triangle attributes from .ele file. */ stringptr = readline(inputline, elefile, elefilename); m->inelements = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { incorners = 3; } else { incorners = (int) strtol(stringptr, &stringptr, 0); if (incorners < 3) { printf("Error: Triangles in %s must have at least 3 vertices.\n", elefilename); triexit(1); } } stringptr = findfield(stringptr); if (*stringptr == '\0') { m->eextras = 0; } else { m->eextras = (int) strtol(stringptr, &stringptr, 0); }#endif /* not TRILIBRARY */ initializetrisubpools(m, b); /* Create the triangles. */ for (elementnumber = 1; elementnumber <= m->inelements; elementnumber++) { maketriangle(m, b, &triangleloop); /* Mark the triangle as living. */ triangleloop.tri[3] = (triangle) triangleloop.tri; } segmentmarkers = 0; if (b->poly) {#ifdef TRILIBRARY m->insegments = numberofsegments; segmentmarkers = segmentmarkerlist != (int *) NULL;#else /* not TRILIBRARY */ /* Read number of segments and number of segment */ /* boundary markers from .poly file. */ stringptr = readline(inputline, polyfile, b->inpolyfilename); m->insegments = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr != '\0') { segmentmarkers = (int) strtol(stringptr, &stringptr, 0); }#endif /* not TRILIBRARY */ /* Create the subsegments. */ for (segmentnumber = 1; segmentnumber <= m->insegments; segmentnumber++) { makesubseg(m, &subsegloop); /* Mark the subsegment as living. */ subsegloop.ss[2] = (subseg) subsegloop.ss; } }#ifdef TRILIBRARY vertexindex = 0; attribindex = 0;#else /* not TRILIBRARY */ if (b->vararea) { /* Open an .area file, check for consistency with the .ele file. */ if (!b->quiet) { printf("Opening %s.\n", areafilename); } areafile = fopen(areafilename, "r"); if (areafile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", areafilename); triexit(1); } stringptr = readline(inputline, areafile, areafilename); areaelements = (int) strtol(stringptr, &stringptr, 0); if (areaelements != m->inelements) { printf("Error: %s and %s disagree on number of triangles.\n", elefilename, areafilename); triexit(1); } }#endif /* not TRILIBRARY */ if (!b->quiet) { printf("Reconstructing mesh.\n"); } /* Allocate a temporary array that maps each vertex to some adjacent */ /* triangle. I took care to allocate all the permanent memory for */ /* triangles and subsegments first. */ vertexarray = (triangle *) trimalloc(m->vertices.items * (int) sizeof(triangle)); /* Each vertex is initially unrepresented. */ for (i = 0; i < m->vertices.items; i++) { vertexarray[i] = (triangle) m->dummytri; } if (b->verbose) { printf(" Assembling triangles.\n"); } /* Read the triangles from the .ele file, and link */ /* together those that share an edge. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) {#ifdef TRILIBRARY /* Copy the triangle's three corners. */ for (j = 0; j < 3; j++) { corner[j] = trianglelist[vertexindex++]; if ((corner[j] < b->firstnumber) || (corner[j] >= b->firstnumber + m->invertices)) { printf("Error: Triangle %ld has an invalid vertex index.\n", elementnumber); triexit(1); } }#else /* not TRILIBRARY */ /* Read triangle number and the triangle's three corners. */ stringptr = readline(inputline, elefile, elefilename); for (j = 0; j < 3; j++) { stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Triangle %ld is missing vertex %d in %s.\n", elementnumber, j + 1, elefilename); triexit(1); } else { corner[j] = (int) strtol(stringptr, &stringptr, 0); if ((corner[j] < b->firstnumber) || (corner[j] >= b->firstnumber + m->invertices)) { printf("Error: Triangle %ld has an invalid vertex index.\n", elementnumber); triexit(1); } } }#endif /* not TRILIBRARY */ /* Find out about (and throw away) extra nodes. */ for (j = 3; j < incorners; j++) {#ifdef TRILIBRARY killvertexindex = trianglelist[vertexindex++];#else /* not TRILIBRARY */ stringptr = findfield(stringptr); if (*stringptr != '\0') { killvertexindex = (int) strtol(stringptr, &stringptr, 0);#endif /* not TRILIBRARY */ if ((killvertexindex >= b->firstnumber) && (killvertexindex < b->firstnumber + m->invertices)) { /* Delete the non-corner vertex if it's not already deleted. */ killvertex = getvertex(m, b, killvertexindex); if (vertextype(killvertex) != DEADVERTEX) { vertexdealloc(m, killvertex); } }#ifndef TRILIBRARY }#endif /* not TRILIBRARY */ } /* Read the triangle's attributes. */ for (j = 0; j < m->eextras; j++) {#ifdef TRILIBRARY setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);#else /* not TRILIBRARY */ stringptr = findfield(stringptr); if (*stringptr == '\0') { setelemattribute(triangleloop, j, 0); } else { setelemattribute(triangleloop, j, (REAL) strtod(stringptr, &stringptr)); }#endif /* not TRILIBRARY */ } if (b->vararea) {#ifdef TRILIBRARY area = trianglearealist[elementnumber - b->firstnumber];#else /* not TRILIBRARY */ /* Read an area constraint from the .area file. */ stringptr = readline(inputline, areafile, areafilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { area = -1.0; /* No constraint on this triangle. */ } else { area = (REAL) strtod(stringptr, &stringptr); }#endif /* not TRILIBRARY */ setareabound(triangleloop, area); } /* Set the triangle's vertices. */ triangleloop.orient = 0; setorg(triangleloop, getvertex(m, b, corner[0])); setdest(triangleloop, getvertex(m, b, corner[1])); setapex(triangleloop, getvertex(m, b, corner[2])); /* Try linking the triangle to others that share these vertices. */ for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { /* Take the number for the origin of triangleloop. */ aroundvertex = corner[triangleloop.orient]; /* Look for other triangles having this vertex. */ nexttri = vertexarray[aroundvertex - b->firstnumber]; /* Link the current triangle to the next one in the stack. */ triangleloop.tri[6 + triangleloop.orient] = nexttri; /* Push the current triangle onto the stack. */ vertexarray[aroundvertex - b->firstnumber] = encode(triangleloop); decode(nexttri, checktri); if (checktri.tri != m->dummytri) { dest(triangleloop, tdest); apex(triangleloop, tapex); /* Look for other triangles that share an edge. */ do { dest(checktri, checkdest); apex(checktri, checkapex); if (tapex == checkdest) { /* The two triangles share an edge; bond them together. */ lprev(triangleloop, triangleleft); bond(triangleleft, checktri); } if (tdest == checkapex) { /* The two triangles share an edge; bond them together. */ lprev(checktri, checkleft); bond(triangleloop, checkleft); } /* Find the next triangle in the stack. */ nexttri = checktri.tri[6 + checktri.orient]; decode(nexttri, checktri); } while (checktri.tri != m->dummytri); } } triangleloop.tri = triangletraverse(m); elementnumber++; }#ifdef TRILIBRARY vertexindex = 0;#else /* not TRILIBRARY */ fclose(elefile); if (b->vararea) { fclose(areafile); }#endif /* not TRILIBRARY */ hullsize = 0; /* Prepare to count the boundary edges. */ if (b->poly) { if (b->verbose) { printf(" Marking segments in triangulation.\n"); } /* Read the segments from the .poly file, and link them */ /* to their neighboring triangles. */ boundmarker = 0; traversalinit(&m->subsegs); subsegloop.ss = subsegtraverse(m); segmentnumber = b->firstnumber; while (subsegloop.ss != (subseg *) NULL) {#ifdef TRILIBRARY end[0] = segmentlist[vertexindex++]; end[1] = segmentlist[vertexindex++]; if (segmentmarkers) { boundmarker = segmentmarkerlist[segmentnumber - b->firstnumber]; }#else /* not TRILIBRARY */ /* Read the endpoints of each segment, and possibly a boundary marker. */ stringptr = readline(inputline, polyfile, b->inpolyfilename); /* Skip the first (segment number) field. */ stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %ld has no endpoints in %s.\n", segmentnumber, polyfilename); triexit(1); } else { end[0] = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %ld is missing its second endpoint in %s.\n", segmentnumber, polyfilename); triexit(1); } else { end[1] = (int) strtol(stringptr, &stringptr, 0); } if (segmentmarkers) { stringptr = findfield(stringptr); if (*stringptr == '\0') { boundmarker = 0; } else { boundmarker = (int) strtol(stringptr, &stringptr, 0); } }#endif /* not TRILIBRARY */ for (j = 0; j < 2; j++) { if ((end[j] < b->firstnumber) || (end[j] >= b->firstnumber + m->invertices)) { printf("Error: Segment %ld has an invalid vertex index.\n", segmentnumber); triexit(1); } } /* set the subsegment's vertices. */ subsegloop.ssorient = 0; segmentorg = getvertex(m, b, end[0]); segmentdest = getvertex(m, b, end[1]); setsorg(subsegloop, segmentorg); setsdest(subsegloop, segmentdest); setsegorg(subsegloop, segmentorg); setsegdest(subsegloop, segmentdest); setmark(subsegloop, boundmarker); /* Try linking the subsegment to triangles that share these vertices. */ for (subsegloop.ssorient = 0; subsegloop.ssorient < 2; subsegloop.ssorient++) { /* Take the number for the destination of subsegloop. */ aroundvertex = end[1 - subsegloop.ssorient]; /* Look for triangles having this vertex. */ prevlink = &vertexarray[aroundvertex - b->firstnumber]; nexttri = vertexarray[aroundvertex - b->firstnumber]; decode(nexttri, checktri); sorg(subsegloop, shorg); notfound = 1; /* Look for triangles having this edge. Note that I'm only */ /* comparing each triangle's destination with the subsegment; */ /* each triangle's apex is handled through a different vertex. */ /* Because each triangle appears on three vertices' lists, each */ /* occurrence of a triangle on a list can (and does) represent */ /* an edge. In this way, most edges are represented twice, and */ /* every triangle-subsegment bond is represented once. */ while (notfound && (checktri.tri != m->dummytri)) { dest(checktri, checkdest); if (shorg == checkdest) { /* We have a match. Remove this triangle from the list. */ *prevlink = checktri.tri[6 + checktri.orient]; /* Bond the subsegment to the triangle. */ tsbond(checktri, subsegloop); /* Check if this is a boundary edge. */ sym(checktri, checkneighbor); if (checkneighbor.tri == m->dummytri) { /* The next line doesn't insert a subsegment (because there's */ /* already one there), but it sets the boundary markers of */ /* the existing subsegment and its vertices. */ insertsubseg(m, b, &checktri, 1); hullsize++; } notfound = 0; } /* Find the next triangle in the stack. */ prevlink = &checktri.tri[6 + checktri.orient]; nexttri = checktri.tri[6 + checktri.orient]; decode(nexttri, checktri); } } subsegloop.ss = subsegtraverse(m); segmentnumber++; } } /* Mark the remaining edges as not being attached to any subsegment. */ /* Also, count the (yet uncounted) boundary edges. */ for (i = 0; i < m->vertices.items; i++) { /* Search the stack of triangles adjacent to a vertex. */ nexttri = vertexarray[i]; decode(nexttri, checktri); while (checktri.tri != m->dummytri) { /* Find the next triangle in the stack before this */ /* information gets overwritten. */ nexttri = checktri.tri[6 + checktri.orient]; /* No adjacent subsegment. (This overwrites the stack info.) */ tsdissolve(checktri); sym(checktri, checkneighbor); if (checkneighbor.tri == m->dummytri) { insertsubseg(m, b, &checktri, 1); hullsize++; } decode(nexttri, checktri); } } trifree((VOID *) vertexarray); return hullsize;}#endif /* not CDT_ONLY *//** **//** **//********* General mesh construction routines end here *********//********* Segment insertion begins here *********//** **//** **//*****************************************************************************//* *//* finddirection() Find the first triangle on the path from one point *//* to another. *//* *//* Finds the triangle that intersects a line segment drawn from the *//* origin of `searchtri' to the point `searchpoint', and returns the result *//* in `searchtri'. The origin of `searchtri' does not change, even though *//* the triangle returned may differ from the one passed in. This routine *//* is used to find the direction to move in to get from one point to *//* another. *//* *//* The return value notes whether the destination or apex of the found *//* triangle is collinear with the two points in question. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSenum finddirectionresult finddirection(struct mesh *m, struct behavior *b, struct otri *searchtri, vertex searchpoint)#else /* not ANSI_DECLARATORS */enum finddirectionresult finddirection(m, b, searchtri, searchpoint)struct mesh *m;struct behavior *b;struct otri *searchtri;vertex searchpoint;#endif /* not ANSI_DECLARATORS */{ struct otri checktri; vertex startvertex; vertex leftvertex, rightvertex; REAL leftccw, rightccw; int leftflag, rightflag; triangle ptr; /* Temporary variable used by onext() and oprev(). */ org(*searchtri, startvertex); dest(*searchtri, rightvertex); apex(*searchtri, leftvertex); /* Is `searchpoint' to the left? */ leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); leftflag = leftccw > 0.0; /* Is `searchpoint' to the right? */ rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); rightflag = rightccw > 0.0; if (leftflag && rightflag) { /* `searchtri' faces directly away from `searchpoint'. We could go left */ /* or right. Ask whether it's a triangle or a boundary on the left. */ onext(*searchtri, checktri); if (checktri.tri == m->dummytri) { leftflag = 0; } else { rightflag = 0; } } while (leftflag) { /* Turn left until satisfied. */ onextself(*searchtri); if (searchtri->tri == m->dummytri) { printf("Internal error in finddirection(): Unable to find a\n"); printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], startvertex[1]); printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); internalerror(); } apex(*searchtri, leftvertex); rightccw = leftccw; leftccw = counterclockwise(m, b, searchpoint, startvertex, leftvertex); leftflag = leftccw > 0.0; } while (rightflag) { /* Turn right until satisfied. */ oprevself(*searchtri); if (searchtri->tri == m->dummytri) { printf("Internal error in finddirection(): Unable to find a\n"); printf(" triangle leading from (%.12g, %.12g) to", startvertex[0], startvertex[1]); printf(" (%.12g, %.12g).\n", searchpoint[0], searchpoint[1]); internalerror(); } dest(*searchtri, rightvertex); leftccw = rightccw; rightccw = counterclockwise(m, b, startvertex, searchpoint, rightvertex); rightflag = rightccw > 0.0; } if (leftccw == 0.0) { return LEFTCOLLINEAR; } else if (rightccw == 0.0) { return RIGHTCOLLINEAR; } else { return WITHIN; }}/*****************************************************************************//* *//* segmentintersection() Find the intersection of an existing segment *//* and a segment that is being inserted. Insert *//* a vertex at the intersection, splitting an *//* existing subsegment. *//* *//* The segment being inserted connects the apex of splittri to endpoint2. *//* splitsubseg is the subsegment being split, and MUST adjoin splittri. *//* Hence, endpoints of the subsegment being split are the origin and *//* destination of splittri. *//* *//* On completion, splittri is a handle having the newly inserted *//* intersection point as its origin, and endpoint1 as its destination. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid segmentintersection(struct mesh *m, struct behavior *b, struct otri *splittri, struct osub *splitsubseg, vertex endpoint2)#else /* not ANSI_DECLARATORS */void segmentintersection(m, b, splittri, splitsubseg, endpoint2)struct mesh *m;struct behavior *b;struct otri *splittri;struct osub *splitsubseg;vertex endpoint2;#endif /* not ANSI_DECLARATORS */{ struct osub opposubseg; vertex endpoint1; vertex torg, tdest; vertex leftvertex, rightvertex; vertex newvertex; enum insertvertexresult success; enum finddirectionresult collinear; REAL ex, ey; REAL tx, ty; REAL etx, ety; REAL split, denom; int i; triangle ptr; /* Temporary variable used by onext(). */ subseg sptr; /* Temporary variable used by snext(). */ /* Find the other three segment endpoints. */ apex(*splittri, endpoint1); org(*splittri, torg); dest(*splittri, tdest); /* Segment intersection formulae; see the Antonio reference. */ tx = tdest[0] - torg[0]; ty = tdest[1] - torg[1]; ex = endpoint2[0] - endpoint1[0]; ey = endpoint2[1] - endpoint1[1]; etx = torg[0] - endpoint2[0]; ety = torg[1] - endpoint2[1]; denom = ty * ex - tx * ey; if (denom == 0.0) { printf("Internal error in segmentintersection():"); printf(" Attempt to find intersection of parallel segments.\n"); internalerror(); } split = (ey * etx - ex * ety) / denom; /* Create the new vertex. */ newvertex = (vertex) poolalloc(&m->vertices); /* Interpolate its coordinate and attributes. */ for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = torg[i] + split * (tdest[i] - torg[i]); } setvertexmark(newvertex, mark(*splitsubseg)); setvertextype(newvertex, INPUTVERTEX); if (b->verbose > 1) { printf( " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", torg[0], torg[1], tdest[0], tdest[1], newvertex[0], newvertex[1]); } /* Insert the intersection vertex. This should always succeed. */ success = insertvertex(m, b, newvertex, splittri, splitsubseg, 0, 0); if (success != SUCCESSFULVERTEX) { printf("Internal error in segmentintersection():\n"); printf(" Failure to split a segment.\n"); internalerror(); } /* Record a triangle whose origin is the new vertex. */ setvertex2tri(newvertex, encode(*splittri)); if (m->steinerleft > 0) { m->steinerleft--; } /* Divide the segment into two, and correct the segment endpoints. */ ssymself(*splitsubseg); spivot(*splitsubseg, opposubseg); sdissolve(*splitsubseg); sdissolve(opposubseg); do { setsegorg(*splitsubseg, newvertex); snextself(*splitsubseg); } while (splitsubseg->ss != m->dummysub); do { setsegorg(opposubseg, newvertex); snextself(opposubseg); } while (opposubseg.ss != m->dummysub); /* Inserting the vertex may have caused edge flips. We wish to rediscover */ /* the edge connecting endpoint1 to the new intersection vertex. */ collinear = finddirection(m, b, splittri, endpoint1); dest(*splittri, rightvertex); apex(*splittri, leftvertex); if ((leftvertex[0] == endpoint1[0]) && (leftvertex[1] == endpoint1[1])) { onextself(*splittri); } else if ((rightvertex[0] != endpoint1[0]) || (rightvertex[1] != endpoint1[1])) { printf("Internal error in segmentintersection():\n"); printf(" Topological inconsistency after splitting a segment.\n"); internalerror(); } /* `splittri' should have destination endpoint1. */}/*****************************************************************************//* *//* scoutsegment() Scout the first triangle on the path from one endpoint *//* to another, and check for completion (reaching the *//* second endpoint), a collinear vertex, or the *//* intersection of two segments. *//* *//* Returns one if the entire segment is successfully inserted, and zero if *//* the job must be finished by conformingedge() or constrainededge(). *//* *//* If the first triangle on the path has the second endpoint as its *//* destination or apex, a subsegment is inserted and the job is done. *//* *//* If the first triangle on the path has a destination or apex that lies on *//* the segment, a subsegment is inserted connecting the first endpoint to *//* the collinear vertex, and the search is continued from the collinear *//* vertex. *//* *//* If the first triangle on the path has a subsegment opposite its origin, *//* then there is a segment that intersects the segment being inserted. *//* Their intersection vertex is inserted, splitting the subsegment. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSint scoutsegment(struct mesh *m, struct behavior *b, struct otri *searchtri, vertex endpoint2, int newmark)#else /* not ANSI_DECLARATORS */int scoutsegment(m, b, searchtri, endpoint2, newmark)struct mesh *m;struct behavior *b;struct otri *searchtri;vertex endpoint2;int newmark;#endif /* not ANSI_DECLARATORS */{ struct otri crosstri; struct osub crosssubseg; vertex leftvertex, rightvertex; enum finddirectionresult collinear; subseg sptr; /* Temporary variable used by tspivot(). */ collinear = finddirection(m, b, searchtri, endpoint2); dest(*searchtri, rightvertex); apex(*searchtri, leftvertex); if (((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) || ((rightvertex[0] == endpoint2[0]) && (rightvertex[1] == endpoint2[1]))) { /* The segment is already an edge in the mesh. */ if ((leftvertex[0] == endpoint2[0]) && (leftvertex[1] == endpoint2[1])) { lprevself(*searchtri); } /* Insert a subsegment, if there isn't already one there. */ insertsubseg(m, b, searchtri, newmark); return 1; } else if (collinear == LEFTCOLLINEAR) { /* We've collided with a vertex between the segment's endpoints. */ /* Make the collinear vertex be the triangle's origin. */ lprevself(*searchtri); insertsubseg(m, b, searchtri, newmark); /* Insert the remainder of the segment. */ return scoutsegment(m, b, searchtri, endpoint2, newmark); } else if (collinear == RIGHTCOLLINEAR) { /* We've collided with a vertex between the segment's endpoints. */ insertsubseg(m, b, searchtri, newmark); /* Make the collinear vertex be the triangle's origin. */ lnextself(*searchtri); /* Insert the remainder of the segment. */ return scoutsegment(m, b, searchtri, endpoint2, newmark); } else { lnext(*searchtri, crosstri); tspivot(crosstri, crosssubseg); /* Check for a crossing segment. */ if (crosssubseg.ss == m->dummysub) { return 0; } else { /* Insert a vertex at the intersection. */ segmentintersection(m, b, &crosstri, &crosssubseg, endpoint2); otricopy(crosstri, *searchtri); insertsubseg(m, b, searchtri, newmark); /* Insert the remainder of the segment. */ return scoutsegment(m, b, searchtri, endpoint2, newmark); } }}/*****************************************************************************//* *//* conformingedge() Force a segment into a conforming Delaunay *//* triangulation by inserting a vertex at its midpoint, *//* and recursively forcing in the two half-segments if *//* necessary. *//* *//* Generates a sequence of subsegments connecting `endpoint1' to *//* `endpoint2'. `newmark' is the boundary marker of the segment, assigned *//* to each new splitting vertex and subsegment. *//* *//* Note that conformingedge() does not always maintain the conforming *//* Delaunay property. Once inserted, segments are locked into place; *//* vertices inserted later (to force other segments in) may render these *//* fixed segments non-Delaunay. The conforming Delaunay property will be *//* restored by enforcequality() by splitting encroached subsegments. *//* *//*****************************************************************************/#ifndef REDUCED#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid conformingedge(struct mesh *m, struct behavior *b, vertex endpoint1, vertex endpoint2, int newmark)#else /* not ANSI_DECLARATORS */void conformingedge(m, b, endpoint1, endpoint2, newmark)struct mesh *m;struct behavior *b;vertex endpoint1;vertex endpoint2;int newmark;#endif /* not ANSI_DECLARATORS */{ struct otri searchtri1, searchtri2; struct osub brokensubseg; vertex newvertex; vertex midvertex1, midvertex2; enum insertvertexresult success; int i; subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose > 2) { printf("Forcing segment into triangulation by recursive splitting:\n"); printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); } /* Create a new vertex to insert in the middle of the segment. */ newvertex = (vertex) poolalloc(&m->vertices); /* Interpolate coordinates and attributes. */ for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = 0.5 * (endpoint1[i] + endpoint2[i]); } setvertexmark(newvertex, newmark); setvertextype(newvertex, SEGMENTVERTEX); /* No known triangle to search from. */ searchtri1.tri = m->dummytri; /* Attempt to insert the new vertex. */ success = insertvertex(m, b, newvertex, &searchtri1, (struct osub *) NULL, 0, 0); if (success == DUPLICATEVERTEX) { if (b->verbose > 2) { printf(" Segment intersects existing vertex (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } /* Use the vertex that's already there. */ vertexdealloc(m, newvertex); org(searchtri1, newvertex); } else { if (success == VIOLATINGVERTEX) { if (b->verbose > 2) { printf(" Two segments intersect at (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } /* By fluke, we've landed right on another segment. Split it. */ tspivot(searchtri1, brokensubseg); success = insertvertex(m, b, newvertex, &searchtri1, &brokensubseg, 0, 0); if (success != SUCCESSFULVERTEX) { printf("Internal error in conformingedge():\n"); printf(" Failure to split a segment.\n"); internalerror(); } } /* The vertex has been inserted successfully. */ if (m->steinerleft > 0) { m->steinerleft--; } } otricopy(searchtri1, searchtri2); /* `searchtri1' and `searchtri2' are fastened at their origins to */ /* `newvertex', and will be directed toward `endpoint1' and `endpoint2' */ /* respectively. First, we must get `searchtri2' out of the way so it */ /* won't be invalidated during the insertion of the first half of the */ /* segment. */ finddirection(m, b, &searchtri2, endpoint2); if (!scoutsegment(m, b, &searchtri1, endpoint1, newmark)) { /* The origin of searchtri1 may have changed if a collision with an */ /* intervening vertex on the segment occurred. */ org(searchtri1, midvertex1); conformingedge(m, b, midvertex1, endpoint1, newmark); } if (!scoutsegment(m, b, &searchtri2, endpoint2, newmark)) { /* The origin of searchtri2 may have changed if a collision with an */ /* intervening vertex on the segment occurred. */ org(searchtri2, midvertex2); conformingedge(m, b, midvertex2, endpoint2, newmark); }}#endif /* not CDT_ONLY */#endif /* not REDUCED *//*****************************************************************************//* *//* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out *//* recursively from an existing vertex. Pay special *//* attention to stacking inverted triangles. *//* *//* This is a support routine for inserting segments into a constrained *//* Delaunay triangulation. *//* *//* The origin of fixuptri is treated as if it has just been inserted, and *//* the local Delaunay condition needs to be enforced. It is only enforced *//* in one sector, however, that being the angular range defined by *//* fixuptri. *//* *//* This routine also needs to make decisions regarding the "stacking" of *//* triangles. (Read the description of constrainededge() below before *//* reading on here, so you understand the algorithm.) If the position of *//* the new vertex (the origin of fixuptri) indicates that the vertex before *//* it on the polygon is a reflex vertex, then "stack" the triangle by *//* doing nothing. (fixuptri is an inverted triangle, which is how stacked *//* triangles are identified.) *//* *//* Otherwise, check whether the vertex before that was a reflex vertex. *//* If so, perform an edge flip, thereby eliminating an inverted triangle *//* (popping it off the stack). The edge flip may result in the creation *//* of a new inverted triangle, depending on whether or not the new vertex *//* is visible to the vertex three edges behind on the polygon. *//* *//* If neither of the two vertices behind the new vertex are reflex *//* vertices, fixuptri and fartri, the triangle opposite it, are not *//* inverted; hence, ensure that the edge between them is locally Delaunay. *//* *//* `leftside' indicates whether or not fixuptri is to the left of the *//* segment being inserted. (Imagine that the segment is pointing up from *//* endpoint1 to endpoint2.) *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid delaunayfixup(struct mesh *m, struct behavior *b, struct otri *fixuptri, int leftside)#else /* not ANSI_DECLARATORS */void delaunayfixup(m, b, fixuptri, leftside)struct mesh *m;struct behavior *b;struct otri *fixuptri;int leftside;#endif /* not ANSI_DECLARATORS */{ struct otri neartri; struct otri fartri; struct osub faredge; vertex nearvertex, leftvertex, rightvertex, farvertex; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ lnext(*fixuptri, neartri); sym(neartri, fartri); /* Check if the edge opposite the origin of fixuptri can be flipped. */ if (fartri.tri == m->dummytri) { return; } tspivot(neartri, faredge); if (faredge.ss != m->dummysub) { return; } /* Find all the relevant vertices. */ apex(neartri, nearvertex); org(neartri, leftvertex); dest(neartri, rightvertex); apex(fartri, farvertex); /* Check whether the previous polygon vertex is a reflex vertex. */ if (leftside) { if (counterclockwise(m, b, nearvertex, leftvertex, farvertex) <= 0.0) { /* leftvertex is a reflex vertex too. Nothing can */ /* be done until a convex section is found. */ return; } } else { if (counterclockwise(m, b, farvertex, rightvertex, nearvertex) <= 0.0) { /* rightvertex is a reflex vertex too. Nothing can */ /* be done until a convex section is found. */ return; } } if (counterclockwise(m, b, rightvertex, leftvertex, farvertex) > 0.0) { /* fartri is not an inverted triangle, and farvertex is not a reflex */ /* vertex. As there are no reflex vertices, fixuptri isn't an */ /* inverted triangle, either. Hence, test the edge between the */ /* triangles to ensure it is locally Delaunay. */ if (incircle(m, b, leftvertex, farvertex, rightvertex, nearvertex) <= 0.0) { return; } /* Not locally Delaunay; go on to an edge flip. */ } /* else fartri is inverted; remove it from the stack by flipping. */ flip(m, b, &neartri); lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */ /* Recursively process the two triangles that result from the flip. */ delaunayfixup(m, b, fixuptri, leftside); delaunayfixup(m, b, &fartri, leftside);}/*****************************************************************************//* *//* constrainededge() Force a segment into a constrained Delaunay *//* triangulation by deleting the triangles it *//* intersects, and triangulating the polygons that *//* form on each side of it. *//* *//* Generates a single subsegment connecting `endpoint1' to `endpoint2'. *//* The triangle `starttri' has `endpoint1' as its origin. `newmark' is the *//* boundary marker of the segment. *//* *//* To insert a segment, every triangle whose interior intersects the *//* segment is deleted. The union of these deleted triangles is a polygon *//* (which is not necessarily monotone, but is close enough), which is *//* divided into two polygons by the new segment. This routine's task is *//* to generate the Delaunay triangulation of these two polygons. *//* *//* You might think of this routine's behavior as a two-step process. The *//* first step is to walk from endpoint1 to endpoint2, flipping each edge *//* encountered. This step creates a fan of edges connected to endpoint1, *//* including the desired edge to endpoint2. The second step enforces the *//* Delaunay condition on each side of the segment in an incremental manner: *//* proceeding along the polygon from endpoint1 to endpoint2 (this is done *//* independently on each side of the segment), each vertex is "enforced" *//* as if it had just been inserted, but affecting only the previous *//* vertices. The result is the same as if the vertices had been inserted *//* in the order they appear on the polygon, so the result is Delaunay. *//* *//* In truth, constrainededge() interleaves these two steps. The procedure *//* walks from endpoint1 to endpoint2, and each time an edge is encountered *//* and flipped, the newly exposed vertex (at the far end of the flipped *//* edge) is "enforced" upon the previously flipped edges, usually affecting *//* only one side of the polygon (depending upon which side of the segment *//* the vertex falls on). *//* *//* The algorithm is complicated by the need to handle polygons that are not *//* convex. Although the polygon is not necessarily monotone, it can be *//* triangulated in a manner similar to the stack-based algorithms for *//* monotone polygons. For each reflex vertex (local concavity) of the *//* polygon, there will be an inverted triangle formed by one of the edge *//* flips. (An inverted triangle is one with negative area - that is, its *//* vertices are arranged in clockwise order - and is best thought of as a *//* wrinkle in the fabric of the mesh.) Each inverted triangle can be *//* thought of as a reflex vertex pushed on the stack, waiting to be fixed *//* later. *//* *//* A reflex vertex is popped from the stack when a vertex is inserted that *//* is visible to the reflex vertex. (However, if the vertex behind the *//* reflex vertex is not visible to the reflex vertex, a new inverted *//* triangle will take its place on the stack.) These details are handled *//* by the delaunayfixup() routine above. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid constrainededge(struct mesh *m, struct behavior *b, struct otri *starttri, vertex endpoint2, int newmark)#else /* not ANSI_DECLARATORS */void constrainededge(m, b, starttri, endpoint2, newmark)struct mesh *m;struct behavior *b;struct otri *starttri;vertex endpoint2;int newmark;#endif /* not ANSI_DECLARATORS */{ struct otri fixuptri, fixuptri2; struct osub crosssubseg; vertex endpoint1; vertex farvertex; REAL area; int collision; int done; triangle ptr; /* Temporary variable used by sym() and oprev(). */ subseg sptr; /* Temporary variable used by tspivot(). */ org(*starttri, endpoint1); lnext(*starttri, fixuptri); flip(m, b, &fixuptri); /* `collision' indicates whether we have found a vertex directly */ /* between endpoint1 and endpoint2. */ collision = 0; done = 0; do { org(fixuptri, farvertex); /* `farvertex' is the extreme point of the polygon we are "digging" */ /* to get from endpoint1 to endpoint2. */ if ((farvertex[0] == endpoint2[0]) && (farvertex[1] == endpoint2[1])) { oprev(fixuptri, fixuptri2); /* Enforce the Delaunay condition around endpoint2. */ delaunayfixup(m, b, &fixuptri, 0); delaunayfixup(m, b, &fixuptri2, 1); done = 1; } else { /* Check whether farvertex is to the left or right of the segment */ /* being inserted, to decide which edge of fixuptri to dig */ /* through next. */ area = counterclockwise(m, b, endpoint1, endpoint2, farvertex); if (area == 0.0) { /* We've collided with a vertex between endpoint1 and endpoint2. */ collision = 1; oprev(fixuptri, fixuptri2); /* Enforce the Delaunay condition around farvertex. */ delaunayfixup(m, b, &fixuptri, 0); delaunayfixup(m, b, &fixuptri2, 1); done = 1; } else { if (area > 0.0) { /* farvertex is to the left of the segment. */ oprev(fixuptri, fixuptri2); /* Enforce the Delaunay condition around farvertex, on the */ /* left side of the segment only. */ delaunayfixup(m, b, &fixuptri2, 1); /* Flip the edge that crosses the segment. After the edge is */ /* flipped, one of its endpoints is the fan vertex, and the */ /* destination of fixuptri is the fan vertex. */ lprevself(fixuptri); } else { /* farvertex is to the right of the segment. */ delaunayfixup(m, b, &fixuptri, 0); /* Flip the edge that crosses the segment. After the edge is */ /* flipped, one of its endpoints is the fan vertex, and the */ /* destination of fixuptri is the fan vertex. */ oprevself(fixuptri); } /* Check for two intersecting segments. */ tspivot(fixuptri, crosssubseg); if (crosssubseg.ss == m->dummysub) { flip(m, b, &fixuptri); /* May create inverted triangle at left. */ } else { /* We've collided with a segment between endpoint1 and endpoint2. */ collision = 1; /* Insert a vertex at the intersection. */ segmentintersection(m, b, &fixuptri, &crosssubseg, endpoint2); done = 1; } } } } while (!done); /* Insert a subsegment to make the segment permanent. */ insertsubseg(m, b, &fixuptri, newmark); /* If there was a collision with an interceding vertex, install another */ /* segment connecting that vertex with endpoint2. */ if (collision) { /* Insert the remainder of the segment. */ if (!scoutsegment(m, b, &fixuptri, endpoint2, newmark)) { constrainededge(m, b, &fixuptri, endpoint2, newmark); } }}/*****************************************************************************//* *//* insertsegment() Insert a PSLG segment into a triangulation. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid insertsegment(struct mesh *m, struct behavior *b, vertex endpoint1, vertex endpoint2, int newmark)#else /* not ANSI_DECLARATORS */void insertsegment(m, b, endpoint1, endpoint2, newmark)struct mesh *m;struct behavior *b;vertex endpoint1;vertex endpoint2;int newmark;#endif /* not ANSI_DECLARATORS */{ struct otri searchtri1, searchtri2; triangle encodedtri; vertex checkvertex; triangle ptr; /* Temporary variable used by sym(). */ if (b->verbose > 1) { printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n", endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]); } /* Find a triangle whose origin is the segment's first endpoint. */ checkvertex = (vertex) NULL; encodedtri = vertex2tri(endpoint1); if (encodedtri != (triangle) NULL) { decode(encodedtri, searchtri1); org(searchtri1, checkvertex); } if (checkvertex != endpoint1) { /* Find a boundary triangle to search from. */ searchtri1.tri = m->dummytri; searchtri1.orient = 0; symself(searchtri1); /* Search for the segment's first endpoint by point location. */ if (locate(m, b, endpoint1, &searchtri1) != ONVERTEX) { printf( "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); printf(" (%.12g, %.12g) in triangulation.\n", endpoint1[0], endpoint1[1]); internalerror(); } } /* Remember this triangle to improve subsequent point location. */ otricopy(searchtri1, m->recenttri); /* Scout the beginnings of a path from the first endpoint */ /* toward the second. */ if (scoutsegment(m, b, &searchtri1, endpoint2, newmark)) { /* The segment was easily inserted. */ return; } /* The first endpoint may have changed if a collision with an intervening */ /* vertex on the segment occurred. */ org(searchtri1, endpoint1); /* Find a triangle whose origin is the segment's second endpoint. */ checkvertex = (vertex) NULL; encodedtri = vertex2tri(endpoint2); if (encodedtri != (triangle) NULL) { decode(encodedtri, searchtri2); org(searchtri2, checkvertex); } if (checkvertex != endpoint2) { /* Find a boundary triangle to search from. */ searchtri2.tri = m->dummytri; searchtri2.orient = 0; symself(searchtri2); /* Search for the segment's second endpoint by point location. */ if (locate(m, b, endpoint2, &searchtri2) != ONVERTEX) { printf( "Internal error in insertsegment(): Unable to locate PSLG vertex\n"); printf(" (%.12g, %.12g) in triangulation.\n", endpoint2[0], endpoint2[1]); internalerror(); } } /* Remember this triangle to improve subsequent point location. */ otricopy(searchtri2, m->recenttri); /* Scout the beginnings of a path from the second endpoint */ /* toward the first. */ if (scoutsegment(m, b, &searchtri2, endpoint1, newmark)) { /* The segment was easily inserted. */ return; } /* The second endpoint may have changed if a collision with an intervening */ /* vertex on the segment occurred. */ org(searchtri2, endpoint2);#ifndef REDUCED#ifndef CDT_ONLY if (b->splitseg) { /* Insert vertices to force the segment into the triangulation. */ conformingedge(m, b, endpoint1, endpoint2, newmark); } else {#endif /* not CDT_ONLY */#endif /* not REDUCED */ /* Insert the segment directly into the triangulation. */ constrainededge(m, b, &searchtri1, endpoint2, newmark);#ifndef REDUCED#ifndef CDT_ONLY }#endif /* not CDT_ONLY */#endif /* not REDUCED */}/*****************************************************************************//* *//* markhull() Cover the convex hull of a triangulation with subsegments. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid markhull(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void markhull(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri hulltri; struct otri nexttri; struct otri starttri; triangle ptr; /* Temporary variable used by sym() and oprev(). */ /* Find a triangle handle on the hull. */ hulltri.tri = m->dummytri; hulltri.orient = 0; symself(hulltri); /* Remember where we started so we know when to stop. */ otricopy(hulltri, starttri); /* Go once counterclockwise around the convex hull. */ do { /* Create a subsegment if there isn't already one here. */ insertsubseg(m, b, &hulltri, 1); /* To find the next hull edge, go clockwise around the next vertex. */ lnextself(hulltri); oprev(hulltri, nexttri); while (nexttri.tri != m->dummytri) { otricopy(nexttri, hulltri); oprev(hulltri, nexttri); } } while (!otriequal(hulltri, starttri));}/*****************************************************************************//* *//* formskeleton() Create the segments of a triangulation, including PSLG *//* segments and edges on the convex hull. *//* *//* The PSLG segments are read from a .poly file. The return value is the *//* number of segments in the file. *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid formskeleton(struct mesh *m, struct behavior *b, int *segmentlist, int *segmentmarkerlist, int numberofsegments)#else /* not ANSI_DECLARATORS */void formskeleton(m, b, segmentlist, segmentmarkerlist, numberofsegments)struct mesh *m;struct behavior *b;int *segmentlist;int *segmentmarkerlist;int numberofsegments;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSvoid formskeleton(struct mesh *m, struct behavior *b, FILE *polyfile, char *polyfilename)#else /* not ANSI_DECLARATORS */void formskeleton(m, b, polyfile, polyfilename)struct mesh *m;struct behavior *b;FILE *polyfile;char *polyfilename;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY char polyfilename[6]; int index;#else /* not TRILIBRARY */ char inputline[INPUTLINESIZE]; char *stringptr;#endif /* not TRILIBRARY */ vertex endpoint1, endpoint2; int segmentmarkers; int end1, end2; int boundmarker; int i; if (b->poly) { if (!b->quiet) { printf("Recovering segments in Delaunay triangulation.\n"); }#ifdef TRILIBRARY strcpy(polyfilename, "input"); m->insegments = numberofsegments; segmentmarkers = segmentmarkerlist != (int *) NULL; index = 0;#else /* not TRILIBRARY */ /* Read the segments from a .poly file. */ /* Read number of segments and number of boundary markers. */ stringptr = readline(inputline, polyfile, polyfilename); m->insegments = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { segmentmarkers = 0; } else { segmentmarkers = (int) strtol(stringptr, &stringptr, 0); }#endif /* not TRILIBRARY */ /* If the input vertices are collinear, there is no triangulation, */ /* so don't try to insert segments. */ if (m->triangles.items == 0) { return; } /* If segments are to be inserted, compute a mapping */ /* from vertices to triangles. */ if (m->insegments > 0) { makevertexmap(m, b); if (b->verbose) { printf(" Recovering PSLG segments.\n"); } } boundmarker = 0; /* Read and insert the segments. */ for (i = 0; i < m->insegments; i++) {#ifdef TRILIBRARY end1 = segmentlist[index++]; end2 = segmentlist[index++]; if (segmentmarkers) { boundmarker = segmentmarkerlist[i]; }#else /* not TRILIBRARY */ stringptr = readline(inputline, polyfile, b->inpolyfilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %d has no endpoints in %s.\n", b->firstnumber + i, polyfilename); triexit(1); } else { end1 = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Segment %d is missing its second endpoint in %s.\n", b->firstnumber + i, polyfilename); triexit(1); } else { end2 = (int) strtol(stringptr, &stringptr, 0); } if (segmentmarkers) { stringptr = findfield(stringptr); if (*stringptr == '\0') { boundmarker = 0; } else { boundmarker = (int) strtol(stringptr, &stringptr, 0); } }#endif /* not TRILIBRARY */ if ((end1 < b->firstnumber) || (end1 >= b->firstnumber + m->invertices)) { if (!b->quiet) { printf("Warning: Invalid first endpoint of segment %d in %s.\n", b->firstnumber + i, polyfilename); } } else if ((end2 < b->firstnumber) || (end2 >= b->firstnumber + m->invertices)) { if (!b->quiet) { printf("Warning: Invalid second endpoint of segment %d in %s.\n", b->firstnumber + i, polyfilename); } } else { /* Find the vertices numbered `end1' and `end2'. */ endpoint1 = getvertex(m, b, end1); endpoint2 = getvertex(m, b, end2); if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) { if (!b->quiet) { printf("Warning: Endpoints of segment %d are coincident in %s.\n", b->firstnumber + i, polyfilename); } } else { insertsegment(m, b, endpoint1, endpoint2, boundmarker); } } } } else { m->insegments = 0; } if (b->convex || !b->poly) { /* Enclose the convex hull with subsegments. */ if (b->verbose) { printf(" Enclosing convex hull with segments.\n"); } markhull(m, b); }}/** **//** **//********* Segment insertion ends here *********//********* Carving out holes and concavities begins here *********//** **//** **//*****************************************************************************//* *//* infecthull() Virally infect all of the triangles of the convex hull *//* that are not protected by subsegments. Where there are *//* subsegments, set boundary markers as appropriate. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid infecthull(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void infecthull(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri hulltri; struct otri nexttri; struct otri starttri; struct osub hullsubseg; triangle **deadtriangle; vertex horg, hdest; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose) { printf(" Marking concavities (external triangles) for elimination.\n"); } /* Find a triangle handle on the hull. */ hulltri.tri = m->dummytri; hulltri.orient = 0; symself(hulltri); /* Remember where we started so we know when to stop. */ otricopy(hulltri, starttri); /* Go once counterclockwise around the convex hull. */ do { /* Ignore triangles that are already infected. */ if (!infected(hulltri)) { /* Is the triangle protected by a subsegment? */ tspivot(hulltri, hullsubseg); if (hullsubseg.ss == m->dummysub) { /* The triangle is not protected; infect it. */ if (!infected(hulltri)) { infect(hulltri); deadtriangle = (triangle **) poolalloc(&m->viri); *deadtriangle = hulltri.tri; } } else { /* The triangle is protected; set boundary markers if appropriate. */ if (mark(hullsubseg) == 0) { setmark(hullsubseg, 1); org(hulltri, horg); dest(hulltri, hdest); if (vertexmark(horg) == 0) { setvertexmark(horg, 1); } if (vertexmark(hdest) == 0) { setvertexmark(hdest, 1); } } } } /* To find the next hull edge, go clockwise around the next vertex. */ lnextself(hulltri); oprev(hulltri, nexttri); while (nexttri.tri != m->dummytri) { otricopy(nexttri, hulltri); oprev(hulltri, nexttri); } } while (!otriequal(hulltri, starttri));}/*****************************************************************************//* *//* plague() Spread the virus from all infected triangles to any neighbors *//* not protected by subsegments. Delete all infected triangles. *//* *//* This is the procedure that actually creates holes and concavities. *//* *//* This procedure operates in two phases. The first phase identifies all *//* the triangles that will die, and marks them as infected. They are *//* marked to ensure that each triangle is added to the virus pool only *//* once, so the procedure will terminate. *//* *//* The second phase actually eliminates the infected triangles. It also *//* eliminates orphaned vertices. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid plague(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void plague(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri testtri; struct otri neighbor; triangle **virusloop; triangle **deadtriangle; struct osub neighborsubseg; vertex testvertex; vertex norg, ndest; vertex deadorg, deaddest, deadapex; int killorg; triangle ptr; /* Temporary variable used by sym() and onext(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose) { printf(" Marking neighbors of marked triangles.\n"); } /* Loop through all the infected triangles, spreading the virus to */ /* their neighbors, then to their neighbors' neighbors. */ traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; /* A triangle is marked as infected by messing with one of its pointers */ /* to subsegments, setting it to an illegal value. Hence, we have to */ /* temporarily uninfect this triangle so that we can examine its */ /* adjacent subsegments. */ uninfect(testtri); if (b->verbose > 2) { /* Assign the triangle an orientation for convenience in */ /* checking its vertices. */ testtri.orient = 0; org(testtri, deadorg); dest(testtri, deaddest); apex(testtri, deadapex); printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", deadorg[0], deadorg[1], deaddest[0], deaddest[1], deadapex[0], deadapex[1]); } /* Check each of the triangle's three neighbors. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { /* Find the neighbor. */ sym(testtri, neighbor); /* Check for a subsegment between the triangle and its neighbor. */ tspivot(testtri, neighborsubseg); /* Check if the neighbor is nonexistent or already infected. */ if ((neighbor.tri == m->dummytri) || infected(neighbor)) { if (neighborsubseg.ss != m->dummysub) { /* There is a subsegment separating the triangle from its */ /* neighbor, but both triangles are dying, so the subsegment */ /* dies too. */ subsegdealloc(m, neighborsubseg.ss); if (neighbor.tri != m->dummytri) { /* Make sure the subsegment doesn't get deallocated again */ /* later when the infected neighbor is visited. */ uninfect(neighbor); tsdissolve(neighbor); infect(neighbor); } } } else { /* The neighbor exists and is not infected. */ if (neighborsubseg.ss == m->dummysub) { /* There is no subsegment protecting the neighbor, so */ /* the neighbor becomes infected. */ if (b->verbose > 2) { org(neighbor, deadorg); dest(neighbor, deaddest); apex(neighbor, deadapex); printf( " Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", deadorg[0], deadorg[1], deaddest[0], deaddest[1], deadapex[0], deadapex[1]); } infect(neighbor); /* Ensure that the neighbor's neighbors will be infected. */ deadtriangle = (triangle **) poolalloc(&m->viri); *deadtriangle = neighbor.tri; } else { /* The neighbor is protected by a subsegment. */ /* Remove this triangle from the subsegment. */ stdissolve(neighborsubseg); /* The subsegment becomes a boundary. Set markers accordingly. */ if (mark(neighborsubseg) == 0) { setmark(neighborsubseg, 1); } org(neighbor, norg); dest(neighbor, ndest); if (vertexmark(norg) == 0) { setvertexmark(norg, 1); } if (vertexmark(ndest) == 0) { setvertexmark(ndest, 1); } } } } /* Remark the triangle as infected, so it doesn't get added to the */ /* virus pool again. */ infect(testtri); virusloop = (triangle **) traverse(&m->viri); } if (b->verbose) { printf(" Deleting marked triangles.\n"); } traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; /* Check each of the three corners of the triangle for elimination. */ /* This is done by walking around each vertex, checking if it is */ /* still connected to at least one live triangle. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { org(testtri, testvertex); /* Check if the vertex has already been tested. */ if (testvertex != (vertex) NULL) { killorg = 1; /* Mark the corner of the triangle as having been tested. */ setorg(testtri, NULL); /* Walk counterclockwise about the vertex. */ onext(testtri, neighbor); /* Stop upon reaching a boundary or the starting triangle. */ while ((neighbor.tri != m->dummytri) && (!otriequal(neighbor, testtri))) { if (infected(neighbor)) { /* Mark the corner of this triangle as having been tested. */ setorg(neighbor, NULL); } else { /* A live triangle. The vertex survives. */ killorg = 0; } /* Walk counterclockwise about the vertex. */ onextself(neighbor); } /* If we reached a boundary, we must walk clockwise as well. */ if (neighbor.tri == m->dummytri) { /* Walk clockwise about the vertex. */ oprev(testtri, neighbor); /* Stop upon reaching a boundary. */ while (neighbor.tri != m->dummytri) { if (infected(neighbor)) { /* Mark the corner of this triangle as having been tested. */ setorg(neighbor, NULL); } else { /* A live triangle. The vertex survives. */ killorg = 0; } /* Walk clockwise about the vertex. */ oprevself(neighbor); } } if (killorg) { if (b->verbose > 1) { printf(" Deleting vertex (%.12g, %.12g)\n", testvertex[0], testvertex[1]); } setvertextype(testvertex, UNDEADVERTEX); m->undeads++; } } } /* Record changes in the number of boundary edges, and disconnect */ /* dead triangles from their neighbors. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { sym(testtri, neighbor); if (neighbor.tri == m->dummytri) { /* There is no neighboring triangle on this edge, so this edge */ /* is a boundary edge. This triangle is being deleted, so this */ /* boundary edge is deleted. */ m->hullsize--; } else { /* Disconnect the triangle from its neighbor. */ dissolve(neighbor); /* There is a neighboring triangle on this edge, so this edge */ /* becomes a boundary edge when this triangle is deleted. */ m->hullsize++; } } /* Return the dead triangle to the pool of triangles. */ triangledealloc(m, testtri.tri); virusloop = (triangle **) traverse(&m->viri); } /* Empty the virus pool. */ poolrestart(&m->viri);}/*****************************************************************************//* *//* regionplague() Spread regional attributes and/or area constraints *//* (from a .poly file) throughout the mesh. *//* *//* This procedure operates in two phases. The first phase spreads an *//* attribute and/or an area constraint through a (segment-bounded) region. *//* The triangles are marked to ensure that each triangle is added to the *//* virus pool only once, so the procedure will terminate. *//* *//* The second phase uninfects all infected triangles, returning them to *//* normal. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid regionplague(struct mesh *m, struct behavior *b, REAL attribute, REAL area)#else /* not ANSI_DECLARATORS */void regionplague(m, b, attribute, area)struct mesh *m;struct behavior *b;REAL attribute;REAL area;#endif /* not ANSI_DECLARATORS */{ struct otri testtri; struct otri neighbor; triangle **virusloop; triangle **regiontri; struct osub neighborsubseg; vertex regionorg, regiondest, regionapex; triangle ptr; /* Temporary variable used by sym() and onext(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (b->verbose > 1) { printf(" Marking neighbors of marked triangles.\n"); } /* Loop through all the infected triangles, spreading the attribute */ /* and/or area constraint to their neighbors, then to their neighbors' */ /* neighbors. */ traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; /* A triangle is marked as infected by messing with one of its pointers */ /* to subsegments, setting it to an illegal value. Hence, we have to */ /* temporarily uninfect this triangle so that we can examine its */ /* adjacent subsegments. */ uninfect(testtri); if (b->regionattrib) { /* Set an attribute. */ setelemattribute(testtri, m->eextras, attribute); } if (b->vararea) { /* Set an area constraint. */ setareabound(testtri, area); } if (b->verbose > 2) { /* Assign the triangle an orientation for convenience in */ /* checking its vertices. */ testtri.orient = 0; org(testtri, regionorg); dest(testtri, regiondest); apex(testtri, regionapex); printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", regionorg[0], regionorg[1], regiondest[0], regiondest[1], regionapex[0], regionapex[1]); } /* Check each of the triangle's three neighbors. */ for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) { /* Find the neighbor. */ sym(testtri, neighbor); /* Check for a subsegment between the triangle and its neighbor. */ tspivot(testtri, neighborsubseg); /* Make sure the neighbor exists, is not already infected, and */ /* isn't protected by a subsegment. */ if ((neighbor.tri != m->dummytri) && !infected(neighbor) && (neighborsubseg.ss == m->dummysub)) { if (b->verbose > 2) { org(neighbor, regionorg); dest(neighbor, regiondest); apex(neighbor, regionapex); printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", regionorg[0], regionorg[1], regiondest[0], regiondest[1], regionapex[0], regionapex[1]); } /* Infect the neighbor. */ infect(neighbor); /* Ensure that the neighbor's neighbors will be infected. */ regiontri = (triangle **) poolalloc(&m->viri); *regiontri = neighbor.tri; } } /* Remark the triangle as infected, so it doesn't get added to the */ /* virus pool again. */ infect(testtri); virusloop = (triangle **) traverse(&m->viri); } /* Uninfect all triangles. */ if (b->verbose > 1) { printf(" Unmarking marked triangles.\n"); } traversalinit(&m->viri); virusloop = (triangle **) traverse(&m->viri); while (virusloop != (triangle **) NULL) { testtri.tri = *virusloop; uninfect(testtri); virusloop = (triangle **) traverse(&m->viri); } /* Empty the virus pool. */ poolrestart(&m->viri);}/*****************************************************************************//* *//* carveholes() Find the holes and infect them. Find the area *//* constraints and infect them. Infect the convex hull. *//* Spread the infection and kill triangles. Spread the *//* area constraints. *//* *//* This routine mainly calls other routines to carry out all these *//* functions. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid carveholes(struct mesh *m, struct behavior *b, REAL *holelist, int holes, REAL *regionlist, int regions)#else /* not ANSI_DECLARATORS */void carveholes(m, b, holelist, holes, regionlist, regions)struct mesh *m;struct behavior *b;REAL *holelist;int holes;REAL *regionlist;int regions;#endif /* not ANSI_DECLARATORS */{ struct otri searchtri; struct otri triangleloop; struct otri *regiontris; triangle **holetri; triangle **regiontri; vertex searchorg, searchdest; enum locateresult intersect; int i; triangle ptr; /* Temporary variable used by sym(). */ if (!(b->quiet || (b->noholes && b->convex))) { printf("Removing unwanted triangles.\n"); if (b->verbose && (holes > 0)) { printf(" Marking holes for elimination.\n"); } } if (regions > 0) { /* Allocate storage for the triangles in which region points fall. */ regiontris = (struct otri *) trimalloc(regions * (int) sizeof(struct otri)); } else { regiontris = (struct otri *) NULL; } if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { /* Initialize a pool of viri to be used for holes, concavities, */ /* regional attributes, and/or regional area constraints. */ poolinit(&m->viri, sizeof(triangle *), VIRUSPERBLOCK, VIRUSPERBLOCK, 0); } if (!b->convex) { /* Mark as infected any unprotected triangles on the boundary. */ /* This is one way by which concavities are created. */ infecthull(m, b); } if ((holes > 0) && !b->noholes) { /* Infect each triangle in which a hole lies. */ for (i = 0; i < 2 * holes; i += 2) { /* Ignore holes that aren't within the bounds of the mesh. */ if ((holelist[i] >= m->xmin) && (holelist[i] <= m->xmax) && (holelist[i + 1] >= m->ymin) && (holelist[i + 1] <= m->ymax)) { /* Start searching from some triangle on the outer boundary. */ searchtri.tri = m->dummytri; searchtri.orient = 0; symself(searchtri); /* Ensure that the hole is to the left of this boundary edge; */ /* otherwise, locate() will falsely report that the hole */ /* falls within the starting triangle. */ org(searchtri, searchorg); dest(searchtri, searchdest); if (counterclockwise(m, b, searchorg, searchdest, &holelist[i]) > 0.0) { /* Find a triangle that contains the hole. */ intersect = locate(m, b, &holelist[i], &searchtri); if ((intersect != OUTSIDE) && (!infected(searchtri))) { /* Infect the triangle. This is done by marking the triangle */ /* as infected and including the triangle in the virus pool. */ infect(searchtri); holetri = (triangle **) poolalloc(&m->viri); *holetri = searchtri.tri; } } } } } /* Now, we have to find all the regions BEFORE we carve the holes, because */ /* locate() won't work when the triangulation is no longer convex. */ /* (Incidentally, this is the reason why regional attributes and area */ /* constraints can't be used when refining a preexisting mesh, which */ /* might not be convex; they can only be used with a freshly */ /* triangulated PSLG.) */ if (regions > 0) { /* Find the starting triangle for each region. */ for (i = 0; i < regions; i++) { regiontris[i].tri = m->dummytri; /* Ignore region points that aren't within the bounds of the mesh. */ if ((regionlist[4 * i] >= m->xmin) && (regionlist[4 * i] <= m->xmax) && (regionlist[4 * i + 1] >= m->ymin) && (regionlist[4 * i + 1] <= m->ymax)) { /* Start searching from some triangle on the outer boundary. */ searchtri.tri = m->dummytri; searchtri.orient = 0; symself(searchtri); /* Ensure that the region point is to the left of this boundary */ /* edge; otherwise, locate() will falsely report that the */ /* region point falls within the starting triangle. */ org(searchtri, searchorg); dest(searchtri, searchdest); if (counterclockwise(m, b, searchorg, searchdest, ®ionlist[4 * i]) > 0.0) { /* Find a triangle that contains the region point. */ intersect = locate(m, b, ®ionlist[4 * i], &searchtri); if ((intersect != OUTSIDE) && (!infected(searchtri))) { /* Record the triangle for processing after the */ /* holes have been carved. */ otricopy(searchtri, regiontris[i]); } } } } } if (m->viri.items > 0) { /* Carve the holes and concavities. */ plague(m, b); } /* The virus pool should be empty now. */ if (regions > 0) { if (!b->quiet) { if (b->regionattrib) { if (b->vararea) { printf("Spreading regional attributes and area constraints.\n"); } else { printf("Spreading regional attributes.\n"); } } else { printf("Spreading regional area constraints.\n"); } } if (b->regionattrib && !b->refine) { /* Assign every triangle a regional attribute of zero. */ traversalinit(&m->triangles); triangleloop.orient = 0; triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { setelemattribute(triangleloop, m->eextras, 0.0); triangleloop.tri = triangletraverse(m); } } for (i = 0; i < regions; i++) { if (regiontris[i].tri != m->dummytri) { /* Make sure the triangle under consideration still exists. */ /* It may have been eaten by the virus. */ if (!deadtri(regiontris[i].tri)) { /* Put one triangle in the virus pool. */ infect(regiontris[i]); regiontri = (triangle **) poolalloc(&m->viri); *regiontri = regiontris[i].tri; /* Apply one region's attribute and/or area constraint. */ regionplague(m, b, regionlist[4 * i + 2], regionlist[4 * i + 3]); /* The virus pool should be empty now. */ } } } if (b->regionattrib && !b->refine) { /* Note the fact that each triangle has an additional attribute. */ m->eextras++; } } /* Free up memory. */ if (((holes > 0) && !b->noholes) || !b->convex || (regions > 0)) { pooldeinit(&m->viri); } if (regions > 0) { trifree((VOID *) regiontris); }}/** **//** **//********* Carving out holes and concavities ends here *********//********* Mesh quality maintenance begins here *********//** **//** **//*****************************************************************************//* *//* tallyencs() Traverse the entire list of subsegments, and check each *//* to see if it is encroached. If so, add it to the list. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid tallyencs(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void tallyencs(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct osub subsegloop; int dummy; traversalinit(&m->subsegs); subsegloop.ssorient = 0; subsegloop.ss = subsegtraverse(m); while (subsegloop.ss != (subseg *) NULL) { /* If the segment is encroached, add it to the list. */ dummy = checkseg4encroach(m, b, &subsegloop); subsegloop.ss = subsegtraverse(m); }}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* precisionerror() Print an error message for precision problems. *//* *//*****************************************************************************/#ifndef CDT_ONLYvoid precisionerror(){ printf("Try increasing the area criterion and/or reducing the minimum\n"); printf(" allowable angle so that tiny triangles are not created.\n");#ifdef SINGLE printf("Alternatively, try recompiling me with double precision\n"); printf(" arithmetic (by removing \"#define SINGLE\" from the\n"); printf(" source file or \"-DSINGLE\" from the makefile).\n");#endif /* SINGLE */}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* splitencsegs() Split all the encroached subsegments. *//* *//* Each encroached subsegment is repaired by splitting it - inserting a *//* vertex at or near its midpoint. Newly inserted vertices may encroach *//* upon other subsegments; these are also repaired. *//* *//* `triflaws' is a flag that specifies whether one should take note of new *//* bad triangles that result from inserting vertices to repair encroached *//* subsegments. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid splitencsegs(struct mesh *m, struct behavior *b, int triflaws)#else /* not ANSI_DECLARATORS */void splitencsegs(m, b, triflaws)struct mesh *m;struct behavior *b;int triflaws;#endif /* not ANSI_DECLARATORS */{ struct otri enctri; struct otri testtri; struct osub testsh; struct osub currentenc; struct badsubseg *encloop; vertex eorg, edest, eapex; vertex newvertex; enum insertvertexresult success; REAL segmentlength, nearestpoweroftwo; REAL split; REAL multiplier, divisor; int acuteorg, acuteorg2, acutedest, acutedest2; int dummy; int i; triangle ptr; /* Temporary variable used by stpivot(). */ subseg sptr; /* Temporary variable used by snext(). */ /* Note that steinerleft == -1 if an unlimited number */ /* of Steiner points is allowed. */ while ((m->badsubsegs.items > 0) && (m->steinerleft != 0)) { traversalinit(&m->badsubsegs); encloop = badsubsegtraverse(m); while ((encloop != (struct badsubseg *) NULL) && (m->steinerleft != 0)) { sdecode(encloop->encsubseg, currentenc); sorg(currentenc, eorg); sdest(currentenc, edest); /* Make sure that this segment is still the same segment it was */ /* when it was determined to be encroached. If the segment was */ /* enqueued multiple times (because several newly inserted */ /* vertices encroached it), it may have already been split. */ if (!deadsubseg(currentenc.ss) && (eorg == encloop->subsegorg) && (edest == encloop->subsegdest)) { /* To decide where to split a segment, we need to know if the */ /* segment shares an endpoint with an adjacent segment. */ /* The concern is that, if we simply split every encroached */ /* segment in its center, two adjacent segments with a small */ /* angle between them might lead to an infinite loop; each */ /* vertex added to split one segment will encroach upon the */ /* other segment, which must then be split with a vertex that */ /* will encroach upon the first segment, and so on forever. */ /* To avoid this, imagine a set of concentric circles, whose */ /* radii are powers of two, about each segment endpoint. */ /* These concentric circles determine where the segment is */ /* split. (If both endpoints are shared with adjacent */ /* segments, split the segment in the middle, and apply the */ /* concentric circles for later splittings.) */ /* Is the origin shared with another segment? */ stpivot(currentenc, enctri); lnext(enctri, testtri); tspivot(testtri, testsh); acuteorg = testsh.ss != m->dummysub; /* Is the destination shared with another segment? */ lnextself(testtri); tspivot(testtri, testsh); acutedest = testsh.ss != m->dummysub; /* If we're using Chew's algorithm (rather than Ruppert's) */ /* to define encroachment, delete free vertices from the */ /* subsegment's diametral circle. */ if (!b->conformdel && !acuteorg && !acutedest) { apex(enctri, eapex); while ((vertextype(eapex) == FREEVERTEX) && ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { deletevertex(m, b, &testtri); stpivot(currentenc, enctri); apex(enctri, eapex); lprev(enctri, testtri); } } /* Now, check the other side of the segment, if there's a triangle */ /* there. */ sym(enctri, testtri); if (testtri.tri != m->dummytri) { /* Is the destination shared with another segment? */ lnextself(testtri); tspivot(testtri, testsh); acutedest2 = testsh.ss != m->dummysub; acutedest = acutedest || acutedest2; /* Is the origin shared with another segment? */ lnextself(testtri); tspivot(testtri, testsh); acuteorg2 = testsh.ss != m->dummysub; acuteorg = acuteorg || acuteorg2; /* Delete free vertices from the subsegment's diametral circle. */ if (!b->conformdel && !acuteorg2 && !acutedest2) { org(testtri, eapex); while ((vertextype(eapex) == FREEVERTEX) && ((eorg[0] - eapex[0]) * (edest[0] - eapex[0]) + (eorg[1] - eapex[1]) * (edest[1] - eapex[1]) < 0.0)) { deletevertex(m, b, &testtri); sym(enctri, testtri); apex(testtri, eapex); lprevself(testtri); } } } /* Use the concentric circles if exactly one endpoint is shared */ /* with another adjacent segment. */ if (acuteorg || acutedest) { segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0]) + (edest[1] - eorg[1]) * (edest[1] - eorg[1])); /* Find the power of two that most evenly splits the segment. */ /* The worst case is a 2:1 ratio between subsegment lengths. */ nearestpoweroftwo = 1.0; while (segmentlength > 3.0 * nearestpoweroftwo) { nearestpoweroftwo *= 2.0; } while (segmentlength < 1.5 * nearestpoweroftwo) { nearestpoweroftwo *= 0.5; } /* Where do we split the segment? */ split = nearestpoweroftwo / segmentlength; if (acutedest) { split = 1.0 - split; } } else { /* If we're not worried about adjacent segments, split */ /* this segment in the middle. */ split = 0.5; } /* Create the new vertex. */ newvertex = (vertex) poolalloc(&m->vertices); /* Interpolate its coordinate and attributes. */ for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = eorg[i] + split * (edest[i] - eorg[i]); } if (!b->noexact) { /* Roundoff in the above calculation may yield a `newvertex' */ /* that is not precisely collinear with `eorg' and `edest'. */ /* Improve collinearity by one step of iterative refinement. */ multiplier = counterclockwise(m, b, eorg, edest, newvertex); divisor = ((eorg[0] - edest[0]) * (eorg[0] - edest[0]) + (eorg[1] - edest[1]) * (eorg[1] - edest[1])); if ((multiplier != 0.0) && (divisor != 0.0)) { multiplier = multiplier / divisor; /* Watch out for NANs. */ if (multiplier == multiplier) { newvertex[0] += multiplier * (edest[1] - eorg[1]); newvertex[1] += multiplier * (eorg[0] - edest[0]); } } } setvertexmark(newvertex, mark(currentenc)); setvertextype(newvertex, SEGMENTVERTEX); if (b->verbose > 1) { printf( " Splitting subsegment (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n", eorg[0], eorg[1], edest[0], edest[1], newvertex[0], newvertex[1]); } /* Check whether the new vertex lies on an endpoint. */ if (((newvertex[0] == eorg[0]) && (newvertex[1] == eorg[1])) || ((newvertex[0] == edest[0]) && (newvertex[1] == edest[1]))) { printf("Error: Ran out of precision at (%.12g, %.12g).\n", newvertex[0], newvertex[1]); printf("I attempted to split a segment to a smaller size than\n"); printf(" can be accommodated by the finite precision of\n"); printf(" floating point arithmetic.\n"); precisionerror(); triexit(1); } /* Insert the splitting vertex. This should always succeed. */ success = insertvertex(m, b, newvertex, &enctri, ¤tenc, 1, triflaws); if ((success != SUCCESSFULVERTEX) && (success != ENCROACHINGVERTEX)) { printf("Internal error in splitencsegs():\n"); printf(" Failure to split a segment.\n"); internalerror(); } if (m->steinerleft > 0) { m->steinerleft--; } /* Check the two new subsegments to see if they're encroached. */ dummy = checkseg4encroach(m, b, ¤tenc); snextself(currentenc); dummy = checkseg4encroach(m, b, ¤tenc); } badsubsegdealloc(m, encloop); encloop = badsubsegtraverse(m); } }}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* tallyfaces() Test every triangle in the mesh for quality measures. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid tallyfaces(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void tallyfaces(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri triangleloop; if (b->verbose) { printf(" Making a list of bad triangles.\n"); } traversalinit(&m->triangles); triangleloop.orient = 0; triangleloop.tri = triangletraverse(m); while (triangleloop.tri != (triangle *) NULL) { /* If the triangle is bad, enqueue it. */ testtriangle(m, b, &triangleloop); triangleloop.tri = triangletraverse(m); }}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* splittriangle() Inserts a vertex at the circumcenter of a triangle. *//* Deletes the newly inserted vertex if it encroaches *//* upon a segment. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid splittriangle(struct mesh *m, struct behavior *b, struct badtriang *badtri)#else /* not ANSI_DECLARATORS */void splittriangle(m, b, badtri)struct mesh *m;struct behavior *b;struct badtriang *badtri;#endif /* not ANSI_DECLARATORS */{ struct otri badotri; vertex borg, bdest, bapex; vertex newvertex; REAL xi, eta; enum insertvertexresult success; int errorflag; int i; decode(badtri->poortri, badotri); org(badotri, borg); dest(badotri, bdest); apex(badotri, bapex); /* Make sure that this triangle is still the same triangle it was */ /* when it was tested and determined to be of bad quality. */ /* Subsequent transformations may have made it a different triangle. */ if (!deadtri(badotri.tri) && (borg == badtri->triangorg) && (bdest == badtri->triangdest) && (bapex == badtri->triangapex)) { if (b->verbose > 1) { printf(" Splitting this triangle at its circumcenter:\n"); printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); } errorflag = 0; /* Create a new vertex at the triangle's circumcenter. */ newvertex = (vertex) poolalloc(&m->vertices); findcircumcenter(m, b, borg, bdest, bapex, newvertex, &xi, &eta, 1); /* Check whether the new vertex lies on a triangle vertex. */ if (((newvertex[0] == borg[0]) && (newvertex[1] == borg[1])) || ((newvertex[0] == bdest[0]) && (newvertex[1] == bdest[1])) || ((newvertex[0] == bapex[0]) && (newvertex[1] == bapex[1]))) { if (!b->quiet) { printf( "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", newvertex[0], newvertex[1]); errorflag = 1; } vertexdealloc(m, newvertex); } else { for (i = 2; i < 2 + m->nextras; i++) { /* Interpolate the vertex attributes at the circumcenter. */ newvertex[i] = borg[i] + xi * (bdest[i] - borg[i]) + eta * (bapex[i] - borg[i]); } /* The new vertex must be in the interior, and therefore is a */ /* free vertex with a marker of zero. */ setvertexmark(newvertex, 0); setvertextype(newvertex, FREEVERTEX); /* Ensure that the handle `badotri' does not represent the longest */ /* edge of the triangle. This ensures that the circumcenter must */ /* fall to the left of this edge, so point location will work. */ /* (If the angle org-apex-dest exceeds 90 degrees, then the */ /* circumcenter lies outside the org-dest edge, and eta is */ /* negative. Roundoff error might prevent eta from being */ /* negative when it should be, so I test eta against xi.) */ if (eta < xi) { lprevself(badotri); } /* Insert the circumcenter, searching from the edge of the triangle, */ /* and maintain the Delaunay property of the triangulation. */ success = insertvertex(m, b, newvertex, &badotri, (struct osub *) NULL, 1, 1); if (success == SUCCESSFULVERTEX) { if (m->steinerleft > 0) { m->steinerleft--; } } else if (success == ENCROACHINGVERTEX) { /* If the newly inserted vertex encroaches upon a subsegment, */ /* delete the new vertex. */ undovertex(m, b); if (b->verbose > 1) { printf(" Rejecting (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } vertexdealloc(m, newvertex); } else if (success == VIOLATINGVERTEX) { /* Failed to insert the new vertex, but some subsegment was */ /* marked as being encroached. */ vertexdealloc(m, newvertex); } else { /* success == DUPLICATEVERTEX */ /* Couldn't insert the new vertex because a vertex is already there. */ if (!b->quiet) { printf( "Warning: New vertex (%.12g, %.12g) falls on existing vertex.\n", newvertex[0], newvertex[1]); errorflag = 1; } vertexdealloc(m, newvertex); } } if (errorflag) { if (b->verbose) { printf(" The new vertex is at the circumcenter of triangle\n"); printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]); } printf("This probably means that I am trying to refine triangles\n"); printf(" to a smaller size than can be accommodated by the finite\n"); printf(" precision of floating point arithmetic. (You can be\n"); printf(" sure of this if I fail to terminate.)\n"); precisionerror(); } }}#endif /* not CDT_ONLY *//*****************************************************************************//* *//* enforcequality() Remove all the encroached subsegments and bad *//* triangles from the triangulation. *//* *//*****************************************************************************/#ifndef CDT_ONLY#ifdef ANSI_DECLARATORSvoid enforcequality(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void enforcequality(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct badtriang *badtri; int i; if (!b->quiet) { printf("Adding Steiner points to enforce quality.\n"); } /* Initialize the pool of encroached subsegments. */ poolinit(&m->badsubsegs, sizeof(struct badsubseg), BADSUBSEGPERBLOCK, BADSUBSEGPERBLOCK, 0); if (b->verbose) { printf(" Looking for encroached subsegments.\n"); } /* Test all segments to see if they're encroached. */ tallyencs(m, b); if (b->verbose && (m->badsubsegs.items > 0)) { printf(" Splitting encroached subsegments.\n"); } /* Fix encroached subsegments without noting bad triangles. */ splitencsegs(m, b, 0); /* At this point, if we haven't run out of Steiner points, the */ /* triangulation should be (conforming) Delaunay. */ /* Next, we worry about enforcing triangle quality. */ if ((b->minangle > 0.0) || b->vararea || b->fixedarea || b->usertest) { /* Initialize the pool of bad triangles. */ poolinit(&m->badtriangles, sizeof(struct badtriang), BADTRIPERBLOCK, BADTRIPERBLOCK, 0); /* Initialize the queues of bad triangles. */ for (i = 0; i < 4096; i++) { m->queuefront[i] = (struct badtriang *) NULL; } m->firstnonemptyq = -1; /* Test all triangles to see if they're bad. */ tallyfaces(m, b); /* Initialize the pool of recently flipped triangles. */ poolinit(&m->flipstackers, sizeof(struct flipstacker), FLIPSTACKERPERBLOCK, FLIPSTACKERPERBLOCK, 0); m->checkquality = 1; if (b->verbose) { printf(" Splitting bad triangles.\n"); } while ((m->badtriangles.items > 0) && (m->steinerleft != 0)) { /* Fix one bad triangle by inserting a vertex at its circumcenter. */ badtri = dequeuebadtriang(m); splittriangle(m, b, badtri); if (m->badsubsegs.items > 0) { /* Put bad triangle back in queue for another try later. */ enqueuebadtriang(m, b, badtri); /* Fix any encroached subsegments that resulted. */ /* Record any new bad triangles that result. */ splitencsegs(m, b, 1); } else { /* Return the bad triangle to the pool. */ pooldealloc(&m->badtriangles, (VOID *) badtri); } } } /* At this point, if the "-D" switch was selected and we haven't run out */ /* of Steiner points, the triangulation should be (conforming) Delaunay */ /* and have no low-quality triangles. */ /* Might we have run out of Steiner points too soon? */ if (!b->quiet && b->conformdel && (m->badsubsegs.items > 0) && (m->steinerleft == 0)) { printf("\nWarning: I ran out of Steiner points, but the mesh has\n"); if (m->badsubsegs.items == 1) { printf(" one encroached subsegment, and therefore might not be truly\n" ); } else { printf(" %ld encroached subsegments, and therefore might not be truly\n" , m->badsubsegs.items); } printf(" Delaunay. If the Delaunay property is important to you,\n"); printf(" try increasing the number of Steiner points (controlled by\n"); printf(" the -S switch) slightly and try again.\n\n"); }}#endif /* not CDT_ONLY *//** **//** **//********* Mesh quality maintenance ends here *********//*****************************************************************************//* *//* highorder() Create extra nodes for quadratic subparametric elements. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid highorder(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void highorder(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri triangleloop, trisym; struct osub checkmark; vertex newvertex; vertex torg, tdest; int i; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */ if (!b->quiet) { printf("Adding vertices for second-order triangles.\n"); } /* The following line ensures that dead items in the pool of nodes */ /* cannot be allocated for the extra nodes associated with high */ /* order elements. This ensures that the primary nodes (at the */ /* corners of elements) will occur earlier in the output files, and */ /* have lower indices, than the extra nodes. */ m->vertices.deaditemstack = (VOID *) NULL; traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); /* To loop over the set of edges, loop over all triangles, and look at */ /* the three edges of each triangle. If there isn't another triangle */ /* adjacent to the edge, operate on the edge. If there is another */ /* adjacent triangle, operate on the edge only if the current triangle */ /* has a smaller pointer than its neighbor. This way, each edge is */ /* considered only once. */ while (triangleloop.tri != (triangle *) NULL) { for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { sym(triangleloop, trisym); if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { org(triangleloop, torg); dest(triangleloop, tdest); /* Create a new node in the middle of the edge. Interpolate */ /* its attributes. */ newvertex = (vertex) poolalloc(&m->vertices); for (i = 0; i < 2 + m->nextras; i++) { newvertex[i] = 0.5 * (torg[i] + tdest[i]); } /* Set the new node's marker to zero or one, depending on */ /* whether it lies on a boundary. */ setvertexmark(newvertex, trisym.tri == m->dummytri); setvertextype(newvertex, trisym.tri == m->dummytri ? FREEVERTEX : SEGMENTVERTEX); if (b->usesegments) { tspivot(triangleloop, checkmark); /* If this edge is a segment, transfer the marker to the new node. */ if (checkmark.ss != m->dummysub) { setvertexmark(newvertex, mark(checkmark)); setvertextype(newvertex, SEGMENTVERTEX); } } if (b->verbose > 1) { printf(" Creating (%.12g, %.12g).\n", newvertex[0], newvertex[1]); } /* Record the new node in the (one or two) adjacent elements. */ triangleloop.tri[m->highorderindex + triangleloop.orient] = (triangle) newvertex; if (trisym.tri != m->dummytri) { trisym.tri[m->highorderindex + trisym.orient] = (triangle) newvertex; } } } triangleloop.tri = triangletraverse(m); }}/********* File I/O routines begin here *********//** **//** **//*****************************************************************************//* *//* readline() Read a nonempty line from a file. *//* *//* A line is considered "nonempty" if it contains something that looks like *//* a number. Comments (prefaced by `#') are ignored. *//* *//*****************************************************************************/#ifndef TRILIBRARY#ifdef ANSI_DECLARATORSchar *readline(char *string, FILE *infile, char *infilename)#else /* not ANSI_DECLARATORS */char *readline(string, infile, infilename)char *string;FILE *infile;char *infilename;#endif /* not ANSI_DECLARATORS */{ char *result; /* Search for something that looks like a number. */ do { result = fgets(string, INPUTLINESIZE, infile); if (result == (char *) NULL) { printf(" Error: Unexpected end of file in %s.\n", infilename); triexit(1); } /* Skip anything that doesn't look like a number, a comment, */ /* or the end of a line. */ while ((*result != '\0') && (*result != '#') && (*result != '.') && (*result != '+') && (*result != '-') && ((*result < '0') || (*result > '9'))) { result++; } /* If it's a comment or end of line, read another line and try again. */ } while ((*result == '#') || (*result == '\0')); return result;}#endif /* not TRILIBRARY *//*****************************************************************************//* *//* findfield() Find the next field of a string. *//* *//* Jumps past the current field by searching for whitespace, then jumps *//* past the whitespace to find the next field. *//* *//*****************************************************************************/#ifndef TRILIBRARY#ifdef ANSI_DECLARATORSchar *findfield(char *string)#else /* not ANSI_DECLARATORS */char *findfield(string)char *string;#endif /* not ANSI_DECLARATORS */{ char *result; result = string; /* Skip the current field. Stop upon reaching whitespace. */ while ((*result != '\0') && (*result != '#') && (*result != ' ') && (*result != '\t')) { result++; } /* Now skip the whitespace and anything else that doesn't look like a */ /* number, a comment, or the end of a line. */ while ((*result != '\0') && (*result != '#') && (*result != '.') && (*result != '+') && (*result != '-') && ((*result < '0') || (*result > '9'))) { result++; } /* Check for a comment (prefixed with `#'). */ if (*result == '#') { *result = '\0'; } return result;}#endif /* not TRILIBRARY *//*****************************************************************************//* *//* readnodes() Read the vertices from a file, which may be a .node or *//* .poly file. *//* *//*****************************************************************************/#ifndef TRILIBRARY#ifdef ANSI_DECLARATORSvoid readnodes(struct mesh *m, struct behavior *b, char *nodefilename, char *polyfilename, FILE **polyfile)#else /* not ANSI_DECLARATORS */void readnodes(m, b, nodefilename, polyfilename, polyfile)struct mesh *m;struct behavior *b;char *nodefilename;char *polyfilename;FILE **polyfile;#endif /* not ANSI_DECLARATORS */{ FILE *infile; vertex vertexloop; char inputline[INPUTLINESIZE]; char *stringptr; char *infilename; REAL x, y; int firstnode; int nodemarkers; int currentmarker; int i, j; if (b->poly) { /* Read the vertices from a .poly file. */ if (!b->quiet) { printf("Opening %s.\n", polyfilename); } *polyfile = fopen(polyfilename, "r"); if (*polyfile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", polyfilename); triexit(1); } /* Read number of vertices, number of dimensions, number of vertex */ /* attributes, and number of boundary markers. */ stringptr = readline(inputline, *polyfile, polyfilename); m->invertices = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { m->mesh_dim = 2; } else { m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { m->nextras = 0; } else { m->nextras = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { nodemarkers = 0; } else { nodemarkers = (int) strtol(stringptr, &stringptr, 0); } if (m->invertices > 0) { infile = *polyfile; infilename = polyfilename; m->readnodefile = 0; } else { /* If the .poly file claims there are zero vertices, that means that */ /* the vertices should be read from a separate .node file. */ m->readnodefile = 1; infilename = nodefilename; } } else { m->readnodefile = 1; infilename = nodefilename; *polyfile = (FILE *) NULL; } if (m->readnodefile) { /* Read the vertices from a .node file. */ if (!b->quiet) { printf("Opening %s.\n", nodefilename); } infile = fopen(nodefilename, "r"); if (infile == (FILE *) NULL) { printf(" Error: Cannot access file %s.\n", nodefilename); triexit(1); } /* Read number of vertices, number of dimensions, number of vertex */ /* attributes, and number of boundary markers. */ stringptr = readline(inputline, infile, nodefilename); m->invertices = (int) strtol(stringptr, &stringptr, 0); stringptr = findfield(stringptr); if (*stringptr == '\0') { m->mesh_dim = 2; } else { m->mesh_dim = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { m->nextras = 0; } else { m->nextras = (int) strtol(stringptr, &stringptr, 0); } stringptr = findfield(stringptr); if (*stringptr == '\0') { nodemarkers = 0; } else { nodemarkers = (int) strtol(stringptr, &stringptr, 0); } } if (m->invertices < 3) { printf("Error: Input must have at least three input vertices.\n"); triexit(1); } if (m->mesh_dim != 2) { printf("Error: Triangle only works with two-dimensional meshes.\n"); triexit(1); } if (m->nextras == 0) { b->weighted = 0; } initializevertexpool(m, b); /* Read the vertices. */ for (i = 0; i < m->invertices; i++) { vertexloop = (vertex) poolalloc(&m->vertices); stringptr = readline(inputline, infile, infilename); if (i == 0) { firstnode = (int) strtol(stringptr, &stringptr, 0); if ((firstnode == 0) || (firstnode == 1)) { b->firstnumber = firstnode; } } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Vertex %d has no x coordinate.\n", b->firstnumber + i); triexit(1); } x = (REAL) strtod(stringptr, &stringptr); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Vertex %d has no y coordinate.\n", b->firstnumber + i); triexit(1); } y = (REAL) strtod(stringptr, &stringptr); vertexloop[0] = x; vertexloop[1] = y; /* Read the vertex attributes. */ for (j = 2; j < 2 + m->nextras; j++) { stringptr = findfield(stringptr); if (*stringptr == '\0') { vertexloop[j] = 0.0; } else { vertexloop[j] = (REAL) strtod(stringptr, &stringptr); } } if (nodemarkers) { /* Read a vertex marker. */ stringptr = findfield(stringptr); if (*stringptr == '\0') { setvertexmark(vertexloop, 0); } else { currentmarker = (int) strtol(stringptr, &stringptr, 0); setvertexmark(vertexloop, currentmarker); } } else { /* If no markers are specified in the file, they default to zero. */ setvertexmark(vertexloop, 0); } setvertextype(vertexloop, INPUTVERTEX); /* Determine the smallest and largest x and y coordinates. */ if (i == 0) { m->xmin = m->xmax = x; m->ymin = m->ymax = y; } else { m->xmin = (x < m->xmin) ? x : m->xmin; m->xmax = (x > m->xmax) ? x : m->xmax; m->ymin = (y < m->ymin) ? y : m->ymin; m->ymax = (y > m->ymax) ? y : m->ymax; } } if (m->readnodefile) { fclose(infile); } /* Nonexistent x value used as a flag to mark circle events in sweepline */ /* Delaunay algorithm. */ m->xminextreme = 10 * m->xmin - 9 * m->xmax;}#endif /* not TRILIBRARY *//*****************************************************************************//* *//* transfernodes() Read the vertices from memory. *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid transfernodes(struct mesh *m, struct behavior *b, REAL *pointlist, REAL *pointattriblist, int *pointmarkerlist, int numberofpoints, int numberofpointattribs)#else /* not ANSI_DECLARATORS */void transfernodes(m, b, pointlist, pointattriblist, pointmarkerlist, numberofpoints, numberofpointattribs)struct mesh *m;struct behavior *b;REAL *pointlist;REAL *pointattriblist;int *pointmarkerlist;int numberofpoints;int numberofpointattribs;#endif /* not ANSI_DECLARATORS */{ vertex vertexloop; REAL x, y; int i, j; int coordindex; int attribindex; m->invertices = numberofpoints; m->mesh_dim = 2; m->nextras = numberofpointattribs; m->readnodefile = 0; if (m->invertices < 3) { printf("Error: Input must have at least three input vertices.\n"); triexit(1); } if (m->nextras == 0) { b->weighted = 0; } initializevertexpool(m, b); /* Read the vertices. */ coordindex = 0; attribindex = 0; for (i = 0; i < m->invertices; i++) { vertexloop = (vertex) poolalloc(&m->vertices); /* Read the vertex coordinates. */ x = vertexloop[0] = pointlist[coordindex++]; y = vertexloop[1] = pointlist[coordindex++]; /* Read the vertex attributes. */ for (j = 0; j < numberofpointattribs; j++) { vertexloop[2 + j] = pointattriblist[attribindex++]; } if (pointmarkerlist != (int *) NULL) { /* Read a vertex marker. */ setvertexmark(vertexloop, pointmarkerlist[i]); } else { /* If no markers are specified, they default to zero. */ setvertexmark(vertexloop, 0); } setvertextype(vertexloop, INPUTVERTEX); /* Determine the smallest and largest x and y coordinates. */ if (i == 0) { m->xmin = m->xmax = x; m->ymin = m->ymax = y; } else { m->xmin = (x < m->xmin) ? x : m->xmin; m->xmax = (x > m->xmax) ? x : m->xmax; m->ymin = (y < m->ymin) ? y : m->ymin; m->ymax = (y > m->ymax) ? y : m->ymax; } } /* Nonexistent x value used as a flag to mark circle events in sweepline */ /* Delaunay algorithm. */ m->xminextreme = 10 * m->xmin - 9 * m->xmax;}#endif /* TRILIBRARY *//*****************************************************************************//* *//* readholes() Read the holes, and possibly regional attributes and area *//* constraints, from a .poly file. *//* *//*****************************************************************************/#ifndef TRILIBRARY#ifdef ANSI_DECLARATORSvoid readholes(struct mesh *m, struct behavior *b, FILE *polyfile, char *polyfilename, REAL **hlist, int *holes, REAL **rlist, int *regions)#else /* not ANSI_DECLARATORS */void readholes(m, b, polyfile, polyfilename, hlist, holes, rlist, regions)struct mesh *m;struct behavior *b;FILE *polyfile;char *polyfilename;REAL **hlist;int *holes;REAL **rlist;int *regions;#endif /* not ANSI_DECLARATORS */{ REAL *holelist; REAL *regionlist; char inputline[INPUTLINESIZE]; char *stringptr; int index; int i; /* Read the holes. */ stringptr = readline(inputline, polyfile, polyfilename); *holes = (int) strtol(stringptr, &stringptr, 0); if (*holes > 0) { holelist = (REAL *) trimalloc(2 * *holes * (int) sizeof(REAL)); *hlist = holelist; for (i = 0; i < 2 * *holes; i += 2) { stringptr = readline(inputline, polyfile, polyfilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d has no x coordinate.\n", b->firstnumber + (i >> 1)); triexit(1); } else { holelist[i] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Hole %d has no y coordinate.\n", b->firstnumber + (i >> 1)); triexit(1); } else { holelist[i + 1] = (REAL) strtod(stringptr, &stringptr); } } } else { *hlist = (REAL *) NULL; }#ifndef CDT_ONLY if ((b->regionattrib || b->vararea) && !b->refine) { /* Read the area constraints. */ stringptr = readline(inputline, polyfile, polyfilename); *regions = (int) strtol(stringptr, &stringptr, 0); if (*regions > 0) { regionlist = (REAL *) trimalloc(4 * *regions * (int) sizeof(REAL)); *rlist = regionlist; index = 0; for (i = 0; i < *regions; i++) { stringptr = readline(inputline, polyfile, polyfilename); stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no x coordinate.\n", b->firstnumber + i); triexit(1); } else { regionlist[index++] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf("Error: Region %d has no y coordinate.\n", b->firstnumber + i); triexit(1); } else { regionlist[index++] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { printf( "Error: Region %d has no region attribute or area constraint.\n", b->firstnumber + i); triexit(1); } else { regionlist[index++] = (REAL) strtod(stringptr, &stringptr); } stringptr = findfield(stringptr); if (*stringptr == '\0') { regionlist[index] = regionlist[index - 1]; } else { regionlist[index] = (REAL) strtod(stringptr, &stringptr); } index++; } } } else { /* Set `*regions' to zero to avoid an accidental free() later. */ *regions = 0; *rlist = (REAL *) NULL; }#endif /* not CDT_ONLY */ fclose(polyfile);}#endif /* not TRILIBRARY *//*****************************************************************************//* *//* finishfile() Write the command line to the output file so the user *//* can remember how the file was generated. Close the file. *//* *//*****************************************************************************/#ifndef TRILIBRARY#ifdef ANSI_DECLARATORSvoid finishfile(FILE *outfile, int argc, char **argv)#else /* not ANSI_DECLARATORS */void finishfile(outfile, argc, argv)FILE *outfile;int argc;char **argv;#endif /* not ANSI_DECLARATORS */{ int i; fprintf(outfile, "# Generated by"); for (i = 0; i < argc; i++) { fprintf(outfile, " "); fputs(argv[i], outfile); } fprintf(outfile, "\n"); fclose(outfile);}#endif /* not TRILIBRARY *//*****************************************************************************//* *//* writenodes() Number the vertices and write them to a .node file. *//* *//* To save memory, the vertex numbers are written over the boundary markers *//* after the vertices are written to a file. *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid writenodes(struct mesh *m, struct behavior *b, REAL **pointlist, REAL **pointattriblist, int **pointmarkerlist)#else /* not ANSI_DECLARATORS */void writenodes(m, b, pointlist, pointattriblist, pointmarkerlist)struct mesh *m;struct behavior *b;REAL **pointlist;REAL **pointattriblist;int **pointmarkerlist;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSvoid writenodes(struct mesh *m, struct behavior *b, char *nodefilename, int argc, char **argv)#else /* not ANSI_DECLARATORS */void writenodes(m, b, nodefilename, argc, argv)struct mesh *m;struct behavior *b;char *nodefilename;int argc;char **argv;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY REAL *plist; REAL *palist; int *pmlist; int coordindex; int attribindex;#else /* not TRILIBRARY */ FILE *outfile;#endif /* not TRILIBRARY */ vertex vertexloop; long outvertices; int vertexnumber; int i; if (b->jettison) { outvertices = m->vertices.items - m->undeads; } else { outvertices = m->vertices.items; }#ifdef TRILIBRARY if (!b->quiet) { printf("Writing vertices.\n"); } /* Allocate memory for output vertices if necessary. */ if (*pointlist == (REAL *) NULL) { *pointlist = (REAL *) trimalloc((int) (outvertices * 2 * sizeof(REAL))); } /* Allocate memory for output vertex attributes if necessary. */ if ((m->nextras > 0) && (*pointattriblist == (REAL *) NULL)) { *pointattriblist = (REAL *) trimalloc((int) (outvertices * m->nextras * sizeof(REAL))); } /* Allocate memory for output vertex markers if necessary. */ if (!b->nobound && (*pointmarkerlist == (int *) NULL)) { *pointmarkerlist = (int *) trimalloc((int) (outvertices * sizeof(int))); } plist = *pointlist; palist = *pointattriblist; pmlist = *pointmarkerlist; coordindex = 0; attribindex = 0;#else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", nodefilename); } outfile = fopen(nodefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", nodefilename); triexit(1); } /* Number of vertices, number of dimensions, number of vertex attributes, */ /* and number of boundary markers (zero or one). */ fprintf(outfile, "%ld %d %d %d\n", outvertices, m->mesh_dim, m->nextras, 1 - b->nobound);#endif /* not TRILIBRARY */ traversalinit(&m->vertices); vertexnumber = b->firstnumber; vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) {#ifdef TRILIBRARY /* X and y coordinates. */ plist[coordindex++] = vertexloop[0]; plist[coordindex++] = vertexloop[1]; /* Vertex attributes. */ for (i = 0; i < m->nextras; i++) { palist[attribindex++] = vertexloop[2 + i]; } if (!b->nobound) { /* Copy the boundary marker. */ pmlist[vertexnumber - b->firstnumber] = vertexmark(vertexloop); }#else /* not TRILIBRARY */ /* Vertex number, x and y coordinates. */ fprintf(outfile, "%4d %.17g %.17g", vertexnumber, vertexloop[0], vertexloop[1]); for (i = 0; i < m->nextras; i++) { /* Write an attribute. */ fprintf(outfile, " %.17g", vertexloop[i + 2]); } if (b->nobound) { fprintf(outfile, "\n"); } else { /* Write the boundary marker. */ fprintf(outfile, " %d\n", vertexmark(vertexloop)); }#endif /* not TRILIBRARY */ setvertexmark(vertexloop, vertexnumber); vertexnumber++; } vertexloop = vertextraverse(m); }#ifndef TRILIBRARY finishfile(outfile, argc, argv);#endif /* not TRILIBRARY */}/*****************************************************************************//* *//* numbernodes() Number the vertices. *//* *//* Each vertex is assigned a marker equal to its number. *//* *//* Used when writenodes() is not called because no .node file is written. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid numbernodes(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void numbernodes(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ vertex vertexloop; int vertexnumber; traversalinit(&m->vertices); vertexnumber = b->firstnumber; vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { setvertexmark(vertexloop, vertexnumber); if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { vertexnumber++; } vertexloop = vertextraverse(m); }}/*****************************************************************************//* *//* writeelements() Write the triangles to an .ele file. *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid writeelements(struct mesh *m, struct behavior *b, int **trianglelist, REAL **triangleattriblist)#else /* not ANSI_DECLARATORS */void writeelements(m, b, trianglelist, triangleattriblist)struct mesh *m;struct behavior *b;int **trianglelist;REAL **triangleattriblist;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSvoid writeelements(struct mesh *m, struct behavior *b, char *elefilename, int argc, char **argv)#else /* not ANSI_DECLARATORS */void writeelements(m, b, elefilename, argc, argv)struct mesh *m;struct behavior *b;char *elefilename;int argc;char **argv;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY int *tlist; REAL *talist; int vertexindex; int attribindex;#else /* not TRILIBRARY */ FILE *outfile;#endif /* not TRILIBRARY */ struct otri triangleloop; vertex p1, p2, p3; vertex mid1, mid2, mid3; long elementnumber; int i;#ifdef TRILIBRARY if (!b->quiet) { printf("Writing triangles.\n"); } /* Allocate memory for output triangles if necessary. */ if (*trianglelist == (int *) NULL) { *trianglelist = (int *) trimalloc((int) (m->triangles.items * ((b->order + 1) * (b->order + 2) / 2) * sizeof(int))); } /* Allocate memory for output triangle attributes if necessary. */ if ((m->eextras > 0) && (*triangleattriblist == (REAL *) NULL)) { *triangleattriblist = (REAL *) trimalloc((int) (m->triangles.items * m->eextras * sizeof(REAL))); } tlist = *trianglelist; talist = *triangleattriblist; vertexindex = 0; attribindex = 0;#else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", elefilename); } outfile = fopen(elefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", elefilename); triexit(1); } /* Number of triangles, vertices per triangle, attributes per triangle. */ fprintf(outfile, "%ld %d %d\n", m->triangles.items, (b->order + 1) * (b->order + 2) / 2, m->eextras);#endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, p1); dest(triangleloop, p2); apex(triangleloop, p3); if (b->order == 1) {#ifdef TRILIBRARY tlist[vertexindex++] = vertexmark(p1); tlist[vertexindex++] = vertexmark(p2); tlist[vertexindex++] = vertexmark(p3);#else /* not TRILIBRARY */ /* Triangle number, indices for three vertices. */ fprintf(outfile, "%4ld %4d %4d %4d", elementnumber, vertexmark(p1), vertexmark(p2), vertexmark(p3));#endif /* not TRILIBRARY */ } else { mid1 = (vertex) triangleloop.tri[m->highorderindex + 1]; mid2 = (vertex) triangleloop.tri[m->highorderindex + 2]; mid3 = (vertex) triangleloop.tri[m->highorderindex];#ifdef TRILIBRARY tlist[vertexindex++] = vertexmark(p1); tlist[vertexindex++] = vertexmark(p2); tlist[vertexindex++] = vertexmark(p3); tlist[vertexindex++] = vertexmark(mid1); tlist[vertexindex++] = vertexmark(mid2); tlist[vertexindex++] = vertexmark(mid3);#else /* not TRILIBRARY */ /* Triangle number, indices for six vertices. */ fprintf(outfile, "%4ld %4d %4d %4d %4d %4d %4d", elementnumber, vertexmark(p1), vertexmark(p2), vertexmark(p3), vertexmark(mid1), vertexmark(mid2), vertexmark(mid3));#endif /* not TRILIBRARY */ }#ifdef TRILIBRARY for (i = 0; i < m->eextras; i++) { talist[attribindex++] = elemattribute(triangleloop, i); }#else /* not TRILIBRARY */ for (i = 0; i < m->eextras; i++) { fprintf(outfile, " %.17g", elemattribute(triangleloop, i)); } fprintf(outfile, "\n");#endif /* not TRILIBRARY */ triangleloop.tri = triangletraverse(m); elementnumber++; }#ifndef TRILIBRARY finishfile(outfile, argc, argv);#endif /* not TRILIBRARY */}/*****************************************************************************//* *//* writepoly() Write the segments and holes to a .poly file. *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid writepoly(struct mesh *m, struct behavior *b, int **segmentlist, int **segmentmarkerlist)#else /* not ANSI_DECLARATORS */void writepoly(m, b, segmentlist, segmentmarkerlist)struct mesh *m;struct behavior *b;int **segmentlist;int **segmentmarkerlist;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSvoid writepoly(struct mesh *m, struct behavior *b, char *polyfilename, REAL *holelist, int holes, REAL *regionlist, int regions, int argc, char **argv)#else /* not ANSI_DECLARATORS */void writepoly(m, b, polyfilename, holelist, holes, regionlist, regions, argc, argv)struct mesh *m;struct behavior *b;char *polyfilename;REAL *holelist;int holes;REAL *regionlist;int regions;int argc;char **argv;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY int *slist; int *smlist; int index;#else /* not TRILIBRARY */ FILE *outfile; long holenumber, regionnumber;#endif /* not TRILIBRARY */ struct osub subsegloop; vertex endpoint1, endpoint2; long subsegnumber;#ifdef TRILIBRARY if (!b->quiet) { printf("Writing segments.\n"); } /* Allocate memory for output segments if necessary. */ if (*segmentlist == (int *) NULL) { *segmentlist = (int *) trimalloc((int) (m->subsegs.items * 2 * sizeof(int))); } /* Allocate memory for output segment markers if necessary. */ if (!b->nobound && (*segmentmarkerlist == (int *) NULL)) { *segmentmarkerlist = (int *) trimalloc((int) (m->subsegs.items * sizeof(int))); } slist = *segmentlist; smlist = *segmentmarkerlist; index = 0;#else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", polyfilename); } outfile = fopen(polyfilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", polyfilename); triexit(1); } /* The zero indicates that the vertices are in a separate .node file. */ /* Followed by number of dimensions, number of vertex attributes, */ /* and number of boundary markers (zero or one). */ fprintf(outfile, "%d %d %d %d\n", 0, m->mesh_dim, m->nextras, 1 - b->nobound); /* Number of segments, number of boundary markers (zero or one). */ fprintf(outfile, "%ld %d\n", m->subsegs.items, 1 - b->nobound);#endif /* not TRILIBRARY */ traversalinit(&m->subsegs); subsegloop.ss = subsegtraverse(m); subsegloop.ssorient = 0; subsegnumber = b->firstnumber; while (subsegloop.ss != (subseg *) NULL) { sorg(subsegloop, endpoint1); sdest(subsegloop, endpoint2);#ifdef TRILIBRARY /* Copy indices of the segment's two endpoints. */ slist[index++] = vertexmark(endpoint1); slist[index++] = vertexmark(endpoint2); if (!b->nobound) { /* Copy the boundary marker. */ smlist[subsegnumber - b->firstnumber] = mark(subsegloop); }#else /* not TRILIBRARY */ /* Segment number, indices of its two endpoints, and possibly a marker. */ if (b->nobound) { fprintf(outfile, "%4ld %4d %4d\n", subsegnumber, vertexmark(endpoint1), vertexmark(endpoint2)); } else { fprintf(outfile, "%4ld %4d %4d %4d\n", subsegnumber, vertexmark(endpoint1), vertexmark(endpoint2), mark(subsegloop)); }#endif /* not TRILIBRARY */ subsegloop.ss = subsegtraverse(m); subsegnumber++; }#ifndef TRILIBRARY#ifndef CDT_ONLY fprintf(outfile, "%d\n", holes); if (holes > 0) { for (holenumber = 0; holenumber < holes; holenumber++) { /* Hole number, x and y coordinates. */ fprintf(outfile, "%4ld %.17g %.17g\n", b->firstnumber + holenumber, holelist[2 * holenumber], holelist[2 * holenumber + 1]); } } if (regions > 0) { fprintf(outfile, "%d\n", regions); for (regionnumber = 0; regionnumber < regions; regionnumber++) { /* Region number, x and y coordinates, attribute, maximum area. */ fprintf(outfile, "%4ld %.17g %.17g %.17g %.17g\n", b->firstnumber + regionnumber, regionlist[4 * regionnumber], regionlist[4 * regionnumber + 1], regionlist[4 * regionnumber + 2], regionlist[4 * regionnumber + 3]); } }#endif /* not CDT_ONLY */ finishfile(outfile, argc, argv);#endif /* not TRILIBRARY */}/*****************************************************************************//* *//* writeedges() Write the edges to an .edge file. *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid writeedges(struct mesh *m, struct behavior *b, int **edgelist, int **edgemarkerlist)#else /* not ANSI_DECLARATORS */void writeedges(m, b, edgelist, edgemarkerlist)struct mesh *m;struct behavior *b;int **edgelist;int **edgemarkerlist;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSvoid writeedges(struct mesh *m, struct behavior *b, char *edgefilename, int argc, char **argv)#else /* not ANSI_DECLARATORS */void writeedges(m, b, edgefilename, argc, argv)struct mesh *m;struct behavior *b;char *edgefilename;int argc;char **argv;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY int *elist; int *emlist; int index;#else /* not TRILIBRARY */ FILE *outfile;#endif /* not TRILIBRARY */ struct otri triangleloop, trisym; struct osub checkmark; vertex p1, p2; long edgenumber; triangle ptr; /* Temporary variable used by sym(). */ subseg sptr; /* Temporary variable used by tspivot(). */#ifdef TRILIBRARY if (!b->quiet) { printf("Writing edges.\n"); } /* Allocate memory for edges if necessary. */ if (*edgelist == (int *) NULL) { *edgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); } /* Allocate memory for edge markers if necessary. */ if (!b->nobound && (*edgemarkerlist == (int *) NULL)) { *edgemarkerlist = (int *) trimalloc((int) (m->edges * sizeof(int))); } elist = *edgelist; emlist = *edgemarkerlist; index = 0;#else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", edgefilename); } outfile = fopen(edgefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", edgefilename); triexit(1); } /* Number of edges, number of boundary markers (zero or one). */ fprintf(outfile, "%ld %d\n", m->edges, 1 - b->nobound);#endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); edgenumber = b->firstnumber; /* To loop over the set of edges, loop over all triangles, and look at */ /* the three edges of each triangle. If there isn't another triangle */ /* adjacent to the edge, operate on the edge. If there is another */ /* adjacent triangle, operate on the edge only if the current triangle */ /* has a smaller pointer than its neighbor. This way, each edge is */ /* considered only once. */ while (triangleloop.tri != (triangle *) NULL) { for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { sym(triangleloop, trisym); if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { org(triangleloop, p1); dest(triangleloop, p2);#ifdef TRILIBRARY elist[index++] = vertexmark(p1); elist[index++] = vertexmark(p2);#endif /* TRILIBRARY */ if (b->nobound) {#ifndef TRILIBRARY /* Edge number, indices of two endpoints. */ fprintf(outfile, "%4ld %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2));#endif /* not TRILIBRARY */ } else { /* Edge number, indices of two endpoints, and a boundary marker. */ /* If there's no subsegment, the boundary marker is zero. */ if (b->usesegments) { tspivot(triangleloop, checkmark); if (checkmark.ss == m->dummysub) {#ifdef TRILIBRARY emlist[edgenumber - b->firstnumber] = 0;#else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2), 0);#endif /* not TRILIBRARY */ } else {#ifdef TRILIBRARY emlist[edgenumber - b->firstnumber] = mark(checkmark);#else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2), mark(checkmark));#endif /* not TRILIBRARY */ } } else {#ifdef TRILIBRARY emlist[edgenumber - b->firstnumber] = trisym.tri == m->dummytri;#else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d %d\n", edgenumber, vertexmark(p1), vertexmark(p2), trisym.tri == m->dummytri);#endif /* not TRILIBRARY */ } } edgenumber++; } } triangleloop.tri = triangletraverse(m); }#ifndef TRILIBRARY finishfile(outfile, argc, argv);#endif /* not TRILIBRARY */}/*****************************************************************************//* *//* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge *//* file. *//* *//* The Voronoi diagram is the geometric dual of the Delaunay triangulation. *//* Hence, the Voronoi vertices are listed by traversing the Delaunay *//* triangles, and the Voronoi edges are listed by traversing the Delaunay *//* edges. *//* *//* WARNING: In order to assign numbers to the Voronoi vertices, this *//* procedure messes up the subsegments or the extra nodes of every *//* element. Hence, you should call this procedure last. *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid writevoronoi(struct mesh *m, struct behavior *b, REAL **vpointlist, REAL **vpointattriblist, int **vpointmarkerlist, int **vedgelist, int **vedgemarkerlist, REAL **vnormlist)#else /* not ANSI_DECLARATORS */void writevoronoi(m, b, vpointlist, vpointattriblist, vpointmarkerlist, vedgelist, vedgemarkerlist, vnormlist)struct mesh *m;struct behavior *b;REAL **vpointlist;REAL **vpointattriblist;int **vpointmarkerlist;int **vedgelist;int **vedgemarkerlist;REAL **vnormlist;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSvoid writevoronoi(struct mesh *m, struct behavior *b, char *vnodefilename, char *vedgefilename, int argc, char **argv)#else /* not ANSI_DECLARATORS */void writevoronoi(m, b, vnodefilename, vedgefilename, argc, argv)struct mesh *m;struct behavior *b;char *vnodefilename;char *vedgefilename;int argc;char **argv;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY REAL *plist; REAL *palist; int *elist; REAL *normlist; int coordindex; int attribindex;#else /* not TRILIBRARY */ FILE *outfile;#endif /* not TRILIBRARY */ struct otri triangleloop, trisym; vertex torg, tdest, tapex; REAL circumcenter[2]; REAL xi, eta; long vnodenumber, vedgenumber; int p1, p2; int i; triangle ptr; /* Temporary variable used by sym(). */#ifdef TRILIBRARY if (!b->quiet) { printf("Writing Voronoi vertices.\n"); } /* Allocate memory for Voronoi vertices if necessary. */ if (*vpointlist == (REAL *) NULL) { *vpointlist = (REAL *) trimalloc((int) (m->triangles.items * 2 * sizeof(REAL))); } /* Allocate memory for Voronoi vertex attributes if necessary. */ if (*vpointattriblist == (REAL *) NULL) { *vpointattriblist = (REAL *) trimalloc((int) (m->triangles.items * m->nextras * sizeof(REAL))); } *vpointmarkerlist = (int *) NULL; plist = *vpointlist; palist = *vpointattriblist; coordindex = 0; attribindex = 0;#else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", vnodefilename); } outfile = fopen(vnodefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", vnodefilename); triexit(1); } /* Number of triangles, two dimensions, number of vertex attributes, */ /* no markers. */ fprintf(outfile, "%ld %d %d %d\n", m->triangles.items, 2, m->nextras, 0);#endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; vnodenumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, torg); dest(triangleloop, tdest); apex(triangleloop, tapex); findcircumcenter(m, b, torg, tdest, tapex, circumcenter, &xi, &eta, 0);#ifdef TRILIBRARY /* X and y coordinates. */ plist[coordindex++] = circumcenter[0]; plist[coordindex++] = circumcenter[1]; for (i = 2; i < 2 + m->nextras; i++) { /* Interpolate the vertex attributes at the circumcenter. */ palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i]) + eta * (tapex[i] - torg[i]); }#else /* not TRILIBRARY */ /* Voronoi vertex number, x and y coordinates. */ fprintf(outfile, "%4ld %.17g %.17g", vnodenumber, circumcenter[0], circumcenter[1]); for (i = 2; i < 2 + m->nextras; i++) { /* Interpolate the vertex attributes at the circumcenter. */ fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i]) + eta * (tapex[i] - torg[i])); } fprintf(outfile, "\n");#endif /* not TRILIBRARY */ * (int *) (triangleloop.tri + 6) = (int) vnodenumber; triangleloop.tri = triangletraverse(m); vnodenumber++; }#ifndef TRILIBRARY finishfile(outfile, argc, argv);#endif /* not TRILIBRARY */#ifdef TRILIBRARY if (!b->quiet) { printf("Writing Voronoi edges.\n"); } /* Allocate memory for output Voronoi edges if necessary. */ if (*vedgelist == (int *) NULL) { *vedgelist = (int *) trimalloc((int) (m->edges * 2 * sizeof(int))); } *vedgemarkerlist = (int *) NULL; /* Allocate memory for output Voronoi norms if necessary. */ if (*vnormlist == (REAL *) NULL) { *vnormlist = (REAL *) trimalloc((int) (m->edges * 2 * sizeof(REAL))); } elist = *vedgelist; normlist = *vnormlist; coordindex = 0;#else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", vedgefilename); } outfile = fopen(vedgefilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", vedgefilename); triexit(1); } /* Number of edges, zero boundary markers. */ fprintf(outfile, "%ld %d\n", m->edges, 0);#endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); vedgenumber = b->firstnumber; /* To loop over the set of edges, loop over all triangles, and look at */ /* the three edges of each triangle. If there isn't another triangle */ /* adjacent to the edge, operate on the edge. If there is another */ /* adjacent triangle, operate on the edge only if the current triangle */ /* has a smaller pointer than its neighbor. This way, each edge is */ /* considered only once. */ while (triangleloop.tri != (triangle *) NULL) { for (triangleloop.orient = 0; triangleloop.orient < 3; triangleloop.orient++) { sym(triangleloop, trisym); if ((triangleloop.tri < trisym.tri) || (trisym.tri == m->dummytri)) { /* Find the number of this triangle (and Voronoi vertex). */ p1 = * (int *) (triangleloop.tri + 6); if (trisym.tri == m->dummytri) { org(triangleloop, torg); dest(triangleloop, tdest);#ifdef TRILIBRARY /* Copy an infinite ray. Index of one endpoint, and -1. */ elist[coordindex] = p1; normlist[coordindex++] = tdest[1] - torg[1]; elist[coordindex] = -1; normlist[coordindex++] = torg[0] - tdest[0];#else /* not TRILIBRARY */ /* Write an infinite ray. Edge number, index of one endpoint, -1, */ /* and x and y coordinates of a vector representing the */ /* direction of the ray. */ fprintf(outfile, "%4ld %d %d %.17g %.17g\n", vedgenumber, p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);#endif /* not TRILIBRARY */ } else { /* Find the number of the adjacent triangle (and Voronoi vertex). */ p2 = * (int *) (trisym.tri + 6); /* Finite edge. Write indices of two endpoints. */#ifdef TRILIBRARY elist[coordindex] = p1; normlist[coordindex++] = 0.0; elist[coordindex] = p2; normlist[coordindex++] = 0.0;#else /* not TRILIBRARY */ fprintf(outfile, "%4ld %d %d\n", vedgenumber, p1, p2);#endif /* not TRILIBRARY */ } vedgenumber++; } } triangleloop.tri = triangletraverse(m); }#ifndef TRILIBRARY finishfile(outfile, argc, argv);#endif /* not TRILIBRARY */}#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid writeneighbors(struct mesh *m, struct behavior *b, int **neighborlist)#else /* not ANSI_DECLARATORS */void writeneighbors(m, b, neighborlist)struct mesh *m;struct behavior *b;int **neighborlist;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSvoid writeneighbors(struct mesh *m, struct behavior *b, char *neighborfilename, int argc, char **argv)#else /* not ANSI_DECLARATORS */void writeneighbors(m, b, neighborfilename, argc, argv)struct mesh *m;struct behavior *b;char *neighborfilename;int argc;char **argv;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{#ifdef TRILIBRARY int *nlist; int index;#else /* not TRILIBRARY */ FILE *outfile;#endif /* not TRILIBRARY */ struct otri triangleloop, trisym; long elementnumber; int neighbor1, neighbor2, neighbor3; triangle ptr; /* Temporary variable used by sym(). */#ifdef TRILIBRARY if (!b->quiet) { printf("Writing neighbors.\n"); } /* Allocate memory for neighbors if necessary. */ if (*neighborlist == (int *) NULL) { *neighborlist = (int *) trimalloc((int) (m->triangles.items * 3 * sizeof(int))); } nlist = *neighborlist; index = 0;#else /* not TRILIBRARY */ if (!b->quiet) { printf("Writing %s.\n", neighborfilename); } outfile = fopen(neighborfilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", neighborfilename); triexit(1); } /* Number of triangles, three neighbors per triangle. */ fprintf(outfile, "%ld %d\n", m->triangles.items, 3);#endif /* not TRILIBRARY */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { * (int *) (triangleloop.tri + 6) = (int) elementnumber; triangleloop.tri = triangletraverse(m); elementnumber++; } * (int *) (m->dummytri + 6) = -1; traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); elementnumber = b->firstnumber; while (triangleloop.tri != (triangle *) NULL) { triangleloop.orient = 1; sym(triangleloop, trisym); neighbor1 = * (int *) (trisym.tri + 6); triangleloop.orient = 2; sym(triangleloop, trisym); neighbor2 = * (int *) (trisym.tri + 6); triangleloop.orient = 0; sym(triangleloop, trisym); neighbor3 = * (int *) (trisym.tri + 6);#ifdef TRILIBRARY nlist[index++] = neighbor1; nlist[index++] = neighbor2; nlist[index++] = neighbor3;#else /* not TRILIBRARY */ /* Triangle number, neighboring triangle numbers. */ fprintf(outfile, "%4ld %d %d %d\n", elementnumber, neighbor1, neighbor2, neighbor3);#endif /* not TRILIBRARY */ triangleloop.tri = triangletraverse(m); elementnumber++; }#ifndef TRILIBRARY finishfile(outfile, argc, argv);#endif /* not TRILIBRARY */}/*****************************************************************************//* *//* writeoff() Write the triangulation to an .off file. *//* *//* OFF stands for the Object File Format, a format used by the Geometry *//* Center's Geomview package. *//* *//*****************************************************************************/#ifndef TRILIBRARY#ifdef ANSI_DECLARATORSvoid writeoff(struct mesh *m, struct behavior *b, char *offfilename, int argc, char **argv)#else /* not ANSI_DECLARATORS */void writeoff(m, b, offfilename, argc, argv)struct mesh *m;struct behavior *b;char *offfilename;int argc;char **argv;#endif /* not ANSI_DECLARATORS */{ FILE *outfile; struct otri triangleloop; vertex vertexloop; vertex p1, p2, p3; long outvertices; if (!b->quiet) { printf("Writing %s.\n", offfilename); } if (b->jettison) { outvertices = m->vertices.items - m->undeads; } else { outvertices = m->vertices.items; } outfile = fopen(offfilename, "w"); if (outfile == (FILE *) NULL) { printf(" Error: Cannot create file %s.\n", offfilename); triexit(1); } /* Number of vertices, triangles, and edges. */ fprintf(outfile, "OFF\n%ld %ld %ld\n", outvertices, m->triangles.items, m->edges); /* Write the vertices. */ traversalinit(&m->vertices); vertexloop = vertextraverse(m); while (vertexloop != (vertex) NULL) { if (!b->jettison || (vertextype(vertexloop) != UNDEADVERTEX)) { /* The "0.0" is here because the OFF format uses 3D coordinates. */ fprintf(outfile, " %.17g %.17g %.17g\n", vertexloop[0], vertexloop[1], 0.0); } vertexloop = vertextraverse(m); } /* Write the triangles. */ traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, p1); dest(triangleloop, p2); apex(triangleloop, p3); /* The "3" means a three-vertex polygon. */ fprintf(outfile, " 3 %4d %4d %4d\n", vertexmark(p1) - b->firstnumber, vertexmark(p2) - b->firstnumber, vertexmark(p3) - b->firstnumber); triangleloop.tri = triangletraverse(m); } finishfile(outfile, argc, argv);}#endif /* not TRILIBRARY *//** **//** **//********* File I/O routines end here *********//*****************************************************************************//* *//* quality_statistics() Print statistics about the quality of the mesh. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid quality_statistics(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void quality_statistics(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ struct otri triangleloop; vertex p[3]; REAL cossquaretable[8]; REAL ratiotable[16]; REAL dx[3], dy[3]; REAL edgelength[3]; REAL dotproduct; REAL cossquare; REAL triarea; REAL shortest, longest; REAL trilongest2; REAL smallestarea, biggestarea; REAL triminaltitude2; REAL minaltitude; REAL triaspect2; REAL worstaspect; REAL smallestangle, biggestangle; REAL radconst, degconst; int angletable[18]; int aspecttable[16]; int aspectindex; int tendegree; int acutebiggest; int i, ii, j, k; printf("Mesh quality statistics:\n\n"); radconst = PI / 18.0; degconst = 180.0 / PI; for (i = 0; i < 8; i++) { cossquaretable[i] = cos(radconst * (REAL) (i + 1)); cossquaretable[i] = cossquaretable[i] * cossquaretable[i]; } for (i = 0; i < 18; i++) { angletable[i] = 0; } ratiotable[0] = 1.5; ratiotable[1] = 2.0; ratiotable[2] = 2.5; ratiotable[3] = 3.0; ratiotable[4] = 4.0; ratiotable[5] = 6.0; ratiotable[6] = 10.0; ratiotable[7] = 15.0; ratiotable[8] = 25.0; ratiotable[9] = 50.0; ratiotable[10] = 100.0; ratiotable[11] = 300.0; ratiotable[12] = 1000.0; ratiotable[13] = 10000.0; ratiotable[14] = 100000.0; ratiotable[15] = 0.0; for (i = 0; i < 16; i++) { aspecttable[i] = 0; } worstaspect = 0.0; minaltitude = m->xmax - m->xmin + m->ymax - m->ymin; minaltitude = minaltitude * minaltitude; shortest = minaltitude; longest = 0.0; smallestarea = minaltitude; biggestarea = 0.0; worstaspect = 0.0; smallestangle = 0.0; biggestangle = 2.0; acutebiggest = 1; traversalinit(&m->triangles); triangleloop.tri = triangletraverse(m); triangleloop.orient = 0; while (triangleloop.tri != (triangle *) NULL) { org(triangleloop, p[0]); dest(triangleloop, p[1]); apex(triangleloop, p[2]); trilongest2 = 0.0; for (i = 0; i < 3; i++) { j = plus1mod3[i]; k = minus1mod3[i]; dx[i] = p[j][0] - p[k][0]; dy[i] = p[j][1] - p[k][1]; edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i]; if (edgelength[i] > trilongest2) { trilongest2 = edgelength[i]; } if (edgelength[i] > longest) { longest = edgelength[i]; } if (edgelength[i] < shortest) { shortest = edgelength[i]; } } triarea = counterclockwise(m, b, p[0], p[1], p[2]); if (triarea < smallestarea) { smallestarea = triarea; } if (triarea > biggestarea) { biggestarea = triarea; } triminaltitude2 = triarea * triarea / trilongest2; if (triminaltitude2 < minaltitude) { minaltitude = triminaltitude2; } triaspect2 = trilongest2 / triminaltitude2; if (triaspect2 > worstaspect) { worstaspect = triaspect2; } aspectindex = 0; while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex]) && (aspectindex < 15)) { aspectindex++; } aspecttable[aspectindex]++; for (i = 0; i < 3; i++) { j = plus1mod3[i]; k = minus1mod3[i]; dotproduct = dx[j] * dx[k] + dy[j] * dy[k]; cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]); tendegree = 8; for (ii = 7; ii >= 0; ii--) { if (cossquare > cossquaretable[ii]) { tendegree = ii; } } if (dotproduct <= 0.0) { angletable[tendegree]++; if (cossquare > smallestangle) { smallestangle = cossquare; } if (acutebiggest && (cossquare < biggestangle)) { biggestangle = cossquare; } } else { angletable[17 - tendegree]++; if (acutebiggest || (cossquare > biggestangle)) { biggestangle = cossquare; acutebiggest = 0; } } } triangleloop.tri = triangletraverse(m); } shortest = sqrt(shortest); longest = sqrt(longest); minaltitude = sqrt(minaltitude); worstaspect = sqrt(worstaspect); smallestarea *= 0.5; biggestarea *= 0.5; if (smallestangle >= 1.0) { smallestangle = 0.0; } else { smallestangle = degconst * acos(sqrt(smallestangle)); } if (biggestangle >= 1.0) { biggestangle = 180.0; } else { if (acutebiggest) { biggestangle = degconst * acos(sqrt(biggestangle)); } else { biggestangle = 180.0 - degconst * acos(sqrt(biggestangle)); } } printf(" Smallest area: %16.5g | Largest area: %16.5g\n", smallestarea, biggestarea); printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n", shortest, longest); printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n", minaltitude, worstaspect); printf(" Triangle aspect ratio histogram:\n"); printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8], aspecttable[8]); for (i = 1; i < 7; i++) { printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n", ratiotable[i - 1], ratiotable[i], aspecttable[i], ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]); } printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n", ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14], aspecttable[15]); printf(" (Aspect ratio is longest edge divided by shortest altitude)\n\n"); printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n", smallestangle, biggestangle); printf(" Angle histogram:\n"); for (i = 0; i < 9; i++) { printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n", i * 10, i * 10 + 10, angletable[i], i * 10 + 90, i * 10 + 100, angletable[i + 9]); } printf("\n");}/*****************************************************************************//* *//* statistics() Print all sorts of cool facts. *//* *//*****************************************************************************/#ifdef ANSI_DECLARATORSvoid statistics(struct mesh *m, struct behavior *b)#else /* not ANSI_DECLARATORS */void statistics(m, b)struct mesh *m;struct behavior *b;#endif /* not ANSI_DECLARATORS */{ printf("\nStatistics:\n\n"); printf(" Input vertices: %d\n", m->invertices); if (b->refine) { printf(" Input triangles: %d\n", m->inelements); } if (b->poly) { printf(" Input segments: %d\n", m->insegments); if (!b->refine) { printf(" Input holes: %d\n", m->holes); } } printf("\n Mesh vertices: %ld\n", m->vertices.items - m->undeads); printf(" Mesh triangles: %ld\n", m->triangles.items); printf(" Mesh edges: %ld\n", m->edges); printf(" Mesh exterior boundary edges: %ld\n", m->hullsize); if (b->poly || b->refine) { printf(" Mesh interior boundary edges: %ld\n", m->subsegs.items - m->hullsize); printf(" Mesh subsegments (constrained edges): %ld\n", m->subsegs.items); } printf("\n"); if (b->verbose) { quality_statistics(m, b); printf("Memory allocation statistics:\n\n"); printf(" Maximum number of vertices: %ld\n", m->vertices.maxitems); printf(" Maximum number of triangles: %ld\n", m->triangles.maxitems); if (m->subsegs.maxitems > 0) { printf(" Maximum number of subsegments: %ld\n", m->subsegs.maxitems); } if (m->viri.maxitems > 0) { printf(" Maximum number of viri: %ld\n", m->viri.maxitems); } if (m->badsubsegs.maxitems > 0) { printf(" Maximum number of encroached subsegments: %ld\n", m->badsubsegs.maxitems); } if (m->badtriangles.maxitems > 0) { printf(" Maximum number of bad triangles: %ld\n", m->badtriangles.maxitems); } if (m->flipstackers.maxitems > 0) { printf(" Maximum number of stacked triangle flips: %ld\n", m->flipstackers.maxitems); } if (m->splaynodes.maxitems > 0) { printf(" Maximum number of splay tree nodes: %ld\n", m->splaynodes.maxitems); } printf(" Approximate heap memory use (bytes): %ld\n\n", m->vertices.maxitems * m->vertices.itembytes + m->triangles.maxitems * m->triangles.itembytes + m->subsegs.maxitems * m->subsegs.itembytes + m->viri.maxitems * m->viri.itembytes + m->badsubsegs.maxitems * m->badsubsegs.itembytes + m->badtriangles.maxitems * m->badtriangles.itembytes + m->flipstackers.maxitems * m->flipstackers.itembytes + m->splaynodes.maxitems * m->splaynodes.itembytes); printf("Algorithmic statistics:\n\n"); if (!b->weighted) { printf(" Number of incircle tests: %ld\n", m->incirclecount); } else { printf(" Number of 3D orientation tests: %ld\n", m->orient3dcount); } printf(" Number of 2D orientation tests: %ld\n", m->counterclockcount); if (m->hyperbolacount > 0) { printf(" Number of right-of-hyperbola tests: %ld\n", m->hyperbolacount); } if (m->circletopcount > 0) { printf(" Number of circle top computations: %ld\n", m->circletopcount); } if (m->circumcentercount > 0) { printf(" Number of triangle circumcenter computations: %ld\n", m->circumcentercount); } printf("\n"); }}/*****************************************************************************//* *//* main() or triangulate() Gosh, do everything. *//* *//* The sequence is roughly as follows. Many of these steps can be skipped, *//* depending on the command line switches. *//* *//* - Initialize constants and parse the command line. *//* - Read the vertices from a file and either *//* - triangulate them (no -r), or *//* - read an old mesh from files and reconstruct it (-r). *//* - Insert the PSLG segments (-p), and possibly segments on the convex *//* hull (-c). *//* - Read the holes (-p), regional attributes (-pA), and regional area *//* constraints (-pa). Carve the holes and concavities, and spread the *//* regional attributes and area constraints. *//* - Enforce the constraints on minimum angle (-q) and maximum area (-a). *//* Also enforce the conforming Delaunay property (-q and -a). *//* - Compute the number of edges in the resulting mesh. *//* - Promote the mesh's linear triangles to higher order elements (-o). *//* - Write the output files and print the statistics. *//* - Check the consistency and Delaunay property of the mesh (-C). *//* *//*****************************************************************************/#ifdef TRILIBRARY#ifdef ANSI_DECLARATORSvoid triangulate(char *triswitches, struct triangulateio *in, struct triangulateio *out, struct triangulateio *vorout)#else /* not ANSI_DECLARATORS */void triangulate(triswitches, in, out, vorout)char *triswitches;struct triangulateio *in;struct triangulateio *out;struct triangulateio *vorout;#endif /* not ANSI_DECLARATORS */#else /* not TRILIBRARY */#ifdef ANSI_DECLARATORSint main(int argc, char **argv)#else /* not ANSI_DECLARATORS */int main(argc, argv)int argc;char **argv;#endif /* not ANSI_DECLARATORS */#endif /* not TRILIBRARY */{ struct mesh m; struct behavior b; REAL *holearray; /* Array of holes. */ REAL *regionarray; /* Array of regional attributes and area constraints. */#ifndef TRILIBRARY FILE *polyfile;#endif /* not TRILIBRARY */#ifndef NO_TIMER /* Variables for timing the performance of Triangle. The types are */ /* defined in sys/time.h. */ struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6; struct timezone tz;#endif /* not NO_TIMER */#ifndef NO_TIMER gettimeofday(&tv0, &tz);#endif /* not NO_TIMER */ triangleinit(&m);#ifdef TRILIBRARY parsecommandline(1, &triswitches, &b);#else /* not TRILIBRARY */ parsecommandline(argc, argv, &b);#endif /* not TRILIBRARY */ m.steinerleft = b.steiner;#ifdef TRILIBRARY transfernodes(&m, &b, in->pointlist, in->pointattributelist, in->pointmarkerlist, in->numberofpoints, in->numberofpointattributes);#else /* not TRILIBRARY */ readnodes(&m, &b, b.innodefilename, b.inpolyfilename, &polyfile);#endif /* not TRILIBRARY */#ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv1, &tz); }#endif /* not NO_TIMER */#ifdef CDT_ONLY m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */#else /* not CDT_ONLY */ if (b.refine) { /* Read and reconstruct a mesh. */#ifdef TRILIBRARY m.hullsize = reconstruct(&m, &b, in->trianglelist, in->triangleattributelist, in->trianglearealist, in->numberoftriangles, in->numberofcorners, in->numberoftriangleattributes, in->segmentlist, in->segmentmarkerlist, in->numberofsegments);#else /* not TRILIBRARY */ m.hullsize = reconstruct(&m, &b, b.inelefilename, b.areafilename, b.inpolyfilename, polyfile);#endif /* not TRILIBRARY */ } else { m.hullsize = delaunay(&m, &b); /* Triangulate the vertices. */ }#endif /* not CDT_ONLY */#ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv2, &tz); if (b.refine) { printf("Mesh reconstruction"); } else { printf("Delaunay"); } printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec) + (tv2.tv_usec - tv1.tv_usec) / 1000l); }#endif /* not NO_TIMER */ /* Ensure that no vertex can be mistaken for a triangular bounding */ /* box vertex in insertvertex(). */ m.infvertex1 = (vertex) NULL; m.infvertex2 = (vertex) NULL; m.infvertex3 = (vertex) NULL; if (b.usesegments) { m.checksegments = 1; /* Segments will be introduced next. */ if (!b.refine) { /* Insert PSLG segments and/or convex hull segments. */#ifdef TRILIBRARY formskeleton(&m, &b, in->segmentlist, in->segmentmarkerlist, in->numberofsegments);#else /* not TRILIBRARY */ formskeleton(&m, &b, polyfile, b.inpolyfilename);#endif /* not TRILIBRARY */ } }#ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv3, &tz); if (b.usesegments && !b.refine) { printf("Segment milliseconds: %ld\n", 1000l * (tv3.tv_sec - tv2.tv_sec) + (tv3.tv_usec - tv2.tv_usec) / 1000l); } }#endif /* not NO_TIMER */ if (b.poly && (m.triangles.items > 0)) {#ifdef TRILIBRARY holearray = in->holelist; m.holes = in->numberofholes; regionarray = in->regionlist; m.regions = in->numberofregions;#else /* not TRILIBRARY */ readholes(&m, &b, polyfile, b.inpolyfilename, &holearray, &m.holes, ®ionarray, &m.regions);#endif /* not TRILIBRARY */ if (!b.refine) { /* Carve out holes and concavities. */ carveholes(&m, &b, holearray, m.holes, regionarray, m.regions); } } else { /* Without a PSLG, there can be no holes or regional attributes */ /* or area constraints. The following are set to zero to avoid */ /* an accidental free() later. */ m.holes = 0; m.regions = 0; }#ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv4, &tz); if (b.poly && !b.refine) { printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec) + (tv4.tv_usec - tv3.tv_usec) / 1000l); } }#endif /* not NO_TIMER */#ifndef CDT_ONLY if (b.quality && (m.triangles.items > 0)) { enforcequality(&m, &b); /* Enforce angle and area constraints. */ }#endif /* not CDT_ONLY */#ifndef NO_TIMER if (!b.quiet) { gettimeofday(&tv5, &tz);#ifndef CDT_ONLY if (b.quality) { printf("Quality milliseconds: %ld\n", 1000l * (tv5.tv_sec - tv4.tv_sec) + (tv5.tv_usec - tv4.tv_usec) / 1000l); }#endif /* not CDT_ONLY */ }#endif /* not NO_TIMER */ /* Calculate the number of edges. */ m.edges = (3l * m.triangles.items + m.hullsize) / 2l; if (b.order > 1) { highorder(&m, &b); /* Promote elements to higher polynomial order. */ } if (!b.quiet) { printf("\n"); }#ifdef TRILIBRARY if (b.jettison) { out->numberofpoints = m.vertices.items - m.undeads; } else { out->numberofpoints = m.vertices.items; } out->numberofpointattributes = m.nextras; out->numberoftriangles = m.triangles.items; out->numberofcorners = (b.order + 1) * (b.order + 2) / 2; out->numberoftriangleattributes = m.eextras; out->numberofedges = m.edges; if (b.usesegments) { out->numberofsegments = m.subsegs.items; } else { out->numberofsegments = m.hullsize; } if (vorout != (struct triangulateio *) NULL) { vorout->numberofpoints = m.triangles.items; vorout->numberofpointattributes = m.nextras; vorout->numberofedges = m.edges; }#endif /* TRILIBRARY */ /* If not using iteration numbers, don't write a .node file if one was */ /* read, because the original one would be overwritten! */ if (b.nonodewritten || (b.noiterationnum && m.readnodefile)) { if (!b.quiet) {#ifdef TRILIBRARY printf("NOT writing vertices.\n");#else /* not TRILIBRARY */ printf("NOT writing a .node file.\n");#endif /* not TRILIBRARY */ } numbernodes(&m, &b); /* We must remember to number the vertices. */ } else { /* writenodes() numbers the vertices too. */#ifdef TRILIBRARY writenodes(&m, &b, &out->pointlist, &out->pointattributelist, &out->pointmarkerlist);#else /* not TRILIBRARY */ writenodes(&m, &b, b.outnodefilename, argc, argv);#endif /* TRILIBRARY */ } if (b.noelewritten) { if (!b.quiet) {#ifdef TRILIBRARY printf("NOT writing triangles.\n");#else /* not TRILIBRARY */ printf("NOT writing an .ele file.\n");#endif /* not TRILIBRARY */ } } else {#ifdef TRILIBRARY writeelements(&m, &b, &out->trianglelist, &out->triangleattributelist);#else /* not TRILIBRARY */ writeelements(&m, &b, b.outelefilename, argc, argv);#endif /* not TRILIBRARY */ } /* The -c switch (convex switch) causes a PSLG to be written */ /* even if none was read. */ if (b.poly || b.convex) { /* If not using iteration numbers, don't overwrite the .poly file. */ if (b.nopolywritten || b.noiterationnum) { if (!b.quiet) {#ifdef TRILIBRARY printf("NOT writing segments.\n");#else /* not TRILIBRARY */ printf("NOT writing a .poly file.\n");#endif /* not TRILIBRARY */ } } else {#ifdef TRILIBRARY writepoly(&m, &b, &out->segmentlist, &out->segmentmarkerlist); out->numberofholes = m.holes; out->numberofregions = m.regions; if (b.poly) { out->holelist = in->holelist; out->regionlist = in->regionlist; } else { out->holelist = (REAL *) NULL; out->regionlist = (REAL *) NULL; }#else /* not TRILIBRARY */ writepoly(&m, &b, b.outpolyfilename, holearray, m.holes, regionarray, m.regions, argc, argv);#endif /* not TRILIBRARY */ } }#ifndef TRILIBRARY#ifndef CDT_ONLY if (m.regions > 0) { trifree((VOID *) regionarray); }#endif /* not CDT_ONLY */ if (m.holes > 0) { trifree((VOID *) holearray); } if (b.geomview) { writeoff(&m, &b, b.offfilename, argc, argv); }#endif /* not TRILIBRARY */ if (b.edgesout) {#ifdef TRILIBRARY writeedges(&m, &b, &out->edgelist, &out->edgemarkerlist);#else /* not TRILIBRARY */ writeedges(&m, &b, b.edgefilename, argc, argv);#endif /* not TRILIBRARY */ } if (b.voronoi) {#ifdef TRILIBRARY writevoronoi(&m, &b, &vorout->pointlist, &vorout->pointattributelist, &vorout->pointmarkerlist, &vorout->edgelist, &vorout->edgemarkerlist, &vorout->normlist);#else /* not TRILIBRARY */ writevoronoi(&m, &b, b.vnodefilename, b.vedgefilename, argc, argv);#endif /* not TRILIBRARY */ } if (b.neighbors) {#ifdef TRILIBRARY writeneighbors(&m, &b, &out->neighborlist);#else /* not TRILIBRARY */ writeneighbors(&m, &b, b.neighborfilename, argc, argv);#endif /* not TRILIBRARY */ } if (!b.quiet) {#ifndef NO_TIMER gettimeofday(&tv6, &tz); printf("\nOutput milliseconds: %ld\n", 1000l * (tv6.tv_sec - tv5.tv_sec) + (tv6.tv_usec - tv5.tv_usec) / 1000l); printf("Total running milliseconds: %ld\n", 1000l * (tv6.tv_sec - tv0.tv_sec) + (tv6.tv_usec - tv0.tv_usec) / 1000l);#endif /* not NO_TIMER */ statistics(&m, &b); }#ifndef REDUCED if (b.docheck) { checkmesh(&m, &b); checkdelaunay(&m, &b); }#endif /* not REDUCED */ triangledeinit(&m, &b);#ifndef TRILIBRARY return 0;#endif /* not TRILIBRARY */} 0 0
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