TKG3d--Package Geom

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Geom_BSplineCurve Class Reference

Definition of the B_spline curve. 
A B-spline curve can be 
Uniform or non-uniform 
Rational or non-rational 
Periodic or non-periodic 

a b-spline curve is defined by : 
its degree; the degree for a 
Geom_BSplineCurve is limited to a value (25) 
which is defined and controlled by the system. 
This value is returned by the function MaxDegree; 

• its periodic or non-periodic nature; 
  
• a table of poles (also called control points), with 
  their associated weights if the BSpline curve is 
  rational. The poles of the curve are "control <br> points" used to deform the curve. If the curve is 
  non-periodic, the first pole is the start point of 
  the curve, and the last pole is the end point of 
  the curve. The segment which joins the first pole 
  to the second pole is the tangent to the curve at 
  its start point, and the segment which joins the 
  last pole to the second-from-last pole is the 
  tangent to the curve at its end point. If the curve 
  is periodic, these geometric properties are not 
  verified. It is more difficult to give a geometric 
  signification to the weights but are useful for 
  providing exact representations of the arcs of a 
  circle or ellipse. Moreover, if the weights of all the 
  poles are equal, the curve has a polynomial 
  equation; it is therefore a non-rational curve. 
  
• a table of knots with their multiplicities. For a 
  Geom_BSplineCurve, the table of knots is an 
  increasing sequence of reals without repetition; 
  the multiplicities define the repetition of the knots. 
  A BSpline curve is a piecewise polynomial or 
  rational curve. The knots are the parameters of 
  junction points between two pieces. The 
  multiplicity Mult(i) of the knot Knot(i) of 
  the BSpline curve is related to the degree of 
  continuity of the curve at the knot Knot(i), 
  which is equal to Degree - Mult(i) 
  where Degree is the degree of the BSpline curve. 
  If the knots are regularly spaced (i.e. the difference 
  between two consecutive knots is a constant), three 
  specific and frequently used cases of knot 
  distribution can be identified: 
  
• "uniform" if all multiplicities are equal to 1, 
  
• "quasi-uniform" if all multiplicities are equal to 1, 
  except the first and the last knot which have a 
  multiplicity of Degree + 1, where Degree is 
  the degree of the BSpline curve, 
  
• "Piecewise Bezier" if all multiplicities are equal to 
  Degree except the first and last knot which 
  have a multiplicity of Degree + 1, where 
  Degree is the degree of the BSpline curve. A 
  curve of this type is a concatenation of arcs of Bezier curves. 
  If the BSpline curve is not periodic: 
  
• the bounds of the Poles and Weights tables are 1 
  and NbPoles, where NbPoles is the number 
  of poles of the BSpline curve, 
  
• the bounds of the Knots and Multiplicities tables 
  are 1 and NbKnots, where NbKnots is the 
  number of knots of the BSpline curve. 
  If the BSpline curve is periodic, and if there are k 
  periodic knots and p periodic poles, the period is: 
  period = Knot(k + 1) - Knot(1) 
  and the poles and knots tables can be considered 
  as infinite tables, verifying: 
  
• Knot(i+k) = Knot(i) + period 
  
• Pole(i+p) = Pole(i) 
  Note: data structures of a periodic BSpline curve 
  are more complex than those of a non-periodic one. 
  Warning 
  In this class, weight value is considered to be zero if 
  the weight is less than or equal to gp::Resolution(). 
  
  References : 
  . A survey of curve and surface methods in CADG Wolfgang BOHM 
  CAGD 1 (1984) 
  . On de Boor-like algorithms and blossoming Wolfgang BOEHM 
  cagd 5 (1988) 
  . Blossoming and knot insertion algorithms for B-spline curves 
  Ronald N. GOLDMAN 
  . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA 
  . Curves and Surfaces for Computer Aided Geometric Design, 
  a practical guide Gerald Farin 
  

#include <Geom_BSplineCurve.hxx>

Inheritance diagram for Geom_BSplineCurve:

[legend]

Public Member Functions

 Geom_BSplineCurve (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, constStandard_Boolean Periodic=Standard_False) Creates a non-rational B_spline curve on the 
basis <Knots, Multiplicities> of degree <Degree>. 
 Geom_BSplineCurve (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, constStandard_Integer Degree, const Standard_Boolean Periodic=Standard_False, const Standard_Boolean CheckRational=Standard_True) Creates a rational B_spline curve on the basis 
<Knots, Multiplicities> of degree <Degree>. 
Raises ConstructionError subject to the following conditions 
0 < Degree <= MaxDegree. 

Weights.Length() == Poles.Length() 

Knots.Length() == Mults.Length() >= 2 

Knots(i) < Knots(i+1) (Knots are increasing) 

1 <= Mults(i) <= Degree 

On a non periodic curve the first and last multiplicities 
may be Degree+1 (this is even recommanded if you want the 
curve to start and finish on the first and last pole). 

On a periodic curve the first and the last multicities 
must be the same. 

on non-periodic curves 

Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2 

on periodic curves 

Poles.Length() == Sum(Mults(i)) except the first or last 
void IncreaseDegree (const Standard_Integer Degree) Increases the degree of this BSpline curve to 
Degree. As a result, the poles, weights and 
multiplicities tables are modified; the knots table is 
not changed. Nothing is done if Degree is less than 
or equal to the current degree. 
Exceptions 
Standard_ConstructionError if Degree is greater than 
Geom_BSplineCurve::MaxDegree(). 
void IncreaseMultiplicity (const Standard_Integer Index, const Standard_Integer M) Increases the multiplicity of the knot <Index> to 
<M>. 

If <M> is lower or equal to the current 
multiplicity nothing is done. If <M> is higher than 
the degree the degree is used. 
//! If <Index> is not in [FirstUKnotIndex, LastUKnotIndex] 
void IncreaseMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M) Increases the multiplicities of the knots in 
[I1,I2] to <M>. 

For each knot if <M> is lower or equal to the 
current multiplicity nothing is done. If <M> is 
higher than the degree the degree is used. 
//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex] 
void IncrementMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M) Increment the multiplicities of the knots in 
[I1,I2] by <M>. 

If <M> is not positive nithing is done. 

For each knot the resulting multiplicity is 
limited to the Degree. 
//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex] 
void InsertKnot (const Standard_Real U, const Standard_Integer M=1, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True) Inserts a knot value in the sequence of knots. If 
<U> is an existing knot the multiplicity is 
increased by <M>. 

If U is not on the parameter range nothing is 
done. 

If the multiplicity is negative or null nothing is 
done. The new multiplicity is limited to the 
degree. 

The tolerance criterion for knots equality is 
the max of Epsilon(U) and ParametricTolerance. 
void InsertKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_False) Inserts a set of knots values in the sequence of 
knots. 

For each U = Knots(i), M = Mults(i) 

If <U> is an existing knot the multiplicity is 
increased by <M> if <Add> is True, increased to 
<M> if <Add> is False. 

If U is not on the parameter range nothing is 
done. 

If the multiplicity is negative or null nothing is 
done. The new multiplicity is limited to the 
degree. 

The tolerance criterion for knots equality is 
the max of Epsilon(U) and ParametricTolerance. 
Standard_Boolean RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance) Reduces the multiplicity of the knot of index Index 
to M. If M is equal to 0, the knot is removed. 
With a modification of this type, the array of poles is also modified. 
Two different algorithms are systematically used to 
compute the new poles of the curve. If, for each 
pole, the distance between the pole calculated 
using the first algorithm and the same pole 
calculated using the second algorithm, is less than 
Tolerance, this ensures that the curve is not 
modified by more than Tolerance. Under these 
conditions, true is returned; otherwise, false is returned. 
A low tolerance is used to prevent modification of 
the curve. A high tolerance is used to "smooth" the curve. 
Exceptions 
Standard_OutOfRange if Index is outside the 
bounds of the knots table. 
//! pole insertion and pole removing 
this operation is limited to the Uniform or QuasiUniform 
BSplineCurve. The knot values are modified . If the BSpline is 
NonUniform or Piecewise Bezier an exception Construction error 
is raised. 
void Reverse () Changes the direction of parametrization of <me>. The Knot 
sequence is modified, the FirstParameter and the 
LastParameter are not modified. The StartPoint of the 
initial curve becomes the EndPoint of the reversed curve 
and the EndPoint of the initial curve becomes the StartPoint 
of the reversed curve. 
Standard_Real ReversedParameter (const Standard_Real U) const Returns the parameter on the reversed curve for 
the point of parameter U on <me>. 

returns UFirst + ULast - U 
void Segment (const Standard_Real U1, const Standard_Real U2) Modifies this BSpline curve by segmenting it between 
U1 and U2. Either of these values can be outside the 
bounds of the curve, but U2 must be greater than U1. 
All data structure tables of this BSpline curve are 
modified, but the knots located between U1 and U2 
are retained. The degree of the curve is not modified. 
Warnings : 
Even if <me> is not closed it can become closed after the 
segmentation for example if U1 or U2 are out of the bounds 
of the curve <me> or if the curve makes loop. 
After the segmentation the length of a curve can be null. 
//! raises if U2 < U1. 
void SetKnot (const Standard_Integer Index, const Standard_Real K) Modifies this BSpline curve by assigning the value K 
to the knot of index Index in the knots table. This is a 
relatively local modification because K must be such that: 
Knots(Index - 1) < K < Knots(Index + 1) 
The second syntax allows you also to increase the 
multiplicity of the knot to M (but it is not possible to 
decrease the multiplicity of the knot with this function). 
Standard_ConstructionError if: 

• K is not such that: 
  Knots(Index - 1) < K < Knots(Index + 1) 
  
• M is greater than the degree of this BSpline curve 
  or lower than the previous multiplicity of knot of 
  index Index in the knots table. 
  Standard_OutOfRange if Index is outside the bounds of the knots table. 
  

void SetKnots (const TColStd_Array1OfReal &K) Modifies this BSpline curve by assigning the array 
K to its knots table. The multiplicity of the knots is not modified. 
Exceptions 
Standard_ConstructionError if the values in the 
array K are not in ascending order. 
Standard_OutOfRange if the bounds of the array 
K are not respectively 1 and the number of knots of this BSpline curve. 
void SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M) Changes the knot of range Index with its multiplicity. 
You can increase the multiplicity of a knot but it is 
not allowed to decrease the multiplicity of an existing knot. 
Raised if K >= Knots(Index+1) or K <= Knots(Index-1). 
Raised if M is greater than Degree or lower than the previous 
multiplicity of knot of range Index. 
//! Raised if Index < 1 || Index > NbKnots 
void PeriodicNormalization (Standard_Real &U) const returns the parameter normalized within 
the period if the curve is periodic : otherwise 
does not do anything 
void SetPeriodic () Changes this BSpline curve into a periodic curve. 
To become periodic, the curve must first be closed. 
Next, the knot sequence must be periodic. For this, 
FirstUKnotIndex and LastUKnotIndex are used 
to compute I1 and I2, the indexes in the knots 
array of the knots corresponding to the first and 
last parameters of this BSpline curve. 
The period is therefore: Knots(I2) - Knots(I1). 
Consequently, the knots and poles tables are modified. 
Exceptions 
Standard_ConstructionError if this BSpline curve is not closed. 
void SetOrigin (const Standard_Integer Index) Assigns the knot of index Index in the knots table as 
the origin of this periodic BSpline curve. As a 
consequence, the knots and poles tables are modified. 
Exceptions 
Standard_NoSuchObject if this curve is not periodic. 
Standard_DomainError if Index is outside the bounds of the knots table. 
void SetOrigin (const Standard_Real U, const Standard_Real Tol) Set the origin of a periodic curve at Knot U. If U 
is not a knot of the BSpline a new knot is 
inseted. KnotVector and poles are modified. 
//! Raised if the curve is not periodic 
void SetNotPeriodic () Changes this BSpline curve into a non-periodic 
curve. If this curve is already non-periodic, it is not modified. 
Note: the poles and knots tables are modified. 
Warning 
If this curve is periodic, as the multiplicity of the first 
and last knots is not modified, and is not equal to 
Degree + 1, where Degree is the degree of 
this BSpline curve, the start and end points of the 
curve are not its first and last poles. 
void SetPole (const Standard_Integer Index, const gp_Pnt &P) Modifies this BSpline curve by assigning P to the pole 
of index Index in the poles table. 
Exceptions 
Standard_OutOfRange if Index is outside the 
bounds of the poles table. 
Standard_ConstructionError if Weight is negative or null. 
void SetPole (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight) Modifies this BSpline curve by assigning P to the pole 
of index Index in the poles table. 
This syntax also allows you to modify the 
weight of the modified pole, which becomes Weight. 
In this case, if this BSpline curve is non-rational, it 
can become rational and vice versa. 
Exceptions 
Standard_OutOfRange if Index is outside the 
bounds of the poles table. 
Standard_ConstructionError if Weight is negative or null. 
void SetWeight (const Standard_Integer Index, const Standard_Real Weight) Changes the weight for the pole of range Index. 
If the curve was non rational it can become rational. 
If the curve was rational it can become non rational. 
Raised if Index < 1 || Index > NbPoles 
//! Raised if Weight <= 0.0 
void MovePoint (const Standard_Real U, const gp_Pnt &P, const Standard_Integer Index1, const Standard_Integer Index2, Standard_Integer &FirstModifiedPole, Standard_Integer&LastModifiedPole) Moves the point of parameter U of this BSpline curve 
to P. Index1 and Index2 are the indexes in the table 
of poles of this BSpline curve of the first and last 
poles designated to be moved. 
FirstModifiedPole and LastModifiedPole are the 
indexes of the first and last poles which are effectively modified. 
In the event of incompatibility between Index1, Index2 and the value U: 

• no change is made to this BSpline curve, and 
  
• the FirstModifiedPole and LastModifiedPole are returned null. 
  Exceptions 
  Standard_OutOfRange if: 
  
• Index1 is greater than or equal to Index2, or 
  
• Index1 or Index2 is less than 1 or greater than the 
  number of poles of this BSpline curve. 
  

void MovePointAndTangent (const Standard_Real U, const gp_Pnt &P, const gp_Vec &Tangent, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_IntegerEndingCondition, Standard_Integer &ErrorStatus) Move a point with parameter U to P. 
and makes it tangent at U be Tangent. 
StartingCondition = -1 means first can move 
EndingCondition = -1 means last point can move 
StartingCondition = 0 means the first point cannot move 
EndingCondition = 0 means the last point cannot move 
StartingCondition = 1 means the first point and tangent cannot move 
EndingCondition = 1 means the last point and tangent cannot move 
and so forth 
ErrorStatus != 0 means that there are not enought degree of freedom 
with the constrain to deform the curve accordingly 

Standard_Boolean IsCN (const Standard_Integer N) const Returns the continuity of the curve, the curve is at least C0. 
//! Raised if N < 0. 
Standard_Boolean IsClosed () const Returns true if the distance between the first point and the 
last point of the curve is lower or equal to Resolution 
from package gp. 
Warnings : 
The first and the last point can be different from the first 
pole and the last pole of the curve. 
Standard_Boolean IsPeriodic () const Returns True if the curve is periodic. 
Standard_Boolean IsRational () const Returns True if the weights are not identical. 
The tolerance criterion is Epsilon of the class Real. 
GeomAbs_Shape Continuity () const Returns the global continuity of the curve : 
C0 : only geometric continuity, 
C1 : continuity of the first derivative all along the Curve, 
C2 : continuity of the second derivative all along the Curve, 
C3 : continuity of the third derivative all along the Curve, 
CN : the order of continuity is infinite. 
For a B-spline curve of degree d if a knot Ui has a 
multiplicity p the B-spline curve is only Cd-p continuous 
at Ui. So the global continuity of the curve can't be greater 
than Cd-p where p is the maximum multiplicity of the interior 
Knots. In the interior of a knot span the curve is infinitely 
continuously differentiable. 
Standard_Integer Degree () const Returns the degree of this BSpline curve. 
The degree of a Geom_BSplineCurve curve cannot 
be greater than Geom_BSplineCurve::MaxDegree(). 
//! Computation of value and derivatives 
void D0 (const Standard_Real U, gp_Pnt &P) const Returns in P the point of parameter U. 
void D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const Raised if the continuity of the curve is not C1. 
void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const Raised if the continuity of the curve is not C2. 
void D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const Raised if the continuity of the curve is not C3. 
gp_Vec DN (const Standard_Real U, const Standard_Integer N) const For the point of parameter U of this BSpline curve, 
computes the vector corresponding to the Nth derivative. 
Warning 
On a point where the continuity of the curve is not the 
one requested, this function impacts the part defined 
by the parameter with a value greater than U, i.e. the 
part of the curve to the "right" of the singularity. 
Exceptions 
Standard_RangeError if N is less than 1. 
The following functions compute the point of parameter U 
and the derivatives at this point on the B-spline curve 
arc defined between the knot FromK1 and the knot ToK2. 
U can be out of bounds [Knot (FromK1), Knot (ToK2)] but 
for the computation we only use the definition of the curve 
between these two knots. This method is useful to compute 
local derivative, if the order of continuity of the whole 
curve is not greater enough. Inside the parametric 
domain Knot (FromK1), Knot (ToK2) the evaluations are 
the same as if we consider the whole definition of the 
curve. Of course the evaluations are different outside 
this parametric domain. 
gp_Pnt LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const Raised if FromK1 = ToK2. 
Raised if FromK1 and ToK2 are not in the range 
[FirstUKnotIndex, LastUKnotIndex]. 
void LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P) const Raised if FromK1 = ToK2. 
Raised if FromK1 and ToK2 are not in the range 
[FirstUKnotIndex, LastUKnotIndex]. 
void LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1) const Raised if the local continuity of the curve is not C1 
between the knot K1 and the knot K2. 
//! Raised if FromK1 = ToK2. 
Raised if FromK1 and ToK2 are not in the range 
[FirstUKnotIndex, LastUKnotIndex]. 
void LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const Raised if the local continuity of the curve is not C2 
between the knot K1 and the knot K2. 
//! Raised if FromK1 = ToK2. 
Raised if FromK1 and ToK2 are not in the range 
[FirstUKnotIndex, LastUKnotIndex]. 
void LocalD3 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const Raised if the local continuity of the curve is not C3 
between the knot K1 and the knot K2. 
//! Raised if FromK1 = ToK2. 
Raised if FromK1 and ToK2 are not in the range 
[FirstUKnotIndex, LastUKnotIndex]. 
gp_Vec LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const Raised if the local continuity of the curve is not CN 
between the knot K1 and the knot K2. 
//! Raised if FromK1 = ToK2. 
//! Raised if N < 1. 
Raises if FromK1 and ToK2 are not in the range 
[FirstUKnotIndex, LastUKnotIndex]. 
gp_Pnt EndPoint () const Returns the last point of the curve. 
Warnings : 
The last point of the curve is different from the last 
pole of the curve if the multiplicity of the last knot 
is lower than Degree. 
Standard_Integer FirstUKnotIndex () const Returns the index in the knot array of the knot 
corresponding to the first or last parameter of this BSpline curve. 
For a BSpline curve, the first (or last) parameter 
(which gives the start (or end) point of the curve) is a 
knot value. However, if the multiplicity of the first (or 
last) knot is less than Degree + 1, where 
Degree is the degree of the curve, it is not the first 
(or last) knot of the curve. 
Standard_Real FirstParameter () const Returns the value of the first parameter of this 
BSpline curve. This is a knot value. 
The first parameter is the one of the start point of the BSpline curve. 
Standard_Real Knot (const Standard_Integer Index) const Returns the knot of range Index. When there is a knot 
with a multiplicity greater than 1 the knot is not repeated. 
The method Multiplicity can be used to get the multiplicity 
of the Knot. 
//! Raised if Index < 1 or Index > NbKnots 
void Knots (TColStd_Array1OfReal &K) const returns the knot values of the B-spline curve; 
Warning 
A knot with a multiplicity greater than 1 is not 
repeated in the knot table. The Multiplicity function 
can be used to obtain the multiplicity of each knot. 
Raised if the length of K is not equal to the number of knots. 
void KnotSequence (TColStd_Array1OfReal &K) const Returns K, the knots sequence of this BSpline curve. 
In this sequence, knots with a multiplicity greater than 1 are repeated. 
In the case of a non-periodic curve the length of the 
sequence must be equal to the sum of the NbKnots 
multiplicities of the knots of the curve (where 
NbKnots is the number of knots of this BSpline 
curve). This sum is also equal to : NbPoles + Degree + 1 
where NbPoles is the number of poles and 
Degree the degree of this BSpline curve. 
In the case of a periodic curve, if there are k periodic 
knots, the period is Knot(k+1) - Knot(1). 
The initial sequence is built by writing knots 1 to k+1, 
which are repeated according to their corresponding multiplicities. 
If Degree is the degree of the curve, the degree of 
continuity of the curve at the knot of index 1 (or k+1) 
is equal to c = Degree + 1 - Mult(1). c 
knots are then inserted at the beginning and end of 
the initial sequence: 

• the c values of knots preceding the first item 
  Knot(k+1) in the initial sequence are inserted 
  at the beginning; the period is subtracted from these c values; 
  
• the c values of knots following the last item 
  Knot(1) in the initial sequence are inserted at 
  the end; the period is added to these c values. 
  The length of the sequence must therefore be equal to: 
  NbPoles + 2*Degree - Mult(1) + 2. 
  Example 
  For a non-periodic BSpline curve of degree 2 where: 
  
• the array of knots is: { k1 k2 k3 k4 }, 
  
• with associated multiplicities: { 3 1 2 3 }, 
  the knot sequence is: 
  K = { k1 k1 k1 k2 k3 k3 k4 k4 k4 } 
  For a periodic BSpline curve of degree 4 , which is 
  "C1" continuous at the first knot, and where : 
  
• the periodic knots are: { k1 k2 k3 (k4) } 
  (3 periodic knots: the points of parameter k1 and k4 
  are identical, the period is p = k4 - k1), 
  
• with associated multiplicities: { 3 1 2 (3) }, 
  the degree of continuity at knots k1 and k4 is: 
  Degree + 1 - Mult(i) = 2. 
  2 supplementary knots are added at the beginning 
  and end of the sequence: 
  
• at the beginning: the 2 knots preceding k4 minus 
  the period; in this example, this is k3 - p both times; 
  
• at the end: the 2 knots following k1 plus the period; 
  in this example, this is k2 + p and k3 + p. 
  The knot sequence is therefore: 
  K = { k3-p k3-p k1 k1 k1 k2 k3 k3 
  k4 k4 k4 k2+p k3+p } 
  Exceptions 
  Standard_DimensionError if the array K is not of 
  the appropriate length.Returns the knots sequence. 
  

GeomAbs_BSplKnotDistribution KnotDistribution () const Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. 
If all the knots differ by a positive constant from the 
preceding knot the BSpline Curve can be : 

• Uniform if all the knots are of multiplicity 1, 
  
• QuasiUniform if all the knots are of multiplicity 1 except for 
  the first and last knot which are of multiplicity Degree + 1, 
  
• PiecewiseBezier if the first and last knots have multiplicity 
  Degree + 1 and if interior knots have multiplicity Degree 
  A piecewise Bezier with only two knots is a BezierCurve. 
  else the curve is non uniform. 
  The tolerance criterion is Epsilon from class Real. 
  

Standard_Integer LastUKnotIndex () const For a BSpline curve the last parameter (which gives the 
end point of the curve) is a knot value but if the 
multiplicity of the last knot index is lower than 
Degree + 1 it is not the last knot of the curve. This 
method computes the index of the knot corresponding to 
the last parameter. 
Standard_Real LastParameter () const Computes the parametric value of the end point of the curve. 
It is a knot value. 
void LocateU (const Standard_Real U, const Standard_Real ParametricTolerance, Standard_Integer &I1, Standard_Integer &I2, const Standard_Boolean WithKnotRepetition=Standard_False) const Locates the parametric value U in the sequence of knots. 
If "WithKnotRepetition" is True we consider the knot's 
representation with repetition of multiple knot value, 
otherwise we consider the knot's representation with 
no repetition of multiple knot values. 
Knots (I1) <= U <= Knots (I2) 
. if I1 = I2 U is a knot value (the tolerance criterion 
ParametricTolerance is used). 
. if I1 < 1 => U < Knots (1) - Abs(ParametricTolerance) 
. if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance) 
Standard_Integer Multiplicity (const Standard_Integer Index) const Returns the multiplicity of the knots of range Index. 
//! Raised if Index < 1 or Index > NbKnots 
void Multiplicities (TColStd_Array1OfInteger &M) const Returns the multiplicity of the knots of the curve. 
Raised if the length of M is not equal to NbKnots. 
Standard_Integer NbKnots () const Returns the number of knots. This method returns the number of 
knot without repetition of multiple knots. 
Standard_Integer NbPoles () const Returns the number of poles 
gp_Pnt Pole (const Standard_Integer Index) const Returns the pole of range Index. 
//! Raised if Index < 1 or Index > NbPoles. 
void Poles (TColgp_Array1OfPnt &P) const Returns the poles of the B-spline curve; 
Raised if the length of P is not equal to the number of poles. 
gp_Pnt StartPoint () const Returns the start point of the curve. 
Warnings : 
This point is different from the first pole of the curve if the 
multiplicity of the first knot is lower than Degree. 
Standard_Real Weight (const Standard_Integer Index) const Returns the weight of the pole of range Index . 
//! Raised if Index < 1 or Index > NbPoles. 
void Weights (TColStd_Array1OfReal &W) const Returns the weights of the B-spline curve; 
Raised if the length of W is not equal to NbPoles. 
void Transform (const gp_Trsf &T) Applies the transformation T to this BSpline curve. 
void Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance) Computes for this BSpline curve the parametric 
tolerance UTolerance for a given 3D tolerance Tolerance3D. 
If f(t) is the equation of this BSpline curve, 
UTolerance ensures that: 
| t1 - t0| < Utolerance ===> 
|f(t1) - f(t0)| < Tolerance3D 
Handle_Geom_Geometry Copy () const Creates a new object which is a copy of this BSpline curve. 

Static Public Member Functions

static Standard_Integer MaxDegree () Returns the value of the maximum degree of the normalized 
B-spline basis functions in this package. 

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Constructor & Destructor Documentation

Geom_BSplineCurve::Geom_BSplineCurve(const TColgp_Array1OfPnt & Poles,  const TColStd_Array1OfReal & Knots,  const TColStd_Array1OfInteger & Multiplicities,  const Standard_Integer Degree,  const Standard_Boolean Periodic = Standard_False  )   

Geom_BSplineCurve::Geom_BSplineCurve(const TColgp_Array1OfPnt & Poles,  const TColStd_Array1OfReal & Weights,  const TColStd_Array1OfReal & Knots,  const TColStd_Array1OfInteger & Multiplicities,  const Standard_Integer Degree,  const Standard_Boolean Periodic = Standard_False,  const Standard_Boolean CheckRational = Standard_True  )   

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Member Function Documentation

GeomAbs_Shape Geom_BSplineCurve::Continuity(  ) const [virtual]

Implements Geom_Curve.

Handle_Geom_Geometry Geom_BSplineCurve::Copy(  ) const [virtual]

Implements Geom_Geometry.

void Geom_BSplineCurve::D0(const Standard_Real U,  gp_Pnt & P  )  const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::D1(const Standard_Real U,  gp_Pnt & P,  gp_Vec & V1  )  const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::D2(const Standard_Real U,  gp_Pnt & P,  gp_Vec & V1,  gp_Vec & V2  )  const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::D3(const Standard_Real U,  gp_Pnt & P,  gp_Vec & V1,  gp_Vec & V2,  gp_Vec & V3  )  const [virtual]

Implements Geom_Curve.

Standard_Integer Geom_BSplineCurve::Degree(  ) const

gp_Vec Geom_BSplineCurve::DN(const Standard_Real U,  const Standard_Integer N  )  const [virtual]

Implements Geom_Curve.

gp_Pnt Geom_BSplineCurve::EndPoint(  ) const [virtual]

Implements Geom_BoundedCurve.

Standard_Real Geom_BSplineCurve::FirstParameter(  ) const [virtual]

Implements Geom_Curve.

Standard_Integer Geom_BSplineCurve::FirstUKnotIndex(  ) const

void Geom_BSplineCurve::IncreaseDegree(const Standard_Integer Degree )  

void Geom_BSplineCurve::IncreaseMultiplicity(const Standard_Integer I1,  const Standard_Integer I2,  const Standard_Integer M  )   

void Geom_BSplineCurve::IncreaseMultiplicity(const Standard_Integer Index,  const Standard_Integer M  )   

void Geom_BSplineCurve::IncrementMultiplicity(const Standard_Integer I1,  const Standard_Integer I2,  const Standard_Integer M  )   

void Geom_BSplineCurve::InsertKnot(const Standard_Real U,  const Standard_Integer M = 1,  const Standard_Real ParametricTolerance = 0.0,  const Standard_Boolean Add = Standard_True  )   

void Geom_BSplineCurve::InsertKnots(const TColStd_Array1OfReal & Knots,  const TColStd_Array1OfInteger & Mults,  const Standard_Real ParametricTolerance = 0.0,  const Standard_Boolean Add = Standard_False  )   

Standard_Boolean Geom_BSplineCurve::IsClosed(  ) const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BSplineCurve::IsCN(const Standard_Integer N ) const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BSplineCurve::IsPeriodic(  ) const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BSplineCurve::IsRational(  ) const

Standard_Real Geom_BSplineCurve::Knot(const Standard_Integer Index ) const

GeomAbs_BSplKnotDistribution Geom_BSplineCurve::KnotDistribution(  ) const

void Geom_BSplineCurve::Knots(TColStd_Array1OfReal & K ) const

void Geom_BSplineCurve::KnotSequence(TColStd_Array1OfReal & K ) const

Standard_Real Geom_BSplineCurve::LastParameter(  ) const [virtual]

Implements Geom_Curve.

Standard_Integer Geom_BSplineCurve::LastUKnotIndex(  ) const

void Geom_BSplineCurve::LocalD0(const Standard_Real U,  const Standard_Integer FromK1,  const Standard_Integer ToK2,  gp_Pnt & P  )  const

void Geom_BSplineCurve::LocalD1(const Standard_Real U,  const Standard_Integer FromK1,  const Standard_Integer ToK2,  gp_Pnt & P,  gp_Vec & V1  )  const

void Geom_BSplineCurve::LocalD2(const Standard_Real U,  const Standard_Integer FromK1,  const Standard_Integer ToK2,  gp_Pnt & P,  gp_Vec & V1,  gp_Vec & V2  )  const

void Geom_BSplineCurve::LocalD3(const Standard_Real U,  const Standard_Integer FromK1,  const Standard_Integer ToK2,  gp_Pnt & P,  gp_Vec & V1,  gp_Vec & V2,  gp_Vec & V3  )  const

gp_Vec Geom_BSplineCurve::LocalDN(const Standard_Real U,  const Standard_Integer FromK1,  const Standard_Integer ToK2,  const Standard_Integer N  )  const

gp_Pnt Geom_BSplineCurve::LocalValue(const Standard_Real U,  const Standard_Integer FromK1,  const Standard_Integer ToK2  )  const

void Geom_BSplineCurve::LocateU(const Standard_Real U,  const Standard_Real ParametricTolerance,  Standard_Integer & I1,  Standard_Integer & I2,  const Standard_Boolean WithKnotRepetition = Standard_False  )  const

static Standard_Integer Geom_BSplineCurve::MaxDegree(  ) [static]

void Geom_BSplineCurve::MovePoint(const Standard_Real U,  const gp_Pnt & P,  const Standard_Integer Index1,  const Standard_Integer Index2,  Standard_Integer & FirstModifiedPole,  Standard_Integer & LastModifiedPole  )   

void Geom_BSplineCurve::MovePointAndTangent(const Standard_Real U,  const gp_Pnt & P,  const gp_Vec & Tangent,  const Standard_Real Tolerance,  const Standard_Integer StartingCondition,  const Standard_Integer EndingCondition,  Standard_Integer & ErrorStatus  )   

void Geom_BSplineCurve::Multiplicities(TColStd_Array1OfInteger & M ) const

Standard_Integer Geom_BSplineCurve::Multiplicity(const Standard_Integer Index ) const

Standard_Integer Geom_BSplineCurve::NbKnots(  ) const

Standard_Integer Geom_BSplineCurve::NbPoles(  ) const

void Geom_BSplineCurve::PeriodicNormalization(Standard_Real & U ) const

gp_Pnt Geom_BSplineCurve::Pole(const Standard_Integer Index ) const

void Geom_BSplineCurve::Poles(TColgp_Array1OfPnt & P ) const

Standard_Boolean Geom_BSplineCurve::RemoveKnot(const Standard_Integer Index,  const Standard_Integer M,  const Standard_Real Tolerance  )   

void Geom_BSplineCurve::Resolution(const Standard_Real Tolerance3D,  Standard_Real & UTolerance  )   

void Geom_BSplineCurve::Reverse(  ) [virtual]

Implements Geom_Curve.

Standard_Real Geom_BSplineCurve::ReversedParameter(const Standard_Real U ) const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::Segment(const Standard_Real U1,  const Standard_Real U2  )   

void Geom_BSplineCurve::SetKnot(const Standard_Integer Index,  const Standard_Real K,  const Standard_Integer M  )   

void Geom_BSplineCurve::SetKnot(const Standard_Integer Index,  const Standard_Real K  )   

void Geom_BSplineCurve::SetKnots(const TColStd_Array1OfReal & K )  

void Geom_BSplineCurve::SetNotPeriodic(  )  

void Geom_BSplineCurve::SetOrigin(const Standard_Real U,  const Standard_Real Tol  )   

void Geom_BSplineCurve::SetOrigin(const Standard_Integer Index )  

void Geom_BSplineCurve::SetPeriodic(  )  

void Geom_BSplineCurve::SetPole(const Standard_Integer Index,  const gp_Pnt & P,  const Standard_Real Weight  )   

void Geom_BSplineCurve::SetPole(const Standard_Integer Index,  const gp_Pnt & P  )   

void Geom_BSplineCurve::SetWeight(const Standard_Integer Index,  const Standard_Real Weight  )   

gp_Pnt Geom_BSplineCurve::StartPoint(  ) const [virtual]

Implements Geom_BoundedCurve.

void Geom_BSplineCurve::Transform(const gp_Trsf & T ) [virtual]

Implements Geom_Geometry.

Standard_Real Geom_BSplineCurve::Weight(const Standard_Integer Index ) const

void Geom_BSplineCurve::Weights(TColStd_Array1OfReal & W ) const