Package Precision

Precision Class Reference

The Precision package offers a set of functions defining precision criteria 
for use in conventional situations when comparing two numbers. 
Generalities 
It is not advisable to use floating number equality. Instead, the difference 
between numbers must be compared with a given precision, i.e. : 
Standard_Real x1, x2 ; 
x1 = ... 
x2 = ... 
If ( x1 == x2 ) ... 
should not be used and must be written as indicated below: 
Standard_Real x1, x2 ; 
Standard_Real Precision = ... 
x1 = ... 
x2 = ... 
If ( Abs ( x1 - x2 ) < Precision ) ... 
Likewise, when ordering floating numbers, you must take the following into account : 
Standard_Real x1, x2 ; 
Standard_Real Precision = ... 
x1 = ... ! a large number 
x2 = ... ! another large number 
If ( x1 < x2 - Precision ) ... 
is incorrect when x1 and x2 are large numbers ; it is better to write : 
Standard_Real x1, x2 ; 
Standard_Real Precision = ... 
x1 = ... ! a large number 
x2 = ... ! another large number 
If ( x2 - x1 > Precision ) ... 
Precision in Cas.Cade 
Generally speaking, the precision criterion is not implicit in Cas.Cade. Low-level geometric algorithms accept 
precision criteria as arguments. As a rule, they should not refer directly to the precision criteria provided by the 
Precision package. 
On the other hand, high-level modeling algorithms have to provide the low-level geometric algorithms that they 
call, with a precision criteria. One way of doing this is to use the above precision criteria. 
Alternatively, the high-level algorithms can have their own system for precision management. For example, the 
Topology Data Structure stores precision criteria for each elementary shape (as a vertex, an edge or a face). When 
a new topological object is constructed, the precision criteria are taken from those provided by the Precision 
package, and stored in the related data structure. Later, a topological algorithm which analyses these objects will 
work with the values stored in the data structure. Also, if this algorithm is to build a new topological object, from 
these precision criteria, it will compute a new precision criterion for the new topological object, and write it into the 
data structure of the new topological object. 
The different precision criteria offered by the Precision package, cover the most common requirements of 
geometric algorithms, such as intersections, approximations, and so on. 
The choice of precision depends on the algorithm and on the geometric space. The geometric space may be : 

• a "real" 2D or 3D space, where the lengths are measured in meters, millimeters, microns, inches, etc ..., or 
  
• a "parametric" space, 1D on a curve or 2D on a surface, where lengths have no dimension. 
  The choice of precision criteria for real space depends on the choice of the product, as it is based on the accuracy 
  of the machine and the unit of measurement. 
  The choice of precision criteria for parametric space depends on both the accuracy of the machine and the 
  dimensions of the curve or the surface, since the parametric precision criterion and the real precision criterion are 
  linked : if the curve is defined by the equation P(t), the inequation : 
  Abs ( t2 - t1 ) < ParametricPrecision 
  means that the parameters t1 and t2 are considered to be equal, and the inequation : 
  Distance ( P(t2) , P(t1) ) < RealPrecision 
  means that the points P(t1) and P(t2) are considered to be coincident. It seems to be the same idea, and it 
  would be wonderful if these two inequations were equivalent. Note that this is rarely the case ! 
  What is provided in this package? 
  The Precision package provides : 
  
• a set of real space precision criteria for the algorithms, in view of checking distances and angles, 
  
• a set of parametric space precision criteria for the algorithms, in view of checking both : 
  
  • the equality of parameters in a parametric space, 
    
  • or the coincidence of points in the real space, by using parameter values, 
    
• the notion of infinite value, composed of a value assumed to be infinite, and checking tests designed to verify 
  if any value could be considered as infinite. 
  All the provided functions are very simple. The returned values result from the adaptation of the applications 
  developed by the Open CASCADE company to Open CASCADE algorithms. The main interest of these functions 
  lies in that it incites engineers developing applications to ask questions on precision factors. Which one is to be 
  used in such or such case ? Tolerance criteria are context dependent. They must first choose : 
  
• either to work in real space, 
  
• or to work in parametric space, 
  
• or to work in a combined real and parametric space. 
  They must next decide which precision factor will give the best answer to the current problem. Within an application 
  environment, it is crucial to master precision even though this process may take a great deal of time. 
  

#include <Precision.hxx>




介绍precision 有两种一种是参数空间(parameter space)，一种是带单位的实数空间（real space ）

注意：在一维情况下，需要注意两者的统一。

OCC 中内部的dimension 是millimeter

• The SI System
• 
  

The SI System is the standard international unit system. It is indicated by SI in the signature of the UnitsAPI functions

The Open CASCADE (former MDTV) System corresponds to the SI international standard bu the length unit and all its derivatives 

use the millimeterinstead of meter

I guess the meter is to big and not convenient for the CAX users