// Created on: 1993-02-17
// Created by: Remi LEQUETTE
// Copyright (c) 1993-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.
#ifndef _Precision_HeaderFile
#define _Precision_HeaderFile
#include
#include
#include
#include
#include
//! 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.
class Precision
{
public:
DEFINE_STANDARD_ALLOC
//! Returns the recommended precision value
//! when checking the equality of two angles (given in radians).
//! Standard_Real Angle1 = ... , Angle2 = ... ;
//! If ( Abs( Angle2 - Angle1 ) < Precision::Angular() ) ...
//! The tolerance of angular equality may be used to check the parallelism of two vectors :
//! gp_Vec V1, V2 ;
//! V1 = ...
//! V2 = ...
//! If ( V1.IsParallel (V2, Precision::Angular() ) ) ...
//! The tolerance of angular equality is equal to 1.e-12.
//! Note : The tolerance of angular equality can be used when working with scalar products or
//! cross products since sines and angles are equivalent for small angles. Therefore, in order to
//! check whether two unit vectors are perpendicular :
//! gp_Dir D1, D2 ;
//! D1 = ...
//! D2 = ...
//! you can use :
//! If ( Abs( D1.D2 ) < Precision::Angular() ) ...
//! (although the function IsNormal does exist).
static Standard_Real Angular() { return 1.e-12; }
//! Returns the recommended precision value when
//! checking coincidence of two points in real space.
//! The tolerance of confusion is used for testing a 3D
//! distance :
//! - Two points are considered to be coincident if their
//! distance is smaller than the tolerance of confusion.
//! gp_Pnt P1, P2 ;
//! P1 = ...
//! P2 = ...
//! if ( P1.IsEqual ( P2 , Precision::Confusion() ) )
//! then ...
//! - A vector is considered to be null if it has a null length :
//! gp_Vec V ;
//! V = ...
//! if ( V.Magnitude() < Precision::Confusion() ) then ...
//! The tolerance of confusion is equal to 1.e-7.
//! The value of the tolerance of confusion is also used to
//! define :
//! - the tolerance of intersection, and
//! - the tolerance of approximation.
//! Note : As a rule, coordinate values in Cas.Cade are not
//! dimensioned, so 1. represents one user unit, whatever
//! value the unit may have : the millimeter, the meter, the
//! inch, or any other unit. Let's say that Cas.Cade
//! algorithms are written to be tuned essentially with
//! mechanical design applications, on the basis of the
//! millimeter. However, these algorithms may be used with
//! any other unit but the tolerance criterion does no longer
//! have the same signification.
//! So pay particular attention to the type of your application,
//! in relation with the impact of your unit on the precision criterion.
//! - For example in mechanical design, if the unit is the
//! millimeter, the tolerance of confusion corresponds to a
//! distance of 1 / 10000 micron, which is rather difficult to measure.
//! - However in other types of applications, such as
//! cartography, where the kilometer is frequently used,
//! the tolerance of confusion corresponds to a greater
//! distance (1 / 10 millimeter). This distance
//! becomes easily measurable, but only within a restricted
//! space which contains some small objects of the complete scene.
static Standard_Real Confusion() { return 1.e-7; }
//! Returns square of Confusion.
//! Created for speed and convenience.
static Standard_Real SquareConfusion() { return Confusion() * Confusion(); }
//! Returns the precision value in real space, frequently
//! used by intersection algorithms to decide that a solution is reached.
//! This function provides an acceptable level of precision
//! for an intersection process to define the adjustment limits.
//! The tolerance of intersection is designed to ensure
//! that a point computed by an iterative algorithm as the
//! intersection between two curves is indeed on the
//! intersection. It is obvious that two tangent curves are
//! close to each other, on a large distance. An iterative
//! algorithm of intersection may find points on these
//! curves within the scope of the confusion tolerance, but
//! still far from the true intersection point. In order to force
//! the intersection algorithm to continue the iteration
//! process until a correct point is found on the tangent
//! objects, the tolerance of intersection must be smaller
//! than the tolerance of confusion.
//! On the other hand, the tolerance of intersection must
//! be large enough to minimize the time required by the
//! process to converge to a solution.
//! The tolerance of intersection is equal to :
//! Precision::Confusion() / 100.
//! (that is, 1.e-9).
static Standard_Real Intersection() { return Confusion() * 0.01; }
//! Returns the precision value in real space, frequently used
//! by approximation algorithms.
//! This function provides an acceptable level of precision for
//! an approximation process to define adjustment limits.
//! The tolerance of approximation is designed to ensure
//! an acceptable computation time when performing an
//! approximation process. That is why the tolerance of
//! approximation is greater than the tolerance of confusion.
//! The tolerance of approximation is equal to :
//! Precision::Confusion() * 10.
//! (that is, 1.e-6).
//! You may use a smaller tolerance in an approximation
//! algorithm, but this option might be costly.
static Standard_Real Approximation() { return Confusion() * 10.0; }
//! Convert a real space precision to a parametric
//! space precision. is the mean value of the
//! length of the tangent of the curve or the surface.
//!
//! Value is P / T
static Standard_Real Parametric (const Standard_Real P, const Standard_Real T) { return P / T; }
//! Returns a precision value in parametric space, which may be used :
//! - to test the coincidence of two points in the real space,
//! by using parameter values, or
//! - to test the equality of two parameter values in a parametric space.
//! The parametric tolerance of confusion is designed to
//! give a mean value in relation with the dimension of
//! the curve or the surface. It considers that a variation of
//! parameter equal to 1. along a curve (or an
//! isoparametric curve of a surface) generates a segment
//! whose length is equal to 100. (default value), or T.
//! The parametric tolerance of confusion is equal to :
//! - Precision::Confusion() / 100., or Precision::Confusion() / T.
//! The value of the parametric tolerance of confusion is also used to define :
//! - the parametric tolerance of intersection, and
//! - the parametric tolerance of approximation.
//! Warning
//! It is rather difficult to define a unique precision value in parametric space.
//! - First consider a curve (c) ; if M is the point of
//! parameter u and M' the point of parameter u+du on
//! the curve, call 'parametric tangent' at point M, for the
//! variation du of the parameter, the quantity :
//! T(u,du)=MM'/du (where MM' represents the
//! distance between the two points M and M', in the real space).
//! - Consider the other curve resulting from a scaling
//! transformation of (c) with a scale factor equal to
//! 10. The 'parametric tangent' at the point of
//! parameter u of this curve is ten times greater than the
//! previous one. This shows that for two different curves,
//! the distance between two points on the curve, resulting
//! from the same variation of parameter du, may vary considerably.
//! - Moreover, the variation of the parameter along the
//! curve is generally not proportional to the curvilinear
//! abscissa along the curve. So the distance between two
//! points resulting from the same variation of parameter
//! du, at two different points of a curve, may completely differ.
//! - Moreover, the parameterization of a surface may
//! generate two quite different 'parametric tangent' values
//! in the u or in the v parametric direction.
//! - Last, close to the poles of a sphere (the points which
//! correspond to the values -Pi/2. and Pi/2. of the
//! v parameter) the u parameter may change from 0 to
//! 2.Pi without impacting on the resulting point.
//! Therefore, take great care when adjusting a parametric
//! tolerance to your own algorithm.
static Standard_Real PConfusion (const Standard_Real T) { return Parametric (Confusion(), T); }
//! Returns a precision value in parametric space, which
//! may be used by intersection algorithms, to decide that
//! a solution is reached. The purpose of this function is to
//! provide an acceptable level of precision in parametric
//! space, for an intersection process to define the adjustment limits.
//! The parametric tolerance of intersection is
//! designed to give a mean value in relation with the
//! dimension of the curve or the surface. It considers
//! that a variation of parameter equal to 1. along a curve
//! (or an isoparametric curve of a surface) generates a
//! segment whose length is equal to 100. (default value), or T.
//! The parametric tolerance of intersection is equal to :
//! - Precision::Intersection() / 100., or Precision::Intersection() / T.
static Standard_Real PIntersection (const Standard_Real T) { return Parametric(Intersection(),T); }
//! Returns a precision value in parametric space, which may
//! be used by approximation algorithms. The purpose of this
//! function is to provide an acceptable level of precision in
//! parametric space, for an approximation process to define
//! the adjustment limits.
//! The parametric tolerance of approximation is
//! designed to give a mean value in relation with the
//! dimension of the curve or the surface. It considers
//! that a variation of parameter equal to 1. along a curve
//! (or an isoparametric curve of a surface) generates a
//! segment whose length is equal to 100. (default value), or T.
//! The parametric tolerance of intersection is equal to :
//! - Precision::Approximation() / 100., or Precision::Approximation() / T.
static Standard_Real PApproximation (const Standard_Real T) { return Parametric(Approximation(),T); }
//! Convert a real space precision to a parametric
//! space precision on a default curve.
//!
//! Value is Parametric(P,1.e+2)
static Standard_Real Parametric (const Standard_Real P) { return Parametric (P, 100.0); }
//! Used to test distances in parametric space on a
//! default curve.
//!
//! This is Precision::Parametric(Precision::Confusion())
static Standard_Real PConfusion() { return Parametric (Confusion()); }
//! Used for Intersections in parametric space on a
//! default curve.
//!
//! This is Precision::Parametric(Precision::Intersection())
static Standard_Real PIntersection() { return Parametric (Intersection()); }
//! Used for Approximations in parametric space on a
//! default curve.
//!
//! This is Precision::Parametric(Precision::Approximation())
static Standard_Real PApproximation() { return Parametric (Approximation()); }
//! Returns True if R may be considered as an infinite
//! number. Currently Abs(R) > 1e100
static Standard_Boolean IsInfinite (const Standard_Real R) { return Abs (R) >= (0.5 * Precision::Infinite()); }
//! Returns True if R may be considered as a positive
//! infinite number. Currently R > 1e100
static Standard_Boolean IsPositiveInfinite (const Standard_Real R) { return R >= (0.5 * Precision::Infinite()); }
//! Returns True if R may be considered as a negative
//! infinite number. Currently R < -1e100
static Standard_Boolean IsNegativeInfinite (const Standard_Real R) { return R <= -(0.5 * Precision::Infinite()); }
//! Returns a big number that can be considered as
//! infinite. Use -Infinite() for a negative big number.
static Standard_Real Infinite() { return 2.e+100; }
};
#endif // _Precision_HeaderFile