-- File:	Precision.cdl
-- Created:	Wed Feb 17 10:39:04 1993
-- Author:	Remi LEQUETTE
--		<rle@phylox>
---Copyright:	 Matra Datavision 1993


package Precision 

	---Purpose: 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.
    
uses
    Standard

is

    Angular returns Real from Standard;
	---Purpose:  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).
	
    Confusion returns Real from Standard;
	---Purpose: 
    	-- 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.
	
    Intersection returns Real from Standard;
	---Purpose: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).

    Approximation returns Real from Standard;
	---Purpose: 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.

    Parametric(P : Real from Standard; T : Real from Standard) 
    returns Real from Standard;
	---Purpose: Convert a real  space precision  to  a  parametric
	--          space precision.   <T>  is the mean  value  of the
	--          length of the tangent of the curve or the surface.
	--          
	--          Value is P / T
	--          
	---C++: inline
	
    PConfusion(T : Real from Standard) returns Real from Standard;
	---Purpose: 
    	-- 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.
	
    PIntersection(T : Real from Standard) returns Real from Standard;
	---Purpose: 
    	-- 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.
 
    PApproximation(T : Real from Standard) returns Real from Standard;
	---Purpose: 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.

    Parametric(P : Real from Standard)
    returns Real from Standard;
	---Purpose: Convert a real  space precision  to  a  parametric
	--          space precision on a default curve.
	--          
	--          Value is Parametric(P,1.e+2)
	--          
	
    PConfusion returns Real from Standard;
	---Purpose: Used  to test distances  in parametric  space on a
	--          default curve.
	--          
	--          This is Precision::Parametric(Precision::Confusion())
	--          
	---C++: inline
	
    PIntersection returns Real from Standard;
	---Purpose: Used for Intersections  in parametric  space  on a
	--          default curve.
	--          
	--          This is Precision::Parametric(Precision::Intersection())
	--          
	---C++: inline

    PApproximation returns Real from Standard;
	---Purpose: Used for  Approximations  in parametric space on a
	--          default curve.
	--          
	--          This is Precision::Parametric(Precision::Approximation())
	--          
	---C++: inline

    IsInfinite(R : Real from Standard) returns Boolean;
	---Purpose: Returns True if R may be considered as an infinite
	--          number. Currently Abs(R) > 1e100

    IsPositiveInfinite(R : Real from Standard) returns Boolean;
	---Purpose: Returns True if R may be considered as  a positive
	--          infinite number. Currently R > 1e100

    IsNegativeInfinite(R : Real from Standard) returns Boolean;
	---Purpose: Returns True if R may  be considered as a negative
	--          infinite number. Currently R < -1e100
	

    Infinite returns Real;
	---Purpose: Returns a  big number that  can  be  considered as
	--          infinite. Use -Infinite() for a negative big number.
	
end Precision;