OCC.Precision module

The Precision package offers a set of functions defining precision criteriafor use in conventional situations when comparing two numbers.GeneralitiesIt is not advisable to use floating number equality. Instead, the differencebetween 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 numberx2 = … ! another large numberIf ( 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 numberx2 = … ! another large numberIf ( x2 - x1 > Precision ) …Precision in Cas.CadeGenerally speaking, the precision criterion is not implicit in Cas.Cade. Low-level geometric algorithms acceptprecision criteria as arguments. As a rule, they should not refer directly to the precision criteria provided by thePrecision package.On the other hand, high-level modeling algorithms have to provide the low-level geometric algorithms that theycall, 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, theTopology Data Structure stores precision criteria for each elementary shape (as a vertex, an edge or a face). Whena new topological object is constructed, the precision criteria are taken from those provided by the Precisionpackage, and stored in the related data structure. Later, a topological algorithm which analyses these objects willwork with the values stored in the data structure. Also, if this algorithm is to build a new topological object, fromthese precision criteria, it will compute a new precision criterion for the new topological object, and write it into thedata structure of the new topological object.The different precision criteria offered by the Precision package, cover the most common requirements ofgeometric 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 accuracyof the machine and the unit of measurement.The choice of precision criteria for parametric space depends on both the accuracy of the machine and thedimensions of the curve or the surface, since the parametric precision criterion and the real precision criterion arelinked : if the curve is defined by the equation P(t), the inequation :Abs ( t2 - t1 ) < ParametricPrecisionmeans that the parameters t1 and t2 are considered to be equal, and the inequation :Distance ( P(t2) , P(t1) ) < RealPrecisionmeans that the points P(t1) and P(t2) are considered to be coincident. It seems to be the same idea, and itwould 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 verifyif any value could be considered as infinite.All the provided functions are very simple. The returned values result from the adaptation of the applicationsdeveloped by the Open CASCADE company to Open CASCADE algorithms. The main interest of these functionslies in that it incites engineers developing applications to ask questions on precision factors. Which one is to beused 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 applicationenvironment, it is crucial to master precision even though this process may take a great deal of time.

class SwigPyIterator(*args, **kwargs)

Bases: object

advance()
copy()
decr()
distance()
equal()
incr()
next()
previous()
thisown

The membership flag

value()
new_instancemethod(func, inst, cls)
class precision

Bases: object

static Angular()
  • 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).
Return type:float
static Approximation()
  • 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.
Return type:float
static Confusion()
  • 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.
Return type:float
static Infinite()
  • Returns a big number that can be considered as infinite. Use -Infinite() for a negative big number.
Return type:float
static Intersection()
  • 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).
Return type:float
static IsInfinite()
  • Returns True if R may be considered as an infinite number. Currently Abs(R) > 1e100
Parameters:R (float) –
Return type:bool
static IsNegativeInfinite()
  • Returns True if R may be considered as a negative infinite number. Currently R < -1e100
Parameters:R (float) –
Return type:bool
static IsPositiveInfinite()
  • Returns True if R may be considered as a positive infinite number. Currently R > 1e100
Parameters:R (float) –
Return type:bool
static PApproximation()
  • 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.
Parameters:T (float) –
Return type:float
  • Used for Approximations in parametric space on a default curve. //! This is Precision::Parametric(Precision::Approximation())
Return type:float
static PConfusion()
  • 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.
Parameters:T (float) –
Return type:float
  • Used to test distances in parametric space on a default curve. //! This is Precision::Parametric(Precision::Confusion())
Return type:float
static PIntersection()
  • 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.
Parameters:T (float) –
Return type:float
  • Used for Intersections in parametric space on a default curve. //! This is Precision::Parametric(Precision::Intersection())
Return type:float
static Parametric()
  • 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
Parameters:
Return type:

float
  • Convert a real space precision to a parametric space precision on a default curve. //! Value is Parametric(P,1.e+2)
Parameters:P (float) –
Return type:float
static SquareConfusion()
  • Returns square of Confusion. Created for speed and convenience.
Return type:float
thisown

The membership flag

precision_Angular()
  • 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).
Return type:float
precision_Approximation()
  • 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.
Return type:float
precision_Confusion()
  • 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.
Return type:float
precision_Infinite()
  • Returns a big number that can be considered as infinite. Use -Infinite() for a negative big number.
Return type:float
precision_Intersection()
  • 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).
Return type:float
precision_IsInfinite()
  • Returns True if R may be considered as an infinite number. Currently Abs(R) > 1e100
Parameters:R (float) –
Return type:bool
precision_IsNegativeInfinite()
  • Returns True if R may be considered as a negative infinite number. Currently R < -1e100
Parameters:R (float) –
Return type:bool
precision_IsPositiveInfinite()
  • Returns True if R may be considered as a positive infinite number. Currently R > 1e100
Parameters:R (float) –
Return type:bool
precision_PApproximation()
  • 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.
Parameters:T (float) –
Return type:float
  • Used for Approximations in parametric space on a default curve. //! This is Precision::Parametric(Precision::Approximation())
Return type:float
precision_PConfusion()
  • 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.
Parameters:T (float) –
Return type:float
  • Used to test distances in parametric space on a default curve. //! This is Precision::Parametric(Precision::Confusion())
Return type:float
precision_PIntersection()
  • 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.
Parameters:T (float) –
Return type:float
  • Used for Intersections in parametric space on a default curve. //! This is Precision::Parametric(Precision::Intersection())
Return type:float
precision_Parametric()
  • 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
Parameters:
Return type:

float
  • Convert a real space precision to a parametric space precision on a default curve. //! Value is Parametric(P,1.e+2)
Parameters:P (float) –
Return type:float
precision_SquareConfusion()
  • Returns square of Confusion. Created for speed and convenience.
Return type:float
register_handle(handle, base_object)

Inserts the handle into the base object to prevent memory corruption in certain cases