BSplSLib Class Reference

BSplSLib B-spline surface Library This package provides an implementation of geometric functions for rational and non rational, periodic and non periodic B-spline surface computation. More...

#include <BSplSLib.hxx>

Static Public Member Functions
static void	RationalDerivative (const int UDeg, const int VDeg, const int N, const int M, double &Ders, double &RDers, const bool All=true)
	this is a one dimensional function typedef void (*EvaluatorFunction) ( int // Derivative Request double * // StartEnd[2][2] // [0] = U // [1] = V // [0] = start // [1] = end double // UParameter double // VParamerer double & // Result int &) ;// Error Code serves to multiply a given vectorial BSpline by a function Computes the derivatives of a ratio of two-variables functions x(u,v) / w(u,v) at orders <N,M>, x(u,v) is a vector in dimension <3>.
static void	D0 (const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt &P)
static void	D1 (const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const int Degree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	D2 (const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	D3 (const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
static void	DN (const double U, const double V, const int Nu, const int Nv, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Vec &Vn)
static void	Iso (const double Param, const bool IsU, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, const int Degree, const bool Periodic, NCollection_Array1< gp_Pnt > &CPoles, NCollection_Array1< double > *CWeights)
	Computes the poles and weights of an isoparametric curve at parameter (UIso if <IsU> is True, VIso else).
static void	Reverse (NCollection_Array2< gp_Pnt > &Poles, const int Last, const bool UDirection)
	Reverses the array of poles. Last is the Index of the new first Row( Col) of Poles. On a non periodic surface Last is Poles.Upper(). On a periodic curve last is (number of flat knots - degree - 1) or (sum of multiplicities(but for the last) + degree.
static void	HomogeneousD0 (const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, double &W, gp_Pnt &P)
	Makes an homogeneous evaluation of Poles and Weights any and returns in P the Numerator value and in W the Denominator value if Weights are present otherwise returns 1.0e0.
static void	HomogeneousD1 (const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt &N, gp_Vec &Nu, gp_Vec &Nv, double &D, double &Du, double &Dv)
	Makes an homogeneous evaluation of Poles and Weights any and returns in P the Numerator value and in W the Denominator value if Weights are present otherwise returns 1.0e0.
static void	Reverse (NCollection_Array2< double > &Weights, const int Last, const bool UDirection)
	Reverses the array of weights.
static bool	IsRational (const NCollection_Array2< double > &Weights, const int I1, const int I2, const int J1, const int J2, const double Epsilon=0.0)
	Returns False if all the weights of the array <Weights> in the area [I1,I2] * [J1,J2] are identic. Epsilon is used for comparing weights. If Epsilon is 0. the Epsilon of the first weight is used.
static void	SetPoles (const NCollection_Array2< gp_Pnt > &Poles, NCollection_Array1< double > &FP, const bool UDirection)
	Copy in FP the coordinates of the poles.
static void	SetPoles (const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > &Weights, NCollection_Array1< double > &FP, const bool UDirection)
	Copy in FP the coordinates of the poles.
static void	GetPoles (const NCollection_Array1< double > &FP, NCollection_Array2< gp_Pnt > &Poles, const bool UDirection)
	Get from FP the coordinates of the poles.
static void	GetPoles (const NCollection_Array1< double > &FP, NCollection_Array2< gp_Pnt > &Poles, NCollection_Array2< double > &Weights, const bool UDirection)
	Get from FP the coordinates of the poles.
static void	MovePoint (const double U, const double V, const gp_Vec &Displ, const int UIndex1, const int UIndex2, const int VIndex1, const int VIndex2, const int UDegree, const int VDegree, const bool Rational, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > &Weights, const NCollection_Array1< double > &UFlatKnots, const NCollection_Array1< double > &VFlatKnots, int &UFirstIndex, int &ULastIndex, int &VFirstIndex, int &VLastIndex, NCollection_Array2< gp_Pnt > &NewPoles)
	Find the new poles which allows an old point (with a given u,v as parameters) to reach a new position UIndex1,UIndex2 indicate the range of poles we can move for U (1, UNbPoles-1) or (2, UNbPoles) -> no constraint for one side in U (2, UNbPoles-1) -> the ends are enforced for U don't enter (1,NbPoles) and (1,VNbPoles) -> error: rigid move if problem in BSplineBasis calculation, no change for the curve and UFirstIndex, VLastIndex = 0 VFirstIndex, VLastIndex = 0.
static void	InsertKnots (const bool UDirection, const int Degree, const bool Periodic, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &AddKnots, const NCollection_Array1< int > *AddMults, NCollection_Array2< gp_Pnt > &NewPoles, NCollection_Array2< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Epsilon, const bool Add=true)
static bool	RemoveKnot (const bool UDirection, const int Index, const int Mult, const int Degree, const bool Periodic, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array2< gp_Pnt > &NewPoles, NCollection_Array2< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Tolerance)
static void	IncreaseDegree (const bool UDirection, const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array2< gp_Pnt > &NewPoles, NCollection_Array2< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults)
static void	Unperiodize (const bool UDirection, const int Degree, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &Knots, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, NCollection_Array1< int > &NewMults, NCollection_Array1< double > &NewKnots, NCollection_Array2< gp_Pnt > &NewPoles, NCollection_Array2< double > *NewWeights)
static NCollection_Array2< double > *	NoWeights ()
	Used as argument for a non rational curve.
static void	BuildCache (const double U, const double V, const double USpanDomain, const double VSpanDomain, const bool UPeriodicFlag, const bool VPeriodicFlag, const int UDegree, const int VDegree, const int UIndex, const int VIndex, const NCollection_Array1< double > &UFlatKnots, const NCollection_Array1< double > &VFlatKnots, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, NCollection_Array2< gp_Pnt > &CachePoles, NCollection_Array2< double > *CacheWeights)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expansion for the numerator and stores it in CachePoles.
static void	BuildCache (const double theU, const double theV, const double theUSpanDomain, const double theVSpanDomain, const bool theUPeriodic, const bool theVPeriodic, const int theUDegree, const int theVDegree, const int theUIndex, const int theVIndex, const NCollection_Array1< double > &theUFlatKnots, const NCollection_Array1< double > &theVFlatKnots, const NCollection_Array2< gp_Pnt > &thePoles, const NCollection_Array2< double > *theWeights, NCollection_Array2< double > &theCacheArray)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplSLib_Cache.
static void	CacheD0 (const double U, const double V, const int UDegree, const int VDegree, const double UCacheParameter, const double VCacheParameter, const double USpanLenght, const double VSpanLength, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, gp_Pnt &Point)
	Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.
static void	CoefsD0 (const double U, const double V, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, gp_Pnt &Point)
	Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!
static void	CacheD1 (const double U, const double V, const int UDegree, const int VDegree, const double UCacheParameter, const double VCacheParameter, const double USpanLenght, const double VSpanLength, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV)
	Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.
static void	CoefsD1 (const double U, const double V, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV)
	Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!
static void	CacheD2 (const double U, const double V, const int UDegree, const int VDegree, const double UCacheParameter, const double VCacheParameter, const double USpanLenght, const double VSpanLength, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV, gp_Vec &VecUU, gp_Vec &VecUV, gp_Vec &VecVV)
	Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.
static void	CoefsD2 (const double U, const double V, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV, gp_Vec &VecUU, gp_Vec &VecUV, gp_Vec &VecVV)
	Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!
static void	PolesCoefficients (const NCollection_Array2< gp_Pnt > &Poles, NCollection_Array2< gp_Pnt > &CachePoles)
	Warning! To be used for BezierSurfaces ONLY!!!
static void	PolesCoefficients (const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, NCollection_Array2< gp_Pnt > &CachePoles, NCollection_Array2< double > *CacheWeights)
	Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziersurfaces at parameters 0.,0.; Warning: To be used for BezierSurfaces ONLY!!!
static void	Resolution (const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > &UMults, const NCollection_Array1< int > &VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, const double Tolerance3D, double &UTolerance, double &VTolerance)
	Given a tolerance in 3D space returns two tolerances, one in U one in V such that for all (u1,v1) and (u0,v0) in the domain of the surface f(u,v) we have : | u1 - u0 | < UTolerance and | v1 - v0 | < VTolerance we have |f (u1,v1) - f (u0,v0)| < Tolerance3D.
static void	Interpolate (const int UDegree, const int VDegree, const NCollection_Array1< double > &UFlatKnots, const NCollection_Array1< double > &VFlatKnots, const NCollection_Array1< double > &UParameters, const NCollection_Array1< double > &VParameters, NCollection_Array2< gp_Pnt > &Poles, NCollection_Array2< double > &Weights, int &InversionProblem)
	Performs the interpolation of the data points given in the Poles array in the form [1,...,RL][1,...,RC][1...PolesDimension]. The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1.
static void	Interpolate (const int UDegree, const int VDegree, const NCollection_Array1< double > &UFlatKnots, const NCollection_Array1< double > &VFlatKnots, const NCollection_Array1< double > &UParameters, const NCollection_Array1< double > &VParameters, NCollection_Array2< gp_Pnt > &Poles, int &InversionProblem)
	Performs the interpolation of the data points given in the Poles array. The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1.
static void	FunctionMultiply (const BSplSLib_EvaluatorFunction &Function, const int UBSplineDegree, const int VBSplineDegree, const NCollection_Array1< double > &UBSplineKnots, const NCollection_Array1< double > &VBSplineKnots, const NCollection_Array1< int > *UMults, const NCollection_Array1< int > *VMults, const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > *Weights, const NCollection_Array1< double > &UFlatKnots, const NCollection_Array1< double > &VFlatKnots, const int UNewDegree, const int VNewDegree, NCollection_Array2< gp_Pnt > &NewNumerator, NCollection_Array2< double > &NewDenominator, int &theStatus)
	this will multiply a given BSpline numerator N(u,v) and denominator D(u,v) defined by its U/VBSplineDegree and U/VBSplineKnots, and U/VMults. Its Poles and Weights are arrays which are coded as array2 of the form [1..UNumPoles][1..VNumPoles] by a function a(u,v) which is assumed to satisfy the following:
static NCollection_Array2< double >	UnitWeights (const int theNbUPoles, const int theNbVPoles)
	Returns an NCollection_Array2<double> filled with 1.0 values. If theNbUPoles * theNbVPoles <= BSplCLib::MaxUnitWeightsSize(), references a pre-allocated global array (zero allocation). Otherwise, allocates a new array and fills with 1.0.

Detailed Description

BSplSLib B-spline surface Library This package provides an implementation of geometric functions for rational and non rational, periodic and non periodic B-spline surface computation.

this package uses the multi-dimensions splines methods provided in the package BSplCLib.

In this package the B-spline surface is defined with: . its control points : Array2OfPnt Poles . its weights : Array2OfReal Weights . its knots and their multiplicity in the two parametric direction U and V: Array1OfReal UKnots, VKnots and Array1OfInteger UMults, VMults. . the degree of the normalized Spline functions: UDegree, VDegree

. the Booleans URational, VRational to know if the weights are constant in the U or V direction.

. the Booleans UPeriodic, VRational to know if the surface is periodic in the U or V direction.

Warnings: The bounds of UKnots and UMults should be the same, the bounds of VKnots and VMults should be the same, the bounds of Poles and Weights should be the same.

The Control points representation is: Poles(Uorigin,Vorigin) ...................Poles(Uorigin,Vend) . . . . Poles(Uend, Vorigin) .....................Poles(Uend, Vend)

For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction.

Note: weight and multiplicity arrays can be passed by pointer for some functions so that NULL pointer is valid. That means no weights/no multiplicities passed.

KeyWords : B-spline surface, Functions, Library

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

Member Function Documentation

BuildCache() [1/2]

static void BSplSLib::BuildCache ( const double theU, const double theV, const double theUSpanDomain, const double theVSpanDomain, const bool theUPeriodic, const bool theVPeriodic, const int theUDegree, const int theVDegree, const int theUIndex, const int theVIndex, const NCollection_Array1< double > & theUFlatKnots, const NCollection_Array1< double > & theVFlatKnots, const NCollection_Array2< gp_Pnt > & thePoles, const NCollection_Array2< double > * theWeights, NCollection_Array2< double > & theCacheArray )

static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplSLib_Cache.

BuildCache() [2/2]

static void BSplSLib::BuildCache ( const double U, const double V, const double USpanDomain, const double VSpanDomain, const bool UPeriodicFlag, const bool VPeriodicFlag, const int UDegree, const int VDegree, const int UIndex, const int VIndex, const NCollection_Array1< double > & UFlatKnots, const NCollection_Array1< double > & VFlatKnots, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, NCollection_Array2< gp_Pnt > & CachePoles, NCollection_Array2< double > * CacheWeights )

static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expansion for the numerator and stores it in CachePoles.

CacheD0()

static void BSplSLib::CacheD0 ( const double U, const double V, const int UDegree, const int VDegree, const double UCacheParameter, const double VCacheParameter, const double USpanLenght, const double VSpanLength, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, gp_Pnt & Point )

static

Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.

CacheD1()

static void BSplSLib::CacheD1 ( const double U, const double V, const int UDegree, const int VDegree, const double UCacheParameter, const double VCacheParameter, const double USpanLenght, const double VSpanLength, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, gp_Pnt & Point, gp_Vec & VecU, gp_Vec & VecV )

static

Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.

CacheD2()

static void BSplSLib::CacheD2 ( const double U, const double V, const int UDegree, const int VDegree, const double UCacheParameter, const double VCacheParameter, const double USpanLenght, const double VSpanLength, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, gp_Pnt & Point, gp_Vec & VecU, gp_Vec & VecV, gp_Vec & VecUU, gp_Vec & VecUV, gp_Vec & VecVV )

static

Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.

CoefsD0()

static void BSplSLib::CoefsD0 ( const double U, const double V, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, gp_Pnt & Point )

static

Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!

CoefsD1()

static void BSplSLib::CoefsD1 ( const double U, const double V, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, gp_Pnt & Point, gp_Vec & VecU, gp_Vec & VecV )

static

Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!

CoefsD2()

static void BSplSLib::CoefsD2 ( const double U, const double V, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, gp_Pnt & Point, gp_Vec & VecU, gp_Vec & VecV, gp_Vec & VecUU, gp_Vec & VecUV, gp_Vec & VecVV )

static

Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!!

D0()

static void BSplSLib::D0 ( const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt & P )

static

D1()

static void BSplSLib::D1 ( const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const int Degree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt & P, gp_Vec & Vu, gp_Vec & Vv )

static

D2()

static void BSplSLib::D2 ( const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt & P, gp_Vec & Vu, gp_Vec & Vv, gp_Vec & Vuu, gp_Vec & Vvv, gp_Vec & Vuv )

static

D3()

static void BSplSLib::D3 ( const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt & P, gp_Vec & Vu, gp_Vec & Vv, gp_Vec & Vuu, gp_Vec & Vvv, gp_Vec & Vuv, gp_Vec & Vuuu, gp_Vec & Vvvv, gp_Vec & Vuuv, gp_Vec & Vuvv )

static

DN()

static void BSplSLib::DN ( const double U, const double V, const int Nu, const int Nv, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Vec & Vn )

static

FunctionMultiply()

static void BSplSLib::FunctionMultiply ( const BSplSLib_EvaluatorFunction & Function, const int UBSplineDegree, const int VBSplineDegree, const NCollection_Array1< double > & UBSplineKnots, const NCollection_Array1< double > & VBSplineKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UFlatKnots, const NCollection_Array1< double > & VFlatKnots, const int UNewDegree, const int VNewDegree, NCollection_Array2< gp_Pnt > & NewNumerator, NCollection_Array2< double > & NewDenominator, int & theStatus )

static

this will multiply a given BSpline numerator N(u,v) and denominator D(u,v) defined by its U/VBSplineDegree and U/VBSplineKnots, and U/VMults. Its Poles and Weights are arrays which are coded as array2 of the form [1..UNumPoles][1..VNumPoles] by a function a(u,v) which is assumed to satisfy the following:

1. a(u,v) * N(u,v) and a(u,v) * D(u,v) is a polynomial BSpline that can be expressed exactly as a BSpline of degree U/VNewDegree on the knots U/VFlatKnots
2. the range of a(u,v) is the same as the range of N(u,v) or D(u,v) Warning: it is the caller's responsibility to insure that conditions 1. and 2. above are satisfied no check whatsoever is made in this method theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(u,v)* N(u,v) and a(u,v) * D(u,v) theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline: the method used is interpolation at Schoenenberg

points of a(u,v)*F(u,v)

GetPoles() [1/2]

static void BSplSLib::GetPoles ( const NCollection_Array1< double > & FP, NCollection_Array2< gp_Pnt > & Poles, const bool UDirection )

static

Get from FP the coordinates of the poles.

GetPoles() [2/2]

static void BSplSLib::GetPoles ( const NCollection_Array1< double > & FP, NCollection_Array2< gp_Pnt > & Poles, NCollection_Array2< double > & Weights, const bool UDirection )

static

Get from FP the coordinates of the poles.

HomogeneousD0()

static void BSplSLib::HomogeneousD0 ( const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, double & W, gp_Pnt & P )

static

Makes an homogeneous evaluation of Poles and Weights any and returns in P the Numerator value and in W the Denominator value if Weights are present otherwise returns 1.0e0.

HomogeneousD1()

static void BSplSLib::HomogeneousD1 ( const double U, const double V, const int UIndex, const int VIndex, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > * UMults, const NCollection_Array1< int > * VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, gp_Pnt & N, gp_Vec & Nu, gp_Vec & Nv, double & D, double & Du, double & Dv )

static

Makes an homogeneous evaluation of Poles and Weights any and returns in P the Numerator value and in W the Denominator value if Weights are present otherwise returns 1.0e0.

IncreaseDegree()

static void BSplSLib::IncreaseDegree ( const bool UDirection, const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array2< gp_Pnt > & NewPoles, NCollection_Array2< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults )

static

InsertKnots()

static void BSplSLib::InsertKnots ( const bool UDirection, const int Degree, const bool Periodic, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & AddKnots, const NCollection_Array1< int > * AddMults, NCollection_Array2< gp_Pnt > & NewPoles, NCollection_Array2< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Epsilon, const bool Add = true )

static

Interpolate() [1/2]

static void BSplSLib::Interpolate ( const int UDegree, const int VDegree, const NCollection_Array1< double > & UFlatKnots, const NCollection_Array1< double > & VFlatKnots, const NCollection_Array1< double > & UParameters, const NCollection_Array1< double > & VParameters, NCollection_Array2< gp_Pnt > & Poles, int & InversionProblem )

static

Performs the interpolation of the data points given in the Poles array. The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1.

The RowLength RL and the Length of VParameters must be the same. The length of VFlatKnots is Degree + RL + 1.

Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot

Interpolate() [2/2]

static void BSplSLib::Interpolate ( const int UDegree, const int VDegree, const NCollection_Array1< double > & UFlatKnots, const NCollection_Array1< double > & VFlatKnots, const NCollection_Array1< double > & UParameters, const NCollection_Array1< double > & VParameters, NCollection_Array2< gp_Pnt > & Poles, NCollection_Array2< double > & Weights, int & InversionProblem )

static

Performs the interpolation of the data points given in the Poles array in the form [1,...,RL][1,...,RC][1...PolesDimension]. The ColLength CL and the Length of UParameters must be the same. The length of VFlatKnots is VDegree + CL + 1.

The RowLength RL and the Length of VParameters must be the same. The length of VFlatKnots is Degree + RL + 1.

Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot

Iso()

static void BSplSLib::Iso ( const double Param, const bool IsU, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, const int Degree, const bool Periodic, NCollection_Array1< gp_Pnt > & CPoles, NCollection_Array1< double > * CWeights )

static

Computes the poles and weights of an isoparametric curve at parameter (UIso if <IsU> is True, VIso else).

IsRational()

static bool BSplSLib::IsRational ( const NCollection_Array2< double > & Weights, const int I1, const int I2, const int J1, const int J2, const double Epsilon = 0.0 )

static

Returns False if all the weights of the array <Weights> in the area [I1,I2] * [J1,J2] are identic. Epsilon is used for comparing weights. If Epsilon is 0. the Epsilon of the first weight is used.

MovePoint()

static void BSplSLib::MovePoint ( const double U, const double V, const gp_Vec & Displ, const int UIndex1, const int UIndex2, const int VIndex1, const int VIndex2, const int UDegree, const int VDegree, const bool Rational, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > & Weights, const NCollection_Array1< double > & UFlatKnots, const NCollection_Array1< double > & VFlatKnots, int & UFirstIndex, int & ULastIndex, int & VFirstIndex, int & VLastIndex, NCollection_Array2< gp_Pnt > & NewPoles )

static

Find the new poles which allows an old point (with a given u,v as parameters) to reach a new position UIndex1,UIndex2 indicate the range of poles we can move for U (1, UNbPoles-1) or (2, UNbPoles) -> no constraint for one side in U (2, UNbPoles-1) -> the ends are enforced for U don't enter (1,NbPoles) and (1,VNbPoles) -> error: rigid move if problem in BSplineBasis calculation, no change for the curve and UFirstIndex, VLastIndex = 0 VFirstIndex, VLastIndex = 0.

NoWeights()

static NCollection_Array2< double > * BSplSLib::NoWeights ( )

static

Used as argument for a non rational curve.

PolesCoefficients() [1/2]

static void BSplSLib::PolesCoefficients ( const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, NCollection_Array2< gp_Pnt > & CachePoles, NCollection_Array2< double > * CacheWeights )

static

Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziersurfaces at parameters 0.,0.; Warning: To be used for BezierSurfaces ONLY!!!

PolesCoefficients() [2/2]

static void BSplSLib::PolesCoefficients ( const NCollection_Array2< gp_Pnt > & Poles, NCollection_Array2< gp_Pnt > & CachePoles )

static

Warning! To be used for BezierSurfaces ONLY!!!

RationalDerivative()

static void BSplSLib::RationalDerivative ( const int UDeg, const int VDeg, const int N, const int M, double & Ders, double & RDers, const bool All = true )

static

this is a one dimensional function typedef void (*EvaluatorFunction) ( int // Derivative Request double * // StartEnd[2][2] // [0] = U // [1] = V // [0] = start // [1] = end double // UParameter double // VParamerer double & // Result int &) ;// Error Code serves to multiply a given vectorial BSpline by a function Computes the derivatives of a ratio of two-variables functions x(u,v) / w(u,v) at orders <N,M>, x(u,v) is a vector in dimension <3>.

<Ders> is an array containing the values of the input derivatives from 0 to std::min(<N>,<UDeg>), 0 to std::min(<M>,<VDeg>). For orders higher than <UDeg,VDeg> the input derivatives are assumed to be 0.

The <Ders> is a 2d array and the dimension of the lines is always (<VDeg>+1) * (<3>+1), even if <N> is smaller than <Udeg> (the derivatives higher than <N> are not used).

Content of <Ders>:

x(i,j)[k] means: the composant k of x derivated (i) times in u and (j) times in v.

... First line ...

x[1],x[2],...,x[3],w x(0,1)[1],...,x(0,1)[3],w(1,0) ... x(0,VDeg)[1],...,x(0,VDeg)[3],w(0,VDeg)

... Then second line ...

x(1,0)[1],...,x(1,0)[3],w(1,0) x(1,1)[1],...,x(1,1)[3],w(1,1) ... x(1,VDeg)[1],...,x(1,VDeg)[3],w(1,VDeg)

...

... Last line ...

x(UDeg,0)[1],...,x(UDeg,0)[3],w(UDeg,0) x(UDeg,1)[1],...,x(UDeg,1)[3],w(UDeg,1) ... x(Udeg,VDeg)[1],...,x(UDeg,VDeg)[3],w(Udeg,VDeg)

If <All> is false, only the derivative at order <N,M> is computed. <RDers> is an array of length 3 which will contain the result :

x(1)/w , x(2)/w , ... derivated <N> <M> times

If <All> is true multiples derivatives are computed. All the derivatives (i,j) with 0 <= i+j <= std::max(N,M) are computed. <RDers> is an array of length 3 * (<N>+1) * (<M>+1) which will contains:

x(1)/w , x(2)/w , ... x(1)/w , x(2)/w , ... derivated <0,1> times x(1)/w , x(2)/w , ... derivated <0,2> times ... x(1)/w , x(2)/w , ... derivated <0,N> times

x(1)/w , x(2)/w , ... derivated <1,0> times x(1)/w , x(2)/w , ... derivated <1,1> times ... x(1)/w , x(2)/w , ... derivated <1,N> times

x(1)/w , x(2)/w , ... derivated <N,0> times .... Warning: <RDers> must be dimensioned properly.

RemoveKnot()

static bool BSplSLib::RemoveKnot ( const bool UDirection, const int Index, const int Mult, const int Degree, const bool Periodic, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array2< gp_Pnt > & NewPoles, NCollection_Array2< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Tolerance )

static

Resolution()

static void BSplSLib::Resolution ( const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, const NCollection_Array1< double > & UKnots, const NCollection_Array1< double > & VKnots, const NCollection_Array1< int > & UMults, const NCollection_Array1< int > & VMults, const int UDegree, const int VDegree, const bool URat, const bool VRat, const bool UPer, const bool VPer, const double Tolerance3D, double & UTolerance, double & VTolerance )

static

Given a tolerance in 3D space returns two tolerances, one in U one in V such that for all (u1,v1) and (u0,v0) in the domain of the surface f(u,v) we have : | u1 - u0 | < UTolerance and | v1 - v0 | < VTolerance we have |f (u1,v1) - f (u0,v0)| < Tolerance3D.

Reverse() [1/2]

static void BSplSLib::Reverse ( NCollection_Array2< double > & Weights, const int Last, const bool UDirection )

static

Reverses the array of weights.

Reverse() [2/2]

static void BSplSLib::Reverse ( NCollection_Array2< gp_Pnt > & Poles, const int Last, const bool UDirection )

static

Reverses the array of poles. Last is the Index of the new first Row( Col) of Poles. On a non periodic surface Last is Poles.Upper(). On a periodic curve last is (number of flat knots - degree - 1) or (sum of multiplicities(but for the last) + degree.

• 1)

SetPoles() [1/2]

static void BSplSLib::SetPoles ( const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > & Weights, NCollection_Array1< double > & FP, const bool UDirection )

static

Copy in FP the coordinates of the poles.

SetPoles() [2/2]

static void BSplSLib::SetPoles ( const NCollection_Array2< gp_Pnt > & Poles, NCollection_Array1< double > & FP, const bool UDirection )

static

Copy in FP the coordinates of the poles.

UnitWeights()

static NCollection_Array2< double > BSplSLib::UnitWeights ( const int theNbUPoles, const int theNbVPoles )

static

Returns an NCollection_Array2<double> filled with 1.0 values. If theNbUPoles * theNbVPoles <= BSplCLib::MaxUnitWeightsSize(), references a pre-allocated global array (zero allocation). Otherwise, allocates a new array and fills with 1.0.

Warning

The returned array may reference global static memory – do NOT modify elements.

Parameters

[in]	theNbUPoles	number of poles in U direction
[in]	theNbVPoles	number of poles in V direction

Returns

array of unit weights with bounds [1, theNbUPoles] x [1, theNbVPoles]

Unperiodize()

static void BSplSLib::Unperiodize ( const bool UDirection, const int Degree, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & Knots, const NCollection_Array2< gp_Pnt > & Poles, const NCollection_Array2< double > * Weights, NCollection_Array1< int > & NewMults, NCollection_Array1< double > & NewKnots, NCollection_Array2< gp_Pnt > & NewPoles, NCollection_Array2< double > * NewWeights )

static

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The documentation for this class was generated from the following file:

• BSplSLib.hxx