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 Standard_Integer UDeg, const Standard_Integer VDeg, const Standard_Integer N, const Standard_Integer M, Standard_Real &Ders, Standard_Real &RDers, const Standard_Boolean All=Standard_True)
	this is a one dimensional function typedef void (EvaluatorFunction) ( Standard_Integer // Derivative Request Standard_Real // StartEnd[2][2] // [0] = U // [1] = V // [0] = start // [1] = end Standard_Real // UParameter Standard_Real // VParamerer Standard_Real & // Result Standard_Integer &) ;// 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>. More...

static void	D0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P)

static void	D1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer Degree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)

static void	D2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)

static void	D3 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean 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 Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Vec &Vn)

static void	Iso (const Standard_Real Param, const Standard_Boolean IsU, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger Mults, const Standard_Integer Degree, const Standard_Boolean Periodic, TColgp_Array1OfPnt &CPoles, TColStd_Array1OfReal *CWeights)
	Computes the poles and weights of an isoparametric curve at parameter (UIso if <IsU> is True, VIso else). More...

static void	Reverse (TColgp_Array2OfPnt &Poles, const Standard_Integer Last, const Standard_Boolean 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. More...

static void	HomogeneousD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, Standard_Real &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. More...

static void	HomogeneousD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger *VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &N, gp_Vec &Nu, gp_Vec &Nv, Standard_Real &D, Standard_Real &Du, Standard_Real &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. More...

static void	Reverse (TColStd_Array2OfReal &Weights, const Standard_Integer Last, const Standard_Boolean UDirection)
	Reverses the array of weights. More...

static Standard_Boolean	IsRational (const TColStd_Array2OfReal &Weights, const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer J1, const Standard_Integer J2, const Standard_Real 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. More...

static void	SetPoles (const TColgp_Array2OfPnt &Poles, TColStd_Array1OfReal &FP, const Standard_Boolean UDirection)
	Copy in FP the coordinates of the poles. More...

static void	SetPoles (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, TColStd_Array1OfReal &FP, const Standard_Boolean UDirection)
	Copy in FP the coordinates of the poles. More...

static void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array2OfPnt &Poles, const Standard_Boolean UDirection)
	Get from FP the coordinates of the poles. More...

static void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal &Weights, const Standard_Boolean UDirection)
	Get from FP the coordinates of the poles. More...

static void	MovePoint (const Standard_Real U, const Standard_Real V, const gp_Vec &Displ, const Standard_Integer UIndex1, const Standard_Integer UIndex2, const Standard_Integer VIndex1, const Standard_Integer VIndex2, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean Rational, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, Standard_Integer &UFirstIndex, Standard_Integer &ULastIndex, Standard_Integer &VFirstIndex, Standard_Integer &VLastIndex, TColgp_Array2OfPnt &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. More...

static void	InsertKnots (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger AddMults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True)

static Standard_Boolean	RemoveKnot (const Standard_Boolean UDirection, const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance)

static void	IncreaseDegree (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults)

static void	Unperiodize (const Standard_Boolean UDirection, const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal NewWeights)

static TColStd_Array2OfReal *	NoWeights ()
	Used as argument for a non rational curve. More...

static void	BuildCache (const Standard_Real U, const Standard_Real V, const Standard_Real USpanDomain, const Standard_Real VSpanDomain, const Standard_Boolean UPeriodicFlag, const Standard_Boolean VPeriodicFlag, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, TColgp_Array2OfPnt &CachePoles, TColStd_Array2OfReal CacheWeights)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expension for the numerator and stores it in CachePoles. More...

static void	BuildCache (const Standard_Real theU, const Standard_Real theV, const Standard_Real theUSpanDomain, const Standard_Real theVSpanDomain, const Standard_Boolean theUPeriodic, const Standard_Boolean theVPeriodic, const Standard_Integer theUDegree, const Standard_Integer theVDegree, const Standard_Integer theUIndex, const Standard_Integer theVIndex, const TColStd_Array1OfReal &theUFlatKnots, const TColStd_Array1OfReal &theVFlatKnots, const TColgp_Array2OfPnt &thePoles, const TColStd_Array2OfReal *theWeights, TColStd_Array2OfReal &theCacheArray)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplSLib_Cache. More...

static void	CacheD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *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. More...

static void	CoefsD0 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, gp_Pnt &Point)
	Calls CacheD0 for Bezier Surfaces Arrays computed with the method PolesCoefficients. Warning: To be used for BezierSurfaces ONLY!!! More...

static void	CacheD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *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. More...

static void	CoefsD1 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *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!!! More...

static void	CacheD2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *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. More...

static void	CoefsD2 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *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!!! More...

static void	PolesCoefficients (const TColgp_Array2OfPnt &Poles, TColgp_Array2OfPnt &CachePoles)
	Warning! To be used for BezierSurfaces ONLY!!! More...

static void	PolesCoefficients (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal Weights, TColgp_Array2OfPnt &CachePoles, TColStd_Array2OfReal 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!!! More...

static void	Resolution (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, const Standard_Real Tolerance3D, Standard_Real &UTolerance, Standard_Real &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. More...

static void	Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColStd_Array1OfReal &UParameters, const TColStd_Array1OfReal &VParameters, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal &Weights, Standard_Integer &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. More...

static void	Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColStd_Array1OfReal &UParameters, const TColStd_Array1OfReal &VParameters, TColgp_Array2OfPnt &Poles, Standard_Integer &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. More...

static void	FunctionMultiply (const BSplSLib_EvaluatorFunction &Function, const Standard_Integer UBSplineDegree, const Standard_Integer VBSplineDegree, const TColStd_Array1OfReal &UBSplineKnots, const TColStd_Array1OfReal &VBSplineKnots, const TColStd_Array1OfInteger UMults, const TColStd_Array1OfInteger VMults, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal *Weights, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const Standard_Integer UNewDegree, const Standard_Integer VNewDegree, TColgp_Array2OfPnt &NewNumerator, TColStd_Array2OfReal &NewDenominator, Standard_Integer &Status)
	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 responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method – Status 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) Status 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) More...

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 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 shoud 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

static void BSplSLib::BuildCache	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Real	USpanDomain,
		const Standard_Real	VSpanDomain,
		const Standard_Boolean	UPeriodicFlag,
		const Standard_Boolean	VPeriodicFlag,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColStd_Array1OfReal &	UFlatKnots,
		const TColStd_Array1OfReal &	VFlatKnots,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		TColgp_Array2OfPnt &	CachePoles,
		TColStd_Array2OfReal *	CacheWeights
	)

static

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

static void BSplSLib::BuildCache	(	const Standard_Real	theU,
		const Standard_Real	theV,
		const Standard_Real	theUSpanDomain,
		const Standard_Real	theVSpanDomain,
		const Standard_Boolean	theUPeriodic,
		const Standard_Boolean	theVPeriodic,
		const Standard_Integer	theUDegree,
		const Standard_Integer	theVDegree,
		const Standard_Integer	theUIndex,
		const Standard_Integer	theVIndex,
		const TColStd_Array1OfReal &	theUFlatKnots,
		const TColStd_Array1OfReal &	theVFlatKnots,
		const TColgp_Array2OfPnt &	thePoles,
		const TColStd_Array2OfReal *	theWeights,
		TColStd_Array2OfReal &	theCacheArray
	)

static

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

static void BSplSLib::CacheD0	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Real	UCacheParameter,
		const Standard_Real	VCacheParameter,
		const Standard_Real	USpanLenght,
		const Standard_Real	VSpanLength,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	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.

static void BSplSLib::CacheD1	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Real	UCacheParameter,
		const Standard_Real	VCacheParameter,
		const Standard_Real	USpanLenght,
		const Standard_Real	VSpanLength,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	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.

static void BSplSLib::CacheD2	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Real	UCacheParameter,
		const Standard_Real	VCacheParameter,
		const Standard_Real	USpanLenght,
		const Standard_Real	VSpanLength,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	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.

static void BSplSLib::CoefsD0	(	const Standard_Real	U,
		const Standard_Real	V,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		gp_Pnt &	Point
	)

static

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

static void BSplSLib::CoefsD1	(	const Standard_Real	U,
		const Standard_Real	V,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	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!!!

static void BSplSLib::CoefsD2	(	const Standard_Real	U,
		const Standard_Real	V,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	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!!!

static void BSplSLib::D0	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	VPer,
		gp_Pnt &	P
	)

static

static void BSplSLib::D1	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const Standard_Integer	Degree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	VPer,
		gp_Pnt &	P,
		gp_Vec &	Vu,
		gp_Vec &	Vv
	)

static

static void BSplSLib::D2	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	VPer,
		gp_Pnt &	P,
		gp_Vec &	Vu,
		gp_Vec &	Vv,
		gp_Vec &	Vuu,
		gp_Vec &	Vvv,
		gp_Vec &	Vuv
	)

static

static void BSplSLib::D3	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	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

static void BSplSLib::DN	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	Nu,
		const Standard_Integer	Nv,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	VPer,
		gp_Vec &	Vn
	)

static

static void BSplSLib::FunctionMultiply	(	const BSplSLib_EvaluatorFunction &	Function,
		const Standard_Integer	UBSplineDegree,
		const Standard_Integer	VBSplineDegree,
		const TColStd_Array1OfReal &	UBSplineKnots,
		const TColStd_Array1OfReal &	VBSplineKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UFlatKnots,
		const TColStd_Array1OfReal &	VFlatKnots,
		const Standard_Integer	UNewDegree,
		const Standard_Integer	VNewDegree,
		TColgp_Array2OfPnt &	NewNumerator,
		TColStd_Array2OfReal &	NewDenominator,
		Standard_Integer &	Status
	)

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 responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method – Status 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) Status 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)

static void BSplSLib::GetPoles	(	const TColStd_Array1OfReal &	FP,
		TColgp_Array2OfPnt &	Poles,
		const Standard_Boolean	UDirection
	)

static

Get from FP the coordinates of the poles.

static void BSplSLib::GetPoles	(	const TColStd_Array1OfReal &	FP,
		TColgp_Array2OfPnt &	Poles,
		TColStd_Array2OfReal &	Weights,
		const Standard_Boolean	UDirection
	)

static

Get from FP the coordinates of the poles.

static void BSplSLib::HomogeneousD0	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	VPer,
		Standard_Real &	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.

static void BSplSLib::HomogeneousD1	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger *	UMults,
		const TColStd_Array1OfInteger *	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	VPer,
		gp_Pnt &	N,
		gp_Vec &	Nu,
		gp_Vec &	Nv,
		Standard_Real &	D,
		Standard_Real &	Du,
		Standard_Real &	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.

static void BSplSLib::IncreaseDegree	(	const Standard_Boolean	UDirection,
		const Standard_Integer	Degree,
		const Standard_Integer	NewDegree,
		const Standard_Boolean	Periodic,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		TColgp_Array2OfPnt &	NewPoles,
		TColStd_Array2OfReal *	NewWeights,
		TColStd_Array1OfReal &	NewKnots,
		TColStd_Array1OfInteger &	NewMults
	)

static

static void BSplSLib::InsertKnots	(	const Standard_Boolean	UDirection,
		const Standard_Integer	Degree,
		const Standard_Boolean	Periodic,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		const TColStd_Array1OfReal &	AddKnots,
		const TColStd_Array1OfInteger *	AddMults,
		TColgp_Array2OfPnt &	NewPoles,
		TColStd_Array2OfReal *	NewWeights,
		TColStd_Array1OfReal &	NewKnots,
		TColStd_Array1OfInteger &	NewMults,
		const Standard_Real	Epsilon,
		const Standard_Boolean	Add = `Standard_True`
	)

static

static void BSplSLib::Interpolate	(	const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const TColStd_Array1OfReal &	UFlatKnots,
		const TColStd_Array1OfReal &	VFlatKnots,
		const TColStd_Array1OfReal &	UParameters,
		const TColStd_Array1OfReal &	VParameters,
		TColgp_Array2OfPnt &	Poles,
		TColStd_Array2OfReal &	Weights,
		Standard_Integer &	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

static void BSplSLib::Interpolate	(	const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const TColStd_Array1OfReal &	UFlatKnots,
		const TColStd_Array1OfReal &	VFlatKnots,
		const TColStd_Array1OfReal &	UParameters,
		const TColStd_Array1OfReal &	VParameters,
		TColgp_Array2OfPnt &	Poles,
		Standard_Integer &	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

static void BSplSLib::Iso	(	const Standard_Real	Param,
		const Standard_Boolean	IsU,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger *	Mults,
		const Standard_Integer	Degree,
		const Standard_Boolean	Periodic,
		TColgp_Array1OfPnt &	CPoles,
		TColStd_Array1OfReal *	CWeights
	)

static

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

static Standard_Boolean BSplSLib::IsRational	(	const TColStd_Array2OfReal &	Weights,
		const Standard_Integer	I1,
		const Standard_Integer	I2,
		const Standard_Integer	J1,
		const Standard_Integer	J2,
		const Standard_Real	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.

static void BSplSLib::MovePoint	(	const Standard_Real	U,
		const Standard_Real	V,
		const gp_Vec &	Displ,
		const Standard_Integer	UIndex1,
		const Standard_Integer	UIndex2,
		const Standard_Integer	VIndex1,
		const Standard_Integer	VIndex2,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	Rational,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal &	Weights,
		const TColStd_Array1OfReal &	UFlatKnots,
		const TColStd_Array1OfReal &	VFlatKnots,
		Standard_Integer &	UFirstIndex,
		Standard_Integer &	ULastIndex,
		Standard_Integer &	VFirstIndex,
		Standard_Integer &	VLastIndex,
		TColgp_Array2OfPnt &	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.

static TColStd_Array2OfReal* BSplSLib::NoWeights ( )

static

Used as argument for a non rational curve.

static void BSplSLib::PolesCoefficients	(	const TColgp_Array2OfPnt &	Poles,
		TColgp_Array2OfPnt &	CachePoles
	)

static

Warning! To be used for BezierSurfaces ONLY!!!

static void BSplSLib::PolesCoefficients	(	const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		TColgp_Array2OfPnt &	CachePoles,
		TColStd_Array2OfReal *	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!!!

static void BSplSLib::RationalDerivative	(	const Standard_Integer	UDeg,
		const Standard_Integer	VDeg,
		const Standard_Integer	N,
		const Standard_Integer	M,
		Standard_Real &	Ders,
		Standard_Real &	RDers,
		const Standard_Boolean	All = `Standard_True`
	)

static

this is a one dimensional function typedef void (*EvaluatorFunction) ( Standard_Integer // Derivative Request Standard_Real * // StartEnd[2][2] // [0] = U // [1] = V // [0] = start // [1] = end Standard_Real // UParameter Standard_Real // VParamerer Standard_Real & // Result Standard_Integer &) ;// 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 Min(<N>,<UDeg>), 0 to 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 <= 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 dimensionned properly.

static Standard_Boolean BSplSLib::RemoveKnot	(	const Standard_Boolean	UDirection,
		const Standard_Integer	Index,
		const Standard_Integer	Mult,
		const Standard_Integer	Degree,
		const Standard_Boolean	Periodic,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		TColgp_Array2OfPnt &	NewPoles,
		TColStd_Array2OfReal *	NewWeights,
		TColStd_Array1OfReal &	NewKnots,
		TColStd_Array1OfInteger &	NewMults,
		const Standard_Real	Tolerance
	)

static

static void BSplSLib::Resolution	(	const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger &	UMults,
		const TColStd_Array1OfInteger &	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	URat,
		const Standard_Boolean	VRat,
		const Standard_Boolean	UPer,
		const Standard_Boolean	VPer,
		const Standard_Real	Tolerance3D,
		Standard_Real &	UTolerance,
		Standard_Real &	VTolerance
	)

static

static void BSplSLib::Reverse	(	TColgp_Array2OfPnt &	Poles,
		const Standard_Integer	Last,
		const Standard_Boolean	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)

static void BSplSLib::Reverse	(	TColStd_Array2OfReal &	Weights,
		const Standard_Integer	Last,
		const Standard_Boolean	UDirection
	)

static

Reverses the array of weights.

static void BSplSLib::SetPoles	(	const TColgp_Array2OfPnt &	Poles,
		TColStd_Array1OfReal &	FP,
		const Standard_Boolean	UDirection
	)

static

Copy in FP the coordinates of the poles.

static void BSplSLib::SetPoles	(	const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal &	Weights,
		TColStd_Array1OfReal &	FP,
		const Standard_Boolean	UDirection
	)

static

Copy in FP the coordinates of the poles.

static void BSplSLib::Unperiodize	(	const Standard_Boolean	UDirection,
		const Standard_Integer	Degree,
		const TColStd_Array1OfInteger &	Mults,
		const TColStd_Array1OfReal &	Knots,
		const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal *	Weights,
		TColStd_Array1OfInteger &	NewMults,
		TColStd_Array1OfReal &	NewKnots,
		TColgp_Array2OfPnt &	NewPoles,
		TColStd_Array2OfReal *	NewWeights
	)

static

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

BSplSLib.hxx

BSplSLib Class Reference

Static Public Member Functions

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

Detailed Description

Member Function Documentation

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