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// This file is generated by WOK (CPPExt).
// Please do not edit this file; modify original file instead.
// The copyright and license terms as defined for the original file apply to
// this header file considered to be the "object code" form of the original source.
#ifndef _BSplSLib_HeaderFile
#define _BSplSLib_HeaderFile
#ifndef _Standard_HeaderFile
#include <Standard.hxx>
#endif
#ifndef _Standard_Macro_HeaderFile
#include <Standard_Macro.hxx>
#endif
#ifndef _Standard_Integer_HeaderFile
#include <Standard_Integer.hxx>
#endif
#ifndef _Standard_Real_HeaderFile
#include <Standard_Real.hxx>
#endif
#ifndef _Standard_Boolean_HeaderFile
#include <Standard_Boolean.hxx>
#endif
#ifndef _BSplSLib_EvaluatorFunction_HeaderFile
#include <BSplSLib_EvaluatorFunction.hxx>
#endif
class TColgp_Array2OfPnt;
class TColStd_Array2OfReal;
class TColStd_Array1OfReal;
class TColStd_Array1OfInteger;
class gp_Pnt;
class gp_Vec;
class TColgp_Array1OfPnt;
//! BSplSLib B-spline surface Library <br>
//! This package provides an implementation of geometric <br>
//! functions for rational and non rational, periodic and non <br>
//! periodic B-spline surface computation. <br>
//! <br>
//! this package uses the multi-dimensions splines methods <br>
//! provided in the package BSplCLib. <br>
//! <br>
//! In this package the B-spline surface is defined with : <br>
//! . its control points : Array2OfPnt Poles <br>
//! . its weights : Array2OfReal Weights <br>
//! . its knots and their multiplicity in the two parametric <br>
//! direction U and V : Array1OfReal UKnots, VKnots and <br>
//! Array1OfInteger UMults, VMults. <br>
//! . the degree of the normalized Spline functions : <br>
//! UDegree, VDegree <br>
//! <br>
//! . the Booleans URational, VRational to know if the weights <br>
//! are constant in the U or V direction. <br>
//! <br>
//! . the Booleans UPeriodic, VRational to know if the the <br>
//! surface is periodic in the U or V direction. <br>
//! <br>
//! Warnings : The bounds of UKnots and UMults should be the <br>
//! same, the bounds of VKnots and VMults should be the same, <br>
//! the bounds of Poles and Weights shoud be the same. <br>
class BSplSLib {
public:
void* operator new(size_t,void* anAddress)
{
return anAddress;
}
void* operator new(size_t size)
{
return Standard::Allocate(size);
}
void operator delete(void *anAddress)
{
if (anAddress) Standard::Free((Standard_Address&)anAddress);
}
//! Computes the derivatives of a ratio of <br>
//! two-variables functions x(u,v) / w(u,v) at orders <br>
//! <N,M>, x(u,v) is a vector in dimension <br>
//! <3>. <br>
//! <br>
//! <Ders> is an array containing the values of the <br>
//! input derivatives from 0 to Min(<N>,<UDeg>), 0 to <br>
//! Min(<M>,<VDeg>). For orders higher than <br>
//! <UDeg,VDeg> the input derivatives are assumed to <br>
//! be 0. <br>
//! <br>
//! The <Ders> is a 2d array and the dimension of the <br>
//! lines is always (<VDeg>+1) * (<3>+1), even <br>
//! if <N> is smaller than <Udeg> (the derivatives <br>
//! higher than <N> are not used). <br>
//! <br>
//! Content of <Ders> : <br>
//! <br>
//! x(i,j)[k] means : the composant k of x derivated <br>
//! (i) times in u and (j) times in v. <br>
//! <br>
//! ... First line ... <br>
//! <br>
//! x[1],x[2],...,x[3],w <br>
//! x(0,1)[1],...,x(0,1)[3],w(1,0) <br>
//! ... <br>
//! x(0,VDeg)[1],...,x(0,VDeg)[3],w(0,VDeg) <br>
//! <br>
//! ... Then second line ... <br>
//! <br>
//! x(1,0)[1],...,x(1,0)[3],w(1,0) <br>
//! x(1,1)[1],...,x(1,1)[3],w(1,1) <br>
//! ... <br>
//! x(1,VDeg)[1],...,x(1,VDeg)[3],w(1,VDeg) <br>
//! <br>
//! ... <br>
//! <br>
//! ... Last line ... <br>
//! <br>
//! x(UDeg,0)[1],...,x(UDeg,0)[3],w(UDeg,0) <br>
//! x(UDeg,1)[1],...,x(UDeg,1)[3],w(UDeg,1) <br>
//! ... <br>
//! x(Udeg,VDeg)[1],...,x(UDeg,VDeg)[3],w(Udeg,VDeg) <br>
//! <br>
//! <br>
//! <br>
//! If <All> is false, only the derivative at order <br>
//! <N,M> is computed. <RDers> is an array of length <br>
//! 3 which will contain the result : <br>
//! <br>
//! x(1)/w , x(2)/w , ... derivated <N> <M> times <br>
//! <br>
//! If <All> is true multiples derivatives are <br>
//! computed. All the derivatives (i,j) with 0 <= i+j <br>
//! <= Max(N,M) are computed. <RDers> is an array of <br>
//! length 3 * (<N>+1) * (<M>+1) which will <br>
//! contains : <br>
//! <br>
//! x(1)/w , x(2)/w , ... <br>
//! x(1)/w , x(2)/w , ... derivated <0,1> times <br>
//! x(1)/w , x(2)/w , ... derivated <0,2> times <br>
//! ... <br>
//! x(1)/w , x(2)/w , ... derivated <0,N> times <br>
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
//! Computes the poles and weights of an isoparametric <br>
//! curve at parameter <Param> (UIso if <IsU> is True, <br>
//! VIso else). <br>
Standard_EXPORT 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) ;
//! Reverses the array of poles. Last is the Index of <br>
//! the new first Row( Col) of Poles. <br>
//! On a non periodic surface Last is <br>
//! Poles.Upper(). <br>
//! On a periodic curve last is <br>
//! (number of flat knots - degree - 1) <br>
//! or <br>
//! (sum of multiplicities(but for the last) + degree <br>
//! - 1) <br>
Standard_EXPORT static void Reverse(TColgp_Array2OfPnt& Poles,const Standard_Integer Last,const Standard_Boolean UDirection) ;
//! Makes an homogeneous evaluation of Poles and Weights <br>
//! any and returns in P the Numerator value and <br>
//! in W the Denominator value if Weights are present <br>
//! otherwise returns 1.0e0 <br>
//! <br>
Standard_EXPORT 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 <br>
//! any and returns in P the Numerator value and <br>
//! in W the Denominator value if Weights are present <br>
//! otherwise returns 1.0e0 <br>
//! <br>
Standard_EXPORT 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) ;
//! Reverses the array of weights. <br>
Standard_EXPORT static void Reverse(TColStd_Array2OfReal& Weights,const Standard_Integer Last,const Standard_Boolean UDirection) ;
//! Returns False if all the weights of the array <Weights> <br>
//! in the area [I1,I2] * [J1,J2] are identic. <br>
//! Epsilon is used for comparing weights. <br>
//! If Epsilon is 0. the Epsilon of the first weight is used. <br>
Standard_EXPORT 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) ;
//! Copy in FP the coordinates of the poles. <br>
Standard_EXPORT static void SetPoles(const TColgp_Array2OfPnt& Poles,TColStd_Array1OfReal& FP,const Standard_Boolean UDirection) ;
//! Copy in FP the coordinates of the poles. <br>
Standard_EXPORT static void SetPoles(const TColgp_Array2OfPnt& Poles,const TColStd_Array2OfReal& Weights,TColStd_Array1OfReal& FP,const Standard_Boolean UDirection) ;
//! Get from FP the coordinates of the poles. <br>
Standard_EXPORT static void GetPoles(const TColStd_Array1OfReal& FP,TColgp_Array2OfPnt& Poles,const Standard_Boolean UDirection) ;
//! Get from FP the coordinates of the poles. <br>
Standard_EXPORT static void GetPoles(const TColStd_Array1OfReal& FP,TColgp_Array2OfPnt& Poles,TColStd_Array2OfReal& Weights,const Standard_Boolean UDirection) ;
//! Find the new poles which allows an old point (with a <br>
//! given u,v as parameters) to reach a new position <br>
//! UIndex1,UIndex2 indicate the range of poles we can <br>
//! move for U <br>
//! (1, UNbPoles-1) or (2, UNbPoles) -> no constraint <br>
//! for one side in U <br>
//! (2, UNbPoles-1) -> the ends are enforced for U <br>
//! don't enter (1,NbPoles) and (1,VNbPoles) <br>
//! -> error: rigid move <br>
//! if problem in BSplineBasis calculation, no change <br>
//! for the curve and <br>
//! UFirstIndex, VLastIndex = 0 <br>
//! VFirstIndex, VLastIndex = 0 <br>
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
Standard_EXPORT 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) ;
//! Used as argument for a non rational curve. <br>
//! <br>
static TColStd_Array2OfReal& NoWeights() ;
//! Perform the evaluation of the Taylor expansion <br>
//! of the Bspline normalized between 0 and 1. <br>
//! If rational computes the homogeneous Taylor expension <br>
//! for the numerator and stores it in CachePoles <br>
//! <br>
//! <br>
Standard_EXPORT 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 of the cache <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effects <br>
//! <br>
Standard_EXPORT 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) ;
//! Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for BezierSurfaces ONLY!!! <br>
static void CoefsD0(const Standard_Real U,const Standard_Real V,const TColgp_Array2OfPnt& Poles,const TColStd_Array2OfReal& Weights,gp_Pnt& Point) ;
//! Perform the evaluation of the of the cache <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effects <br>
//! <br>
Standard_EXPORT 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) ;
//! Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for BezierSurfaces ONLY!!! <br>
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) ;
//! Perform the evaluation of the of the cache <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effects <br>
//! <br>
Standard_EXPORT 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) ;
//! Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for BezierSurfaces ONLY!!! <br>
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) ;
//! Warning! To be used for BezierSurfaces ONLY!!! <br>
static void PolesCoefficients(const TColgp_Array2OfPnt& Poles,TColgp_Array2OfPnt& CachePoles) ;
//! Encapsulation of BuildCache to perform the <br>
//! evaluation of the Taylor expansion for beziersurfaces <br>
//! at parameters 0.,0.; <br>
//! Warning: To be used for BezierSurfaces ONLY!!! <br>
//! <br>
Standard_EXPORT static void PolesCoefficients(const TColgp_Array2OfPnt& Poles,const TColStd_Array2OfReal& Weights,TColgp_Array2OfPnt& CachePoles,TColStd_Array2OfReal& CacheWeights) ;
//! Given a tolerance in 3D space returns two <br>
//! tolerances, one in U one in V such that for <br>
//! all (u1,v1) and (u0,v0) in the domain of <br>
//! the surface f(u,v) we have : <br>
//! | u1 - u0 | < UTolerance and <br>
//! | v1 - v0 | < VTolerance <br>
//! we have |f (u1,v1) - f (u0,v0)| < Tolerance3D <br>
Standard_EXPORT 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) ;
//! Performs the interpolation of the data points given in <br>
//! the Poles array in the form <br>
//! [1,...,RL][1,...,RC][1...PolesDimension] . The <br>
//! ColLength CL and the Length of UParameters must be the <br>
//! same. The length of VFlatKnots is VDegree + CL + 1. <br>
//! <br>
//! The RowLength RL and the Length of VParameters must be <br>
//! the same. The length of VFlatKnots is Degree + RL + 1. <br>
//! <br>
//! Warning: the method used to do that interpolation <br>
//! is gauss elimination WITHOUT pivoting. Thus if the <br>
//! diagonal is not dominant there is no guarantee that <br>
//! the algorithm will work. Nevertheless for Cubic <br>
//! interpolation at knots or interpolation at Scheonberg <br>
//! points the method will work. The InversionProblem <br>
//! will report 0 if there was no problem else it will <br>
//! give the index of the faulty pivot <br>
Standard_EXPORT 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 <br>
//! the Poles array. <br>
//! The ColLength CL and the Length of UParameters must be <br>
//! the same. The length of VFlatKnots is VDegree + CL + 1. <br>
//! <br>
//! The RowLength RL and the Length of VParameters must be <br>
//! the same. The length of VFlatKnots is Degree + RL + 1. <br>
//! <br>
//! Warning: the method used to do that interpolation <br>
//! is gauss elimination WITHOUT pivoting. Thus if the <br>
//! diagonal is not dominant there is no guarantee that <br>
//! the algorithm will work. Nevertheless for Cubic <br>
//! interpolation at knots or interpolation at Scheonberg <br>
//! points the method will work. The InversionProblem <br>
//! will report 0 if there was no problem else it will <br>
//! give the index of the faulty pivot <br>
Standard_EXPORT 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) ;
//! this will multiply a given BSpline numerator N(u,v) <br>
//! and denominator D(u,v) defined by its <br>
//! U/VBSplineDegree and U/VBSplineKnots, and <br>
//! U/VMults. Its Poles and Weights are arrays which are <br>
//! coded as array2 of the form <br>
//! [1..UNumPoles][1..VNumPoles] by a function a(u,v) <br>
//! which is assumed to satisfy the following : 1. <br>
//! a(u,v) * N(u,v) and a(u,v) * D(u,v) is a polynomial <br>
//! BSpline that can be expressed exactly as a BSpline of <br>
//! degree U/VNewDegree on the knots U/VFlatKnots 2. the range <br>
//! of a(u,v) is the same as the range of N(u,v) <br>
//! or D(u,v) <br>
//! ---Warning: it is the caller's responsability to <br>
//! insure that conditions 1. and 2. above are satisfied <br>
//! : no check whatsoever is made in this method -- <br>
//! Status will return 0 if OK else it will return the <br>
//! pivot index -- of the matrix that was inverted to <br>
//! compute the multiplied -- BSpline : the method used <br>
//! is interpolation at Schoenenberg -- points of <br>
//! a(u,v)* N(u,v) and a(u,v) * D(u,v) <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of a(u,v)*F(u,v) <br>
//! -- <br>
//! <br>
Standard_EXPORT 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) ;
protected:
private:
};
#include <BSplSLib.lxx>
// other Inline functions and methods (like "C++: function call" methods)
#endif
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