// Created on: 1991-08-26 // Created by: JCV // Copyright (c) 1991-1999 Matra Datavision // Copyright (c) 1999-2014 OPEN CASCADE SAS // // This file is part of Open CASCADE Technology software library. // // This library is free software; you can redistribute it and/or modify it under // the terms of the GNU Lesser General Public License version 2.1 as published // by the Free Software Foundation, with special exception defined in the file // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT // distribution for complete text of the license and disclaimer of any warranty. // // Alternatively, this file may be used under the terms of Open CASCADE // commercial license or contractual agreement. #ifndef _BSplSLib_HeaderFile #define _BSplSLib_HeaderFile #include #include #include #include #include #include #include #include #include #include #include #include class gp_Pnt; class gp_Vec; //! 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 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 class BSplSLib { public: DEFINE_STANDARD_ALLOC //! 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 //! , x(u,v) is a vector in dimension //! <3>. //! //! is an array containing the values of the //! input derivatives from 0 to Min(,), 0 to //! Min(,). For orders higher than //! the input derivatives are assumed to //! be 0. //! //! The is a 2d array and the dimension of the //! lines is always (+1) * (<3>+1), even //! if is smaller than (the derivatives //! higher than are not used). //! //! Content of : //! //! 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 is false, only the derivative at order //! is computed. is an array of length //! 3 which will contain the result : //! //! x(1)/w , x(2)/w , ... derivated times //! //! If is true multiples derivatives are //! computed. All the derivatives (i,j) with 0 <= i+j //! <= Max(N,M) are computed. is an array of //! length 3 * (+1) * (+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 times //! .... //! Warning: must be dimensionned properly. 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 //! curve at parameter (UIso if is True, //! VIso else). 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 //! 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) Standard_EXPORT static void Reverse (TColgp_Array2OfPnt& Poles, const Standard_Integer Last, const Standard_Boolean UDirection); //! 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 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 //! any and returns in P the Numerator value and //! in W the Denominator value if Weights are present //! otherwise returns 1.0e0 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. 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 //! 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. 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. Standard_EXPORT static void SetPoles (const TColgp_Array2OfPnt& Poles, TColStd_Array1OfReal& FP, const Standard_Boolean UDirection); //! Copy in FP the coordinates of the poles. 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. Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array2OfPnt& Poles, const Standard_Boolean UDirection); //! Get from FP the coordinates of the poles. 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 //! 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 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. static TColStd_Array2OfReal* NoWeights(); //! 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 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 Taylor expansion //! of the Bspline normalized between 0 and 1. //! Structure of result optimized for BSplSLib_Cache. Standard_EXPORT 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 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 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 //! the method PolesCoefficients. //! Warning: To be used for BezierSurfaces ONLY!!! 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 //! 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 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 //! the method PolesCoefficients. //! Warning: To be used for BezierSurfaces ONLY!!! 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 //! 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 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 //! the method PolesCoefficients. //! Warning: To be used for BezierSurfaces ONLY!!! 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!!! static void PolesCoefficients (const TColgp_Array2OfPnt& Poles, TColgp_Array2OfPnt& CachePoles); //! Encapsulation of BuildCache to perform the //! evaluation of the Taylor expansion for beziersurfaces //! at parameters 0.,0.; //! Warning: To be used for BezierSurfaces ONLY!!! 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 //! 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 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 //! 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 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 //! 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 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) //! 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) //! -- 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& theStatus); protected: private: }; #include #endif // _BSplSLib_HeaderFile