// Created on: 1996-10-08 // Created by: Jeannine PANTIATICI // Copyright (c) 1996-1999 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 _PLib_JacobiPolynomial_HeaderFile #define _PLib_JacobiPolynomial_HeaderFile #include #include #include #include #include #include #include #include #include class Standard_ConstructionError; class PLib_JacobiPolynomial; DEFINE_STANDARD_HANDLE(PLib_JacobiPolynomial, PLib_Base) //! This class provides method to work with Jacobi Polynomials //! relatively to an order of constraint //! q = myWorkDegree-2*(myNivConstr+1) //! Jk(t) for k=0,q compose the Jacobi Polynomial base relatively to the weigth W(t) //! iorder is the integer value for the constraints: //! iorder = 0 <=> ConstraintOrder = GeomAbs_C0 //! iorder = 1 <=> ConstraintOrder = GeomAbs_C1 //! iorder = 2 <=> ConstraintOrder = GeomAbs_C2 //! P(t) = R(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2) //! the coefficients JacCoeff represents P(t) JacCoeff are stored as follow: //! //! c0(1) c0(2) .... c0(Dimension) //! c1(1) c1(2) .... c1(Dimension) //! //! cDegree(1) cDegree(2) .... cDegree(Dimension) //! //! The coefficients //! c0(1) c0(2) .... c0(Dimension) //! c2*ordre+1(1) ... c2*ordre+1(dimension) //! //! represents the part of the polynomial in the //! canonical base: R(t) //! R(t) = c0 + c1 t + ...+ c2*iordre+1 t**2*iordre+1 //! The following coefficients represents the part of the //! polynomial in the Jacobi base ie Q(t) //! Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2 class PLib_JacobiPolynomial : public PLib_Base { public: //! Initialize the polynomial class //! Degree has to be <= 30 //! ConstraintOrder has to be GeomAbs_C0 //! GeomAbs_C1 //! GeomAbs_C2 Standard_EXPORT PLib_JacobiPolynomial(const Standard_Integer WorkDegree, const GeomAbs_Shape ConstraintOrder); //! returns the Jacobi Points for Gauss integration ie //! the positive values of the Legendre roots by increasing values //! NbGaussPoints is the number of points chosen for the integral //! computation. //! TabPoints (0,NbGaussPoints/2) //! TabPoints (0) is loaded only for the odd values of NbGaussPoints //! The possible values for NbGaussPoints are : 8, 10, //! 15, 20, 25, 30, 35, 40, 50, 61 //! NbGaussPoints must be greater than Degree Standard_EXPORT void Points (const Standard_Integer NbGaussPoints, TColStd_Array1OfReal& TabPoints) const; //! returns the Jacobi weigths for Gauss integration only for //! the positive values of the Legendre roots in the order they //! are given by the method Points //! NbGaussPoints is the number of points chosen for the integral //! computation. //! TabWeights (0,NbGaussPoints/2,0,Degree) //! TabWeights (0,.) are only loaded for the odd values of NbGaussPoints //! The possible values for NbGaussPoints are : 8 , 10 , 15 ,20 ,25 , 30, //! 35 , 40 , 50 , 61 NbGaussPoints must be greater than Degree Standard_EXPORT void Weights (const Standard_Integer NbGaussPoints, TColStd_Array2OfReal& TabWeights) const; //! this method loads for k=0,q the maximum value of //! abs ( W(t)*Jk(t) )for t bellonging to [-1,1] //! This values are loaded is the array TabMax(0,myWorkDegree-2*(myNivConst+1)) //! MaxValue ( me ; TabMaxPointer : in out Real ); Standard_EXPORT void MaxValue (TColStd_Array1OfReal& TabMax) const; //! This method computes the maximum error on the polynomial //! W(t) Q(t) obtained by missing the coefficients of JacCoeff from //! NewDegree +1 to Degree Standard_EXPORT Standard_Real MaxError (const Standard_Integer Dimension, Standard_Real& JacCoeff, const Standard_Integer NewDegree) const; //! Compute NewDegree <= MaxDegree so that MaxError is lower //! than Tol. //! MaxError can be greater than Tol if it is not possible //! to find a NewDegree <= MaxDegree. //! In this case NewDegree = MaxDegree Standard_EXPORT void ReduceDegree (const Standard_Integer Dimension, const Standard_Integer MaxDegree, const Standard_Real Tol, Standard_Real& JacCoeff, Standard_Integer& NewDegree, Standard_Real& MaxError) const Standard_OVERRIDE; Standard_EXPORT Standard_Real AverageError (const Standard_Integer Dimension, Standard_Real& JacCoeff, const Standard_Integer NewDegree) const; //! Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base. Standard_EXPORT void ToCoefficients (const Standard_Integer Dimension, const Standard_Integer Degree, const TColStd_Array1OfReal& JacCoeff, TColStd_Array1OfReal& Coefficients) const Standard_OVERRIDE; //! Compute the values of the basis functions in u Standard_EXPORT void D0 (const Standard_Real U, TColStd_Array1OfReal& BasisValue) Standard_OVERRIDE; //! Compute the values and the derivatives values of //! the basis functions in u Standard_EXPORT void D1 (const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1) Standard_OVERRIDE; //! Compute the values and the derivatives values of //! the basis functions in u Standard_EXPORT void D2 (const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1, TColStd_Array1OfReal& BasisD2) Standard_OVERRIDE; //! Compute the values and the derivatives values of //! the basis functions in u Standard_EXPORT void D3 (const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1, TColStd_Array1OfReal& BasisD2, TColStd_Array1OfReal& BasisD3) Standard_OVERRIDE; //! returns WorkDegree Standard_Integer WorkDegree() const Standard_OVERRIDE; //! returns NivConstr Standard_Integer NivConstr() const; DEFINE_STANDARD_RTTIEXT(PLib_JacobiPolynomial,PLib_Base) protected: private: //! Compute the values and the derivatives values of //! the basis functions in u Standard_EXPORT void D0123 (const Standard_Integer NDerive, const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1, TColStd_Array1OfReal& BasisD2, TColStd_Array1OfReal& BasisD3); Standard_Integer myWorkDegree; Standard_Integer myNivConstr; Standard_Integer myDegree; Handle(TColStd_HArray1OfReal) myTNorm; Handle(TColStd_HArray1OfReal) myCofA; Handle(TColStd_HArray1OfReal) myCofB; Handle(TColStd_HArray1OfReal) myDenom; }; #include #endif // _PLib_JacobiPolynomial_HeaderFile