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0001 // Created on: 1996-10-08 0002 // Created by: Jeannine PANTIATICI 0003 // Copyright (c) 1996-1999 Matra Datavision 0004 // Copyright (c) 1999-2014 OPEN CASCADE SAS 0005 // 0006 // This file is part of Open CASCADE Technology software library. 0007 // 0008 // This library is free software; you can redistribute it and/or modify it under 0009 // the terms of the GNU Lesser General Public License version 2.1 as published 0010 // by the Free Software Foundation, with special exception defined in the file 0011 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT 0012 // distribution for complete text of the license and disclaimer of any warranty. 0013 // 0014 // Alternatively, this file may be used under the terms of Open CASCADE 0015 // commercial license or contractual agreement. 0016 0017 #ifndef _PLib_JacobiPolynomial_HeaderFile 0018 #define _PLib_JacobiPolynomial_HeaderFile 0019 0020 #include <Standard.hxx> 0021 0022 #include <Standard_Integer.hxx> 0023 #include <GeomAbs_Shape.hxx> 0024 #include <NCollection_Array1.hxx> 0025 #include <NCollection_Array2.hxx> 0026 0027 //! This class provides method to work with Jacobi Polynomials 0028 //! relatively to an order of constraint 0029 //! q = myWorkDegree-2*(myNivConstr+1) 0030 //! Jk(t) for k=0,q compose the Jacobi Polynomial base relatively to the weight W(t) 0031 //! iorder is the integer value for the constraints: 0032 //! iorder = 0 <=> ConstraintOrder = GeomAbs_C0 0033 //! iorder = 1 <=> ConstraintOrder = GeomAbs_C1 0034 //! iorder = 2 <=> ConstraintOrder = GeomAbs_C2 0035 //! P(t) = R(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2) 0036 //! the coefficients JacCoeff represents P(t) JacCoeff are stored as follow: 0037 //! 0038 //! c0(1) c0(2) .... c0(Dimension) 0039 //! c1(1) c1(2) .... c1(Dimension) 0040 //! 0041 //! cDegree(1) cDegree(2) .... cDegree(Dimension) 0042 //! 0043 //! The coefficients 0044 //! c0(1) c0(2) .... c0(Dimension) 0045 //! c2*ordre+1(1) ... c2*ordre+1(dimension) 0046 //! 0047 //! represents the part of the polynomial in the 0048 //! canonical base: R(t) 0049 //! R(t) = c0 + c1 t + ...+ c2*iordre+1 t**2*iordre+1 0050 //! The following coefficients represents the part of the 0051 //! polynomial in the Jacobi base ie Q(t) 0052 //! Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2 0053 class PLib_JacobiPolynomial 0054 { 0055 0056 public: 0057 //! Initialize the polynomial class 0058 //! Degree has to be <= 30 0059 //! ConstraintOrder has to be GeomAbs_C0 0060 //! GeomAbs_C1 0061 //! GeomAbs_C2 0062 Standard_EXPORT PLib_JacobiPolynomial(const int theWorkDegree, 0063 const GeomAbs_Shape theConstraintOrder); 0064 0065 //! returns the Jacobi Points for Gauss integration ie 0066 //! the positive values of the Legendre roots by increasing values 0067 //! NbGaussPoints is the number of points chosen for the integral 0068 //! computation. 0069 //! TabPoints (0,NbGaussPoints/2) 0070 //! TabPoints (0) is loaded only for the odd values of NbGaussPoints 0071 //! The possible values for NbGaussPoints are : 8, 10, 0072 //! 15, 20, 25, 30, 35, 40, 50, 61 0073 //! NbGaussPoints must be greater than Degree 0074 Standard_EXPORT void Points(const int theNbGaussPoints, 0075 NCollection_Array1<double>& theTabPoints) const; 0076 0077 //! returns the Jacobi weights for Gauss integration only for 0078 //! the positive values of the Legendre roots in the order they 0079 //! are given by the method Points 0080 //! NbGaussPoints is the number of points chosen for the integral 0081 //! computation. 0082 //! TabWeights (0,NbGaussPoints/2,0,Degree) 0083 //! TabWeights (0,.) are only loaded for the odd values of NbGaussPoints 0084 //! The possible values for NbGaussPoints are: 8, 10, 15, 20, 25, 30, 0085 //! 35, 40, 50, 61 NbGaussPoints must be greater than Degree 0086 Standard_EXPORT void Weights(const int theNbGaussPoints, 0087 NCollection_Array2<double>& theTabWeights) const; 0088 0089 //! this method loads for k=0,q the maximum value of 0090 //! abs ( W(t)*Jk(t) ) for t bellonging to [-1,1] 0091 //! This values are loaded is the array TabMax(0,myWorkDegree-2*(myNivConst+1)) 0092 //! MaxValue ( me ; TabMaxPointer : in out Real ); 0093 Standard_EXPORT void MaxValue(NCollection_Array1<double>& theTabMax) const; 0094 0095 //! This method computes the maximum error on the polynomial 0096 //! W(t) Q(t) obtained by missing the coefficients of JacCoeff from 0097 //! NewDegree +1 to Degree 0098 Standard_EXPORT double MaxError(const int theDimension, 0099 double& theJacCoeff, 0100 const int theNewDegree) const; 0101 0102 //! Compute NewDegree <= MaxDegree so that MaxError is lower 0103 //! than Tol. 0104 //! MaxError can be greater than Tol if it is not possible 0105 //! to find a NewDegree <= MaxDegree. 0106 //! In this case NewDegree = MaxDegree 0107 Standard_EXPORT void ReduceDegree(const int theDimension, 0108 const int theMaxDegree, 0109 const double theTol, 0110 double& theJacCoeff, 0111 int& theNewDegree, 0112 double& theMaxError) const; 0113 0114 Standard_EXPORT double AverageError(const int theDimension, 0115 double& theJacCoeff, 0116 const int theNewDegree) const; 0117 0118 //! Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base. 0119 Standard_EXPORT void ToCoefficients(const int theDimension, 0120 const int theDegree, 0121 const NCollection_Array1<double>& theJacCoeff, 0122 NCollection_Array1<double>& theCoefficients) const; 0123 0124 //! Compute the values of the basis functions in u 0125 Standard_EXPORT void D0(const double theU, NCollection_Array1<double>& theBasisValue) const; 0126 0127 //! Compute the values and the derivatives values of 0128 //! the basis functions in u 0129 Standard_EXPORT void D1(const double theU, 0130 NCollection_Array1<double>& theBasisValue, 0131 NCollection_Array1<double>& theBasisD1) const; 0132 0133 //! Compute the values and the derivatives values of 0134 //! the basis functions in u 0135 Standard_EXPORT void D2(const double theU, 0136 NCollection_Array1<double>& theBasisValue, 0137 NCollection_Array1<double>& theBasisD1, 0138 NCollection_Array1<double>& theBasisD2) const; 0139 0140 //! Compute the values and the derivatives values of 0141 //! the basis functions in u 0142 Standard_EXPORT void D3(const double theU, 0143 NCollection_Array1<double>& theBasisValue, 0144 NCollection_Array1<double>& theBasisD1, 0145 NCollection_Array1<double>& theBasisD2, 0146 NCollection_Array1<double>& theBasisD3) const; 0147 0148 //! returns WorkDegree 0149 int WorkDegree() const noexcept { return myWorkDegree; } 0150 0151 //! returns NivConstr 0152 int NivConstr() const noexcept { return myNivConstr; } 0153 0154 protected: 0155 //! Compute the values and the derivatives values of 0156 //! the basis functions in u 0157 Standard_EXPORT void D0123(const int theNDeriv, 0158 const double theU, 0159 NCollection_Array1<double>& theBasisValue, 0160 NCollection_Array1<double>& theBasisD1, 0161 NCollection_Array1<double>& theBasisD2, 0162 NCollection_Array1<double>& theBasisD3) const; 0163 0164 private: 0165 const int myWorkDegree; 0166 const int myNivConstr; 0167 const int myDegree; 0168 }; 0169 0170 #endif // _PLib_JacobiPolynomial_HeaderFile
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