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0001 // Created on: 1997-10-22 0002 // Created by: Philippe MANGIN 0003 // Copyright (c) 1997-1999 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_HermitJacobi_HeaderFile 0018 #define _PLib_HermitJacobi_HeaderFile 0019 0020 #include <Standard.hxx> 0021 0022 #include <NCollection_Array1.hxx> 0023 #include <Standard_Integer.hxx> 0024 #include <GeomAbs_Shape.hxx> 0025 #include <PLib_JacobiPolynomial.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) = H(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 //! @code 0038 //! c0(1) c0(2) .... c0(Dimension) 0039 //! c1(1) c1(2) .... c1(Dimension) 0040 //! 0041 //! cDegree(1) cDegree(2) .... cDegree(Dimension) 0042 //! @endcode 0043 //! The coefficients 0044 //! @code 0045 //! c0(1) c0(2) .... c0(Dimension) 0046 //! c2*ordre+1(1) ... c2*ordre+1(dimension) 0047 //! @endcode 0048 //! represents the part of the polynomial in the 0049 //! Hermit's base: H(t) 0050 //! @code 0051 //! H(t) = c0H00(t) + c1H01(t) + ...c(iordre)H(0 ;iorder)+ c(iordre+1)H10(t)+... 0052 //! @endcode 0053 //! The following coefficients represents the part of the 0054 //! polynomial in the Jacobi base ie Q(t) 0055 //! @code 0056 //! Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2 0057 //! @endcode 0058 class PLib_HermitJacobi 0059 { 0060 0061 public: 0062 //! Initialize the polynomial class 0063 //! Degree has to be <= 30 0064 //! ConstraintOrder has to be GeomAbs_C0 0065 //! GeomAbs_C1 0066 //! GeomAbs_C2 0067 Standard_EXPORT PLib_HermitJacobi(const int WorkDegree, const GeomAbs_Shape ConstraintOrder); 0068 0069 //! This method computes the maximum error on the polynomial 0070 //! W(t) Q(t) obtained by missing the coefficients of JacCoeff from 0071 //! NewDegree +1 to Degree 0072 Standard_EXPORT double MaxError(const int Dimension, 0073 double& HermJacCoeff, 0074 const int NewDegree) const; 0075 0076 //! Compute NewDegree <= MaxDegree so that MaxError is lower 0077 //! than Tol. 0078 //! MaxError can be greater than Tol if it is not possible 0079 //! to find a NewDegree <= MaxDegree. 0080 //! In this case NewDegree = MaxDegree 0081 Standard_EXPORT void ReduceDegree(const int Dimension, 0082 const int MaxDegree, 0083 const double Tol, 0084 double& HermJacCoeff, 0085 int& NewDegree, 0086 double& MaxError) const; 0087 0088 Standard_EXPORT double AverageError(const int Dimension, 0089 double& HermJacCoeff, 0090 const int NewDegree) const; 0091 0092 //! Convert the polynomial P(t) = H(t) + W(t) Q(t) in the canonical base. 0093 Standard_EXPORT void ToCoefficients(const int Dimension, 0094 const int Degree, 0095 const NCollection_Array1<double>& HermJacCoeff, 0096 NCollection_Array1<double>& Coefficients) const; 0097 0098 //! Compute the values of the basis functions in u 0099 Standard_EXPORT void D0(const double U, NCollection_Array1<double>& BasisValue) const; 0100 0101 //! Compute the values and the derivatives values of 0102 //! the basis functions in u 0103 Standard_EXPORT void D1(const double U, 0104 NCollection_Array1<double>& BasisValue, 0105 NCollection_Array1<double>& BasisD1) const; 0106 0107 //! Compute the values and the derivatives values of 0108 //! the basis functions in u 0109 Standard_EXPORT void D2(const double U, 0110 NCollection_Array1<double>& BasisValue, 0111 NCollection_Array1<double>& BasisD1, 0112 NCollection_Array1<double>& BasisD2) const; 0113 0114 //! Compute the values and the derivatives values of 0115 //! the basis functions in u 0116 Standard_EXPORT void D3(const double U, 0117 NCollection_Array1<double>& BasisValue, 0118 NCollection_Array1<double>& BasisD1, 0119 NCollection_Array1<double>& BasisD2, 0120 NCollection_Array1<double>& BasisD3) const; 0121 0122 //! returns WorkDegree 0123 int WorkDegree() const noexcept { return myJacobi.WorkDegree(); } 0124 0125 //! returns NivConstr 0126 int NivConstr() const noexcept { return myJacobi.NivConstr(); } 0127 0128 protected: 0129 //! Compute the values and the derivatives values of 0130 //! the basis functions in u 0131 Standard_EXPORT void D0123(const int NDerive, 0132 const double U, 0133 NCollection_Array1<double>& BasisValue, 0134 NCollection_Array1<double>& BasisD1, 0135 NCollection_Array1<double>& BasisD2, 0136 NCollection_Array1<double>& BasisD3) const; 0137 0138 private: 0139 const PLib_JacobiPolynomial myJacobi; 0140 }; 0141 0142 #endif // _PLib_HermitJacobi_HeaderFile
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