1 // Created on: 1996-10-08
2 // Created by: Jeannine PANTIATICI
3 // Copyright (c) 1996-1999 Matra Datavision
4 // Copyright (c) 1999-2014 OPEN CASCADE SAS
6 // This file is part of Open CASCADE Technology software library.
8 // This library is free software; you can redistribute it and/or modify it under
9 // the terms of the GNU Lesser General Public License version 2.1 as published
10 // by the Free Software Foundation, with special exception defined in the file
11 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
12 // distribution for complete text of the license and disclaimer of any warranty.
14 // Alternatively, this file may be used under the terms of Open CASCADE
15 // commercial license or contractual agreement.
17 #ifndef _PLib_JacobiPolynomial_HeaderFile
18 #define _PLib_JacobiPolynomial_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
23 #include <Standard_Integer.hxx>
24 #include <TColStd_HArray1OfReal.hxx>
25 #include <PLib_Base.hxx>
26 #include <GeomAbs_Shape.hxx>
27 #include <TColStd_Array1OfReal.hxx>
28 #include <TColStd_Array2OfReal.hxx>
29 #include <Standard_Real.hxx>
30 class Standard_ConstructionError;
33 class PLib_JacobiPolynomial;
34 DEFINE_STANDARD_HANDLE(PLib_JacobiPolynomial, PLib_Base)
36 //! This class provides method to work with Jacobi Polynomials
37 //! relativly to an order of constraint
38 //! q = myWorkDegree-2*(myNivConstr+1)
39 //! Jk(t) for k=0,q compose the Jacobi Polynomial base relativly to the weigth W(t)
40 //! iorder is the integer value for the constraints:
41 //! iorder = 0 <=> ConstraintOrder = GeomAbs_C0
42 //! iorder = 1 <=> ConstraintOrder = GeomAbs_C1
43 //! iorder = 2 <=> ConstraintOrder = GeomAbs_C2
44 //! P(t) = R(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2)
45 //! the coefficients JacCoeff represents P(t) JacCoeff are stored as follow:
47 //! c0(1) c0(2) .... c0(Dimension)
48 //! c1(1) c1(2) .... c1(Dimension)
50 //! cDegree(1) cDegree(2) .... cDegree(Dimension)
53 //! c0(1) c0(2) .... c0(Dimension)
54 //! c2*ordre+1(1) ... c2*ordre+1(dimension)
56 //! represents the part of the polynomial in the
57 //! canonical base: R(t)
58 //! R(t) = c0 + c1 t + ...+ c2*iordre+1 t**2*iordre+1
59 //! The following coefficients represents the part of the
60 //! polynomial in the Jacobi base ie Q(t)
61 //! Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2
62 class PLib_JacobiPolynomial : public PLib_Base
69 //! Initialize the polynomial class
70 //! Degree has to be <= 30
71 //! ConstraintOrder has to be GeomAbs_C0
74 Standard_EXPORT PLib_JacobiPolynomial(const Standard_Integer WorkDegree, const GeomAbs_Shape ConstraintOrder);
77 //! returns the Jacobi Points for Gauss integration ie
78 //! the positive values of the Legendre roots by increasing values
79 //! NbGaussPoints is the number of points choosen for the integral
81 //! TabPoints (0,NbGaussPoints/2)
82 //! TabPoints (0) is loaded only for the odd values of NbGaussPoints
83 //! The possible values for NbGaussPoints are : 8, 10,
84 //! 15, 20, 25, 30, 35, 40, 50, 61
85 //! NbGaussPoints must be greater than Degree
86 Standard_EXPORT void Points (const Standard_Integer NbGaussPoints, TColStd_Array1OfReal& TabPoints) const;
89 //! returns the Jacobi weigths for Gauss integration only for
90 //! the positive values of the Legendre roots in the order they
91 //! are given by the method Points
92 //! NbGaussPoints is the number of points choosen for the integral
94 //! TabWeights (0,NbGaussPoints/2,0,Degree)
95 //! TabWeights (0,.) are only loaded for the odd values of NbGaussPoints
96 //! The possible values for NbGaussPoints are : 8 , 10 , 15 ,20 ,25 , 30,
97 //! 35 , 40 , 50 , 61 NbGaussPoints must be greater than Degree
98 Standard_EXPORT void Weights (const Standard_Integer NbGaussPoints, TColStd_Array2OfReal& TabWeights) const;
101 //! this method loads for k=0,q the maximum value of
102 //! abs ( W(t)*Jk(t) )for t bellonging to [-1,1]
103 //! This values are loaded is the array TabMax(0,myWorkDegree-2*(myNivConst+1))
104 //! MaxValue ( me ; TabMaxPointer : in out Real );
105 Standard_EXPORT void MaxValue (TColStd_Array1OfReal& TabMax) const;
108 //! This method computes the maximum error on the polynomial
109 //! W(t) Q(t) obtained by missing the coefficients of JacCoeff from
110 //! NewDegree +1 to Degree
111 Standard_EXPORT Standard_Real MaxError (const Standard_Integer Dimension, Standard_Real& JacCoeff, const Standard_Integer NewDegree) const;
114 //! Compute NewDegree <= MaxDegree so that MaxError is lower
116 //! MaxError can be greater than Tol if it is not possible
117 //! to find a NewDegree <= MaxDegree.
118 //! In this case NewDegree = MaxDegree
119 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;
121 Standard_EXPORT Standard_Real AverageError (const Standard_Integer Dimension, Standard_Real& JacCoeff, const Standard_Integer NewDegree) const;
124 //! Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base.
125 Standard_EXPORT void ToCoefficients (const Standard_Integer Dimension, const Standard_Integer Degree, const TColStd_Array1OfReal& JacCoeff, TColStd_Array1OfReal& Coefficients) const Standard_OVERRIDE;
127 //! Compute the values of the basis functions in u
128 Standard_EXPORT void D0 (const Standard_Real U, TColStd_Array1OfReal& BasisValue) Standard_OVERRIDE;
130 //! Compute the values and the derivatives values of
131 //! the basis functions in u
132 Standard_EXPORT void D1 (const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1) Standard_OVERRIDE;
134 //! Compute the values and the derivatives values of
135 //! the basis functions in u
136 Standard_EXPORT void D2 (const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1, TColStd_Array1OfReal& BasisD2) Standard_OVERRIDE;
138 //! Compute the values and the derivatives values of
139 //! the basis functions in u
140 Standard_EXPORT void D3 (const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1, TColStd_Array1OfReal& BasisD2, TColStd_Array1OfReal& BasisD3) Standard_OVERRIDE;
142 //! returns WorkDegree
143 Standard_Integer WorkDegree() const Standard_OVERRIDE;
145 //! returns NivConstr
146 Standard_Integer NivConstr() const;
151 DEFINE_STANDARD_RTTIEXT(PLib_JacobiPolynomial,PLib_Base)
161 //! Compute the values and the derivatives values of
162 //! the basis functions in u
163 Standard_EXPORT void D0123 (const Standard_Integer NDerive, const Standard_Real U, TColStd_Array1OfReal& BasisValue, TColStd_Array1OfReal& BasisD1, TColStd_Array1OfReal& BasisD2, TColStd_Array1OfReal& BasisD3);
165 Standard_Integer myWorkDegree;
166 Standard_Integer myNivConstr;
167 Standard_Integer myDegree;
168 Handle(TColStd_HArray1OfReal) myTNorm;
169 Handle(TColStd_HArray1OfReal) myCofA;
170 Handle(TColStd_HArray1OfReal) myCofB;
171 Handle(TColStd_HArray1OfReal) myDenom;
177 #include <PLib_JacobiPolynomial.lxx>
183 #endif // _PLib_JacobiPolynomial_HeaderFile