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186 lines
8.1 KiB
C++
186 lines
8.1 KiB
C++
// Created on: 1996-10-08
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// Created by: Jeannine PANTIATICI
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// Copyright (c) 1996-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#ifndef _PLib_JacobiPolynomial_HeaderFile
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#define _PLib_JacobiPolynomial_HeaderFile
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#include <Standard.hxx>
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#include <Standard_Type.hxx>
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#include <Standard_Integer.hxx>
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#include <TColStd_HArray1OfReal.hxx>
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#include <PLib_Base.hxx>
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#include <GeomAbs_Shape.hxx>
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#include <TColStd_Array1OfReal.hxx>
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#include <TColStd_Array2OfReal.hxx>
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class PLib_JacobiPolynomial;
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DEFINE_STANDARD_HANDLE(PLib_JacobiPolynomial, PLib_Base)
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//! This class provides method to work with Jacobi Polynomials
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//! relatively to an order of constraint
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//! q = myWorkDegree-2*(myNivConstr+1)
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//! Jk(t) for k=0,q compose the Jacobi Polynomial base relatively to the weight W(t)
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//! iorder is the integer value for the constraints:
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//! iorder = 0 <=> ConstraintOrder = GeomAbs_C0
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//! iorder = 1 <=> ConstraintOrder = GeomAbs_C1
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//! iorder = 2 <=> ConstraintOrder = GeomAbs_C2
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//! P(t) = R(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2)
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//! the coefficients JacCoeff represents P(t) JacCoeff are stored as follow:
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//!
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//! c0(1) c0(2) .... c0(Dimension)
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//! c1(1) c1(2) .... c1(Dimension)
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//!
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//! cDegree(1) cDegree(2) .... cDegree(Dimension)
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//!
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//! The coefficients
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//! c0(1) c0(2) .... c0(Dimension)
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//! c2*ordre+1(1) ... c2*ordre+1(dimension)
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//!
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//! represents the part of the polynomial in the
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//! canonical base: R(t)
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//! R(t) = c0 + c1 t + ...+ c2*iordre+1 t**2*iordre+1
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//! The following coefficients represents the part of the
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//! polynomial in the Jacobi base ie Q(t)
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//! Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2
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class PLib_JacobiPolynomial : public PLib_Base
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{
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public:
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//! Initialize the polynomial class
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//! Degree has to be <= 30
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//! ConstraintOrder has to be GeomAbs_C0
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//! GeomAbs_C1
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//! GeomAbs_C2
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Standard_EXPORT PLib_JacobiPolynomial(const Standard_Integer WorkDegree,
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const GeomAbs_Shape ConstraintOrder);
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//! returns the Jacobi Points for Gauss integration ie
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//! the positive values of the Legendre roots by increasing values
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//! NbGaussPoints is the number of points chosen for the integral
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//! computation.
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//! TabPoints (0,NbGaussPoints/2)
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//! TabPoints (0) is loaded only for the odd values of NbGaussPoints
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//! The possible values for NbGaussPoints are : 8, 10,
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//! 15, 20, 25, 30, 35, 40, 50, 61
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//! NbGaussPoints must be greater than Degree
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Standard_EXPORT void Points(const Standard_Integer NbGaussPoints,
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TColStd_Array1OfReal& TabPoints) const;
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//! returns the Jacobi weights for Gauss integration only for
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//! the positive values of the Legendre roots in the order they
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//! are given by the method Points
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//! NbGaussPoints is the number of points chosen for the integral
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//! computation.
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//! TabWeights (0,NbGaussPoints/2,0,Degree)
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//! TabWeights (0,.) are only loaded for the odd values of NbGaussPoints
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//! The possible values for NbGaussPoints are : 8 , 10 , 15 ,20 ,25 , 30,
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//! 35 , 40 , 50 , 61 NbGaussPoints must be greater than Degree
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Standard_EXPORT void Weights(const Standard_Integer NbGaussPoints,
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TColStd_Array2OfReal& TabWeights) const;
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//! this method loads for k=0,q the maximum value of
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//! abs ( W(t)*Jk(t) )for t bellonging to [-1,1]
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//! This values are loaded is the array TabMax(0,myWorkDegree-2*(myNivConst+1))
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//! MaxValue ( me ; TabMaxPointer : in out Real );
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Standard_EXPORT void MaxValue(TColStd_Array1OfReal& TabMax) const;
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//! This method computes the maximum error on the polynomial
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//! W(t) Q(t) obtained by missing the coefficients of JacCoeff from
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//! NewDegree +1 to Degree
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Standard_EXPORT Standard_Real MaxError(const Standard_Integer Dimension,
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Standard_Real& JacCoeff,
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const Standard_Integer NewDegree) const;
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//! Compute NewDegree <= MaxDegree so that MaxError is lower
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//! than Tol.
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//! MaxError can be greater than Tol if it is not possible
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//! to find a NewDegree <= MaxDegree.
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//! In this case NewDegree = MaxDegree
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Standard_EXPORT void ReduceDegree(const Standard_Integer Dimension,
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const Standard_Integer MaxDegree,
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const Standard_Real Tol,
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Standard_Real& JacCoeff,
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Standard_Integer& NewDegree,
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Standard_Real& MaxError) const Standard_OVERRIDE;
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Standard_EXPORT Standard_Real AverageError(const Standard_Integer Dimension,
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Standard_Real& JacCoeff,
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const Standard_Integer NewDegree) const;
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//! Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base.
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Standard_EXPORT void ToCoefficients(const Standard_Integer Dimension,
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const Standard_Integer Degree,
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const TColStd_Array1OfReal& JacCoeff,
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TColStd_Array1OfReal& Coefficients) const Standard_OVERRIDE;
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//! Compute the values of the basis functions in u
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Standard_EXPORT void D0(const Standard_Real U,
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TColStd_Array1OfReal& BasisValue) Standard_OVERRIDE;
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//! Compute the values and the derivatives values of
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//! the basis functions in u
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Standard_EXPORT void D1(const Standard_Real U,
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TColStd_Array1OfReal& BasisValue,
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TColStd_Array1OfReal& BasisD1) Standard_OVERRIDE;
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//! Compute the values and the derivatives values of
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//! the basis functions in u
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Standard_EXPORT void D2(const Standard_Real U,
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TColStd_Array1OfReal& BasisValue,
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TColStd_Array1OfReal& BasisD1,
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TColStd_Array1OfReal& BasisD2) Standard_OVERRIDE;
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//! Compute the values and the derivatives values of
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//! the basis functions in u
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Standard_EXPORT void D3(const Standard_Real U,
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TColStd_Array1OfReal& BasisValue,
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TColStd_Array1OfReal& BasisD1,
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TColStd_Array1OfReal& BasisD2,
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TColStd_Array1OfReal& BasisD3) Standard_OVERRIDE;
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//! returns WorkDegree
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Standard_Integer WorkDegree() const Standard_OVERRIDE;
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//! returns NivConstr
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Standard_Integer NivConstr() const;
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DEFINE_STANDARD_RTTIEXT(PLib_JacobiPolynomial, PLib_Base)
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protected:
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private:
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//! Compute the values and the derivatives values of
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//! the basis functions in u
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Standard_EXPORT void D0123(const Standard_Integer NDerive,
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const Standard_Real U,
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TColStd_Array1OfReal& BasisValue,
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TColStd_Array1OfReal& BasisD1,
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TColStd_Array1OfReal& BasisD2,
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TColStd_Array1OfReal& BasisD3);
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Standard_Integer myWorkDegree;
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Standard_Integer myNivConstr;
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Standard_Integer myDegree;
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Handle(TColStd_HArray1OfReal) myTNorm;
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Handle(TColStd_HArray1OfReal) myCofA;
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Handle(TColStd_HArray1OfReal) myCofB;
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Handle(TColStd_HArray1OfReal) myDenom;
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};
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#include <PLib_JacobiPolynomial.lxx>
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#endif // _PLib_JacobiPolynomial_HeaderFile
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