[occt.git] / src / PLib / PLib.hxx

// Created on: 1995-08-28
// Created by: Laurent BOURESCHE
// Copyright (c) 1995-1999 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_HeaderFile
#define _PLib_HeaderFile

#include <Standard.hxx>
#include <Standard_DefineAlloc.hxx>
#include <Standard_Handle.hxx>

#include <TColStd_Array1OfReal.hxx>
#include <TColStd_Array2OfReal.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <Standard_Real.hxx>
#include <Standard_Integer.hxx>
#include <Standard_Boolean.hxx>
#include <TColgp_Array2OfPnt.hxx>
#include <GeomAbs_Shape.hxx>
class math_Matrix;
class PLib_Base;
class PLib_JacobiPolynomial;
class PLib_HermitJacobi;
class PLib_DoubleJacobiPolynomial;


//! PLib means Polynomial  functions library.  This pk
//! provides  basic       computation    functions for
//! polynomial functions.
class PLib 
{
public:

  DEFINE_STANDARD_ALLOC

  
  //! Used as argument for a non rational functions
    static TColStd_Array1OfReal& NoWeights();
  
  //! Used as argument for a non rational functions
    static TColStd_Array2OfReal& NoWeights2();
  
  //! Copy in FP the coordinates of the poles.
  Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt& Poles, TColStd_Array1OfReal& FP);
  
  //! Copy in FP the coordinates of the poles.
  Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt& Poles, const TColStd_Array1OfReal& Weights, TColStd_Array1OfReal& FP);
  
  //! Get from FP the coordinates of the poles.
  Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt& Poles);
  
  //! Get from FP the coordinates of the poles.
  Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt& Poles, TColStd_Array1OfReal& Weights);
  
  //! Copy in FP the coordinates of the poles.
  Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt2d& Poles, TColStd_Array1OfReal& FP);
  
  //! Copy in FP the coordinates of the poles.
  Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt2d& Poles, const TColStd_Array1OfReal& Weights, TColStd_Array1OfReal& FP);
  
  //! Get from FP the coordinates of the poles.
  Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt2d& Poles);
  
  //! Get from FP the coordinates of the poles.
  Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt2d& Poles, TColStd_Array1OfReal& Weights);
  
  //! Returns the Binomial Cnp. N should be <= BSplCLib::MaxDegree().
  Standard_EXPORT static Standard_Real Bin (const Standard_Integer N, const Standard_Integer P);
  
  //! Computes the derivatives of a ratio at order
  //! <N> in dimension <Dimension>.
  //!
  //! <Ders> is an  array containing the  values  of the
  //! input   derivatives from  0 to  Min(<N>,<Degree>).
  //! For   orders   higher  than <Degree>    the  inputcd /s2d1/BMDL/
  //! derivatives   are assumed to be  0.
  //!
  //! Content of <Ders> :
  //!
  //! x(1),x(2),...,x(Dimension),w
  //! x'(1),x'(2),...,x'(Dimension),w'
  //! x''(1),x''(2),...,x''(Dimension),w''
  //!
  //! If  <All> is false, only the   derivative at order
  //! <N> is computed.  <RDers>  is an array   of length
  //! Dimension which will contain the result :
  //!
  //! x(1)/w , x(2)/w ,  ... derivated <N> times
  //!
  //! If <All> is  true all the  derivatives up to order
  //! <N> are computed.   <RDers> is an array of  length
  //! Dimension * (N+1) which will contains :
  //!
  //! x(1)/w , x(2)/w ,  ...
  //! x(1)/w , x(2)/w ,  ... derivated <1> times
  //! x(1)/w , x(2)/w ,  ... derivated <2> times
  //! ...
  //! x(1)/w , x(2)/w ,  ... derivated <N> times
  //!
  //! Warning: <RDers> must be dimensionned properly.
  Standard_EXPORT static void RationalDerivative (const Standard_Integer Degree, const Standard_Integer N, const Standard_Integer Dimension, Standard_Real& Ders, Standard_Real& RDers, const Standard_Boolean All = Standard_True);
  
  //! Computes DerivativesRequest derivatives of a ratio at
  //! of a BSpline function of degree <Degree>
  //! dimension <Dimension>.
  //!
  //! <PolesDerivatives> is an  array containing the  values
  //! of the input   derivatives from  0 to  <DerivativeRequest>
  //! For   orders   higher  than <Degree>    the  input
  //! derivatives   are assumed to be  0.
  //!
  //! Content of <PoleasDerivatives> :
  //!
  //! x(1),x(2),...,x(Dimension)
  //! x'(1),x'(2),...,x'(Dimension)
  //! x''(1),x''(2),...,x''(Dimension)
  //!
  //! WeightsDerivatives is an array that contains derivatives
  //! from 0 to  <DerivativeRequest>
  //! After returning from the routine the array
  //! RationalDerivatives contains the following
  //! x(1)/w , x(2)/w ,  ...
  //! x(1)/w , x(2)/w ,  ...   derivated once
  //! x(1)/w , x(2)/w ,  ...   twice
  //! x(1)/w , x(2)/w ,  ... derivated <DerivativeRequest> times
  //!
  //! The array RationalDerivatives and PolesDerivatives
  //! can be same since the overwrite is non destructive within
  //! the algorithm
  //!
  //! Warning: <RationalDerivates> must be dimensionned properly.
  Standard_EXPORT static void RationalDerivatives (const Standard_Integer DerivativesRequest, const Standard_Integer Dimension, Standard_Real& PolesDerivatives, Standard_Real& WeightsDerivatives, Standard_Real& RationalDerivates);
  
  //! Performs Horner method with synthethic division
  //! for derivatives
  //! parameter <U>, with <Degree> and <Dimension>.
  //! PolynomialCoeff are stored in the following fashion
  //! c0(1)      c0(2) ....       c0(Dimension)
  //! c1(1)      c1(2) ....       c1(Dimension)
  //!
  //! cDegree(1) cDegree(2) ....  cDegree(Dimension)
  //! where the polynomial is defined as :
  //!
  //! 2                     Degree
  //! c0 + c1 X + c2 X  +  ....   cDegree X
  //!
  //! Results stores the result in the following format
  //!
  //! f(1)             f(2)  ....     f(Dimension)
  //! (1)           (1)              (1)
  //! f  (1)        f   (2) ....     f   (Dimension)
  //!
  //! (DerivativeRequest)            (DerivativeRequest)
  //! f  (1)                         f   (Dimension)
  //!
  //! this just evaluates the point at parameter U
  //!
  //! Warning: <Results> and <PolynomialCoeff> must be dimensioned properly
  Standard_EXPORT static void EvalPolynomial (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, Standard_Real& Results);
  
  //! Same as above with DerivativeOrder = 0;
  Standard_EXPORT static void NoDerivativeEvalPolynomial (const Standard_Real U, const Standard_Integer Degree, const Standard_Integer Dimension, const Standard_Integer DegreeDimension, Standard_Real& PolynomialCoeff, Standard_Real& Results);
  
  //! Applies EvalPolynomial twice to evaluate the derivative
  //! of orders UDerivativeOrder in U, VDerivativeOrder in V
  //! at parameters U,V
  //!
  //! PolynomialCoeff are stored in the following fashion
  //! c00(1)  ....       c00(Dimension)
  //! c10(1)  ....       c10(Dimension)
  //! ....
  //! cm0(1)  ....       cm0(Dimension)
  //! ....
  //! c01(1)  ....       c01(Dimension)
  //! c11(1)  ....       c11(Dimension)
  //! ....
  //! cm1(1)  ....       cm1(Dimension)
  //! ....
  //! c0n(1)  ....       c0n(Dimension)
  //! c1n(1)  ....       c1n(Dimension)
  //! ....
  //! cmn(1)  ....       cmn(Dimension)
  //!
  //! where the polynomial is defined as :
  //! 2                 m
  //! c00 + c10 U + c20 U  +  ....  + cm0 U
  //! 2                   m
  //! + c01 V + c11 UV + c21 U V  +  ....  + cm1 U  V
  //! n               m n
  //! + .... + c0n V +  ....  + cmn U V
  //!
  //! with m = UDegree and n = VDegree
  //!
  //! Results stores the result in the following format
  //!
  //! f(1)             f(2)  ....     f(Dimension)
  //!
  //! Warning: <Results> and <PolynomialCoeff> must be dimensioned properly
  Standard_EXPORT static void EvalPoly2Var (const Standard_Real U, const Standard_Real V, const Standard_Integer UDerivativeOrder, const Standard_Integer VDerivativeOrder, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, Standard_Real& Results);
  
  //! Performs the Lagrange Interpolation of
  //! given series of points with given parameters
  //! with the requested derivative order
  //! Results will store things in the following format
  //! with d = DerivativeOrder
  //!
  //! [0],             [Dimension-1]              : value
  //! [Dimension],     [Dimension  + Dimension-1] : first derivative
  //!
  //! [d *Dimension],  [d*Dimension + Dimension-1]: dth   derivative
  Standard_EXPORT static Standard_Integer EvalLagrange (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& ValueArray, Standard_Real& ParameterArray, Standard_Real& Results);
  
  //! Performs the Cubic Hermite Interpolation of
  //! given series of points with given parameters
  //! with the requested derivative order.
  //! ValueArray stores the value at the first and
  //! last parameter. It has the following format :
  //! [0],             [Dimension-1]              : value at first param
  //! [Dimension],     [Dimension  + Dimension-1] : value at last param
  //! Derivative array stores the value of the derivatives
  //! at the first parameter and at the last parameter
  //! in the following format
  //! [0],             [Dimension-1]              : derivative at
  //! first param
  //! [Dimension],     [Dimension  + Dimension-1] : derivative at
  //! last param
  //!
  //! ParameterArray  stores the first and last parameter
  //! in the following format :
  //! [0] : first parameter
  //! [1] : last  parameter
  //!
  //! Results will store things in the following format
  //! with d = DerivativeOrder
  //!
  //! [0],             [Dimension-1]              : value
  //! [Dimension],     [Dimension  + Dimension-1] : first derivative
  //!
  //! [d *Dimension],  [d*Dimension + Dimension-1]: dth   derivative
  Standard_EXPORT static Standard_Integer EvalCubicHermite (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Dimension, Standard_Real& ValueArray, Standard_Real& DerivativeArray, Standard_Real& ParameterArray, Standard_Real& Results);
  
  //! This build the coefficient of Hermite's polynomes on
  //! [FirstParameter, LastParameter]
  //!
  //! if j <= FirstOrder+1 then
  //!
  //! MatrixCoefs[i, j] = ith coefficient of the polynome H0,j-1
  //!
  //! else
  //!
  //! MatrixCoefs[i, j] = ith coefficient of the polynome H1,k
  //! with k = j - FirstOrder - 2
  //!
  //! return false if
  //! - |FirstParameter| > 100
  //! - |LastParameter| > 100
  //! - |FirstParameter| +|LastParameter| < 1/100
  //! -   |LastParameter - FirstParameter|
  //! / (|FirstParameter| +|LastParameter|)  < 1/100
  Standard_EXPORT static Standard_Boolean HermiteCoefficients (const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, math_Matrix& MatrixCoefs);
  
  Standard_EXPORT static void CoefficientsPoles (const TColgp_Array1OfPnt& Coefs, const TColStd_Array1OfReal& WCoefs, TColgp_Array1OfPnt& Poles, TColStd_Array1OfReal& WPoles);
  
  Standard_EXPORT static void CoefficientsPoles (const TColgp_Array1OfPnt2d& Coefs, const TColStd_Array1OfReal& WCoefs, TColgp_Array1OfPnt2d& Poles, TColStd_Array1OfReal& WPoles);
  
  Standard_EXPORT static void CoefficientsPoles (const TColStd_Array1OfReal& Coefs, const TColStd_Array1OfReal& WCoefs, TColStd_Array1OfReal& Poles, TColStd_Array1OfReal& WPoles);
  
  Standard_EXPORT static void CoefficientsPoles (const Standard_Integer dim, const TColStd_Array1OfReal& Coefs, const TColStd_Array1OfReal& WCoefs, TColStd_Array1OfReal& Poles, TColStd_Array1OfReal& WPoles);
  
  Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt& Coeffs, TColStd_Array1OfReal& WCoeffs);
  
  Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt2d& Coeffs, TColStd_Array1OfReal& WCoeffs);
  
  Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal& Coeffs, TColStd_Array1OfReal& WCoeffs);
  
  Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, const Standard_Integer dim, TColStd_Array1OfReal& Coeffs, TColStd_Array1OfReal& WCoeffs);
  
  Standard_EXPORT static void CoefficientsPoles (const TColgp_Array2OfPnt& Coefs, const TColStd_Array2OfReal& WCoefs, TColgp_Array2OfPnt& Poles, TColStd_Array2OfReal& WPoles);
  
  Standard_EXPORT static void UTrimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array2OfPnt& Coeffs, TColStd_Array2OfReal& WCoeffs);
  
  Standard_EXPORT static void VTrimming (const Standard_Real V1, const Standard_Real V2, TColgp_Array2OfPnt& Coeffs, TColStd_Array2OfReal& WCoeffs);
  
  //! Compute the coefficients in the canonical base of the
  //! polynomial satisfying the given constraints
  //! at the given parameters
  //! The array FirstContr(i,j) i=1,Dimension j=0,FirstOrder
  //! contains the values of the constraint at parameter FirstParameter
  //! idem for LastConstr
  Standard_EXPORT static Standard_Boolean HermiteInterpolate (const Standard_Integer Dimension, const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, const TColStd_Array2OfReal& FirstConstr, const TColStd_Array2OfReal& LastConstr, TColStd_Array1OfReal& Coefficients);
  
  //! Compute the number of points used for integral
  //! computations (NbGaussPoints) and the degree of Jacobi
  //! Polynomial (WorkDegree).
  //! ConstraintOrder has to be GeomAbs_C0, GeomAbs_C1 or GeomAbs_C2
  //! Code: Code d' init. des parametres de discretisation.
  //! = -5
  //! = -4
  //! = -3
  //! = -2
  //! = -1
  //! =  1 calcul rapide avec precision moyenne.
  //! =  2 calcul rapide avec meilleure precision.
  //! =  3 calcul un peu plus lent avec bonne precision.
  //! =  4 calcul lent avec la meilleure precision possible.
  Standard_EXPORT static void JacobiParameters (const GeomAbs_Shape ConstraintOrder, const Standard_Integer MaxDegree, const Standard_Integer Code, Standard_Integer& NbGaussPoints, Standard_Integer& WorkDegree);
  
  //! translates from GeomAbs_Shape to Integer
  Standard_EXPORT static Standard_Integer NivConstr (const GeomAbs_Shape ConstraintOrder);
  
  //! translates from Integer to GeomAbs_Shape
  Standard_EXPORT static GeomAbs_Shape ConstraintOrder (const Standard_Integer NivConstr);
  
  Standard_EXPORT static void EvalLength (const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, const Standard_Real U1, const Standard_Real U2, Standard_Real& Length);
  
  Standard_EXPORT static void EvalLength (const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, const Standard_Real U1, const Standard_Real U2, const Standard_Real Tol, Standard_Real& Length, Standard_Real& Error);


protected:


private:


friend class PLib_Base;
friend class PLib_JacobiPolynomial;
friend class PLib_HermitJacobi;
friend class PLib_DoubleJacobiPolynomial;

};


#include <PLib.lxx>


#endif // _PLib_HeaderFile
Commit	Line	Data
42cf5bc1	1	// Created on: 1995-08-28
	2	// Created by: Laurent BOURESCHE
	3	// Copyright (c) 1995-1999 Matra Datavision
	4	// Copyright (c) 1999-2014 OPEN CASCADE SAS
	5	//
	6	// This file is part of Open CASCADE Technology software library.
	7	//
	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.
	13	//
	14	// Alternatively, this file may be used under the terms of Open CASCADE
	15	// commercial license or contractual agreement.
	16
	17	#ifndef _PLib_HeaderFile
	18	#define _PLib_HeaderFile
	19
	20	#include <Standard.hxx>
	21	#include <Standard_DefineAlloc.hxx>
	22	#include <Standard_Handle.hxx>
	23
	24	#include <TColStd_Array1OfReal.hxx>
	25	#include <TColStd_Array2OfReal.hxx>
	26	#include <TColgp_Array1OfPnt.hxx>
	27	#include <TColgp_Array1OfPnt2d.hxx>
	28	#include <Standard_Real.hxx>
	29	#include <Standard_Integer.hxx>
	30	#include <Standard_Boolean.hxx>
	31	#include <TColgp_Array2OfPnt.hxx>
	32	#include <GeomAbs_Shape.hxx>
	33	class math_Matrix;
	34	class PLib_Base;
	35	class PLib_JacobiPolynomial;
	36	class PLib_HermitJacobi;
	37	class PLib_DoubleJacobiPolynomial;
	38
	39
	40	//! PLib means Polynomial functions library. This pk
	41	//! provides basic computation functions for
	42	//! polynomial functions.
	43	class PLib
	44	{
	45	public:
	46
	47	DEFINE_STANDARD_ALLOC
	48
	49
	50	//! Used as argument for a non rational functions
	51	static TColStd_Array1OfReal& NoWeights();
	52
	53	//! Used as argument for a non rational functions
	54	static TColStd_Array2OfReal& NoWeights2();
	55
	56	//! Copy in FP the coordinates of the poles.
	57	Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt& Poles, TColStd_Array1OfReal& FP);
	58
	59	//! Copy in FP the coordinates of the poles.
	60	Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt& Poles, const TColStd_Array1OfReal& Weights, TColStd_Array1OfReal& FP);
	61
	62	//! Get from FP the coordinates of the poles.
	63	Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt& Poles);
	64
65	//! Get from FP the coordinates of the poles.
66	Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt& Poles, TColStd_Array1OfReal& Weights);
67
68	//! Copy in FP the coordinates of the poles.
69	Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt2d& Poles, TColStd_Array1OfReal& FP);
70
71	//! Copy in FP the coordinates of the poles.
72	Standard_EXPORT static void SetPoles (const TColgp_Array1OfPnt2d& Poles, const TColStd_Array1OfReal& Weights, TColStd_Array1OfReal& FP);
73
74	//! Get from FP the coordinates of the poles.
75	Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt2d& Poles);
76
77	//! Get from FP the coordinates of the poles.
78	Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array1OfPnt2d& Poles, TColStd_Array1OfReal& Weights);
79
80	//! Returns the Binomial Cnp. N should be <= BSplCLib::MaxDegree().
81	Standard_EXPORT static Standard_Real Bin (const Standard_Integer N, const Standard_Integer P);
82
83	//! Computes the derivatives of a ratio at order
84	//! <N> in dimension <Dimension>.
85	//!
86	//! <Ders> is an array containing the values of the
87	//! input derivatives from 0 to Min(<N>,<Degree>).
88	//! For orders higher than <Degree> the inputcd /s2d1/BMDL/
89	//! derivatives are assumed to be 0.
90	//!
91	//! Content of <Ders> :
92	//!
93	//! x(1),x(2),...,x(Dimension),w
94	//! x'(1),x'(2),...,x'(Dimension),w'
95	//! x''(1),x''(2),...,x''(Dimension),w''
96	//!
97	//! If <All> is false, only the derivative at order
98	//! <N> is computed. <RDers> is an array of length
99	//! Dimension which will contain the result :
100	//!
101	//! x(1)/w , x(2)/w , ... derivated <N> times
102	//!
103	//! If <All> is true all the derivatives up to order
104	//! <N> are computed. <RDers> is an array of length
105	//! Dimension * (N+1) which will contains :
106	//!
107	//! x(1)/w , x(2)/w , ...
108	//! x(1)/w , x(2)/w , ... derivated <1> times
109	//! x(1)/w , x(2)/w , ... derivated <2> times
110	//! ...
111	//! x(1)/w , x(2)/w , ... derivated <N> times
112	//!
113	//! Warning: <RDers> must be dimensionned properly.
114	Standard_EXPORT static void RationalDerivative (const Standard_Integer Degree, const Standard_Integer N, const Standard_Integer Dimension, Standard_Real& Ders, Standard_Real& RDers, const Standard_Boolean All = Standard_True);
115
116	//! Computes DerivativesRequest derivatives of a ratio at
117	//! of a BSpline function of degree <Degree>
118	//! dimension <Dimension>.
119	//!
120	//! <PolesDerivatives> is an array containing the values
121	//! of the input derivatives from 0 to <DerivativeRequest>
122	//! For orders higher than <Degree> the input
123	//! derivatives are assumed to be 0.
124	//!
125	//! Content of <PoleasDerivatives> :
126	//!
127	//! x(1),x(2),...,x(Dimension)
128	//! x'(1),x'(2),...,x'(Dimension)
129	//! x''(1),x''(2),...,x''(Dimension)
130	//!
131	//! WeightsDerivatives is an array that contains derivatives
132	//! from 0 to <DerivativeRequest>
133	//! After returning from the routine the array
134	//! RationalDerivatives contains the following
135	//! x(1)/w , x(2)/w , ...
136	//! x(1)/w , x(2)/w , ... derivated once
137	//! x(1)/w , x(2)/w , ... twice
138	//! x(1)/w , x(2)/w , ... derivated <DerivativeRequest> times
139	//!
140	//! The array RationalDerivatives and PolesDerivatives
141	//! can be same since the overwrite is non destructive within
142	//! the algorithm
143	//!
144	//! Warning: <RationalDerivates> must be dimensionned properly.
145	Standard_EXPORT static void RationalDerivatives (const Standard_Integer DerivativesRequest, const Standard_Integer Dimension, Standard_Real& PolesDerivatives, Standard_Real& WeightsDerivatives, Standard_Real& RationalDerivates);
146
147	//! Performs Horner method with synthethic division
148	//! for derivatives
149	//! parameter <U>, with <Degree> and <Dimension>.
150	//! PolynomialCoeff are stored in the following fashion
151	//! c0(1) c0(2) .... c0(Dimension)
152	//! c1(1) c1(2) .... c1(Dimension)
153	//!
154	//! cDegree(1) cDegree(2) .... cDegree(Dimension)
155	//! where the polynomial is defined as :
156	//!
157	//! 2 Degree
158	//! c0 + c1 X + c2 X + .... cDegree X
159	//!
160	//! Results stores the result in the following format
161	//!
162	//! f(1) f(2) .... f(Dimension)
163	//! (1) (1) (1)
164	//! f (1) f (2) .... f (Dimension)
165	//!
166	//! (DerivativeRequest) (DerivativeRequest)
167	//! f (1) f (Dimension)
168	//!
169	//! this just evaluates the point at parameter U
170	//!
171	//! Warning: <Results> and <PolynomialCoeff> must be dimensioned properly
172	Standard_EXPORT static void EvalPolynomial (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, Standard_Real& Results);
173
174	//! Same as above with DerivativeOrder = 0;
175	Standard_EXPORT static void NoDerivativeEvalPolynomial (const Standard_Real U, const Standard_Integer Degree, const Standard_Integer Dimension, const Standard_Integer DegreeDimension, Standard_Real& PolynomialCoeff, Standard_Real& Results);
176
177	//! Applies EvalPolynomial twice to evaluate the derivative
178	//! of orders UDerivativeOrder in U, VDerivativeOrder in V
179	//! at parameters U,V
180	//!
181	//! PolynomialCoeff are stored in the following fashion
182	//! c00(1) .... c00(Dimension)
183	//! c10(1) .... c10(Dimension)
184	//! ....
185	//! cm0(1) .... cm0(Dimension)
186	//! ....
187	//! c01(1) .... c01(Dimension)
188	//! c11(1) .... c11(Dimension)
189	//! ....
190	//! cm1(1) .... cm1(Dimension)
191	//! ....
192	//! c0n(1) .... c0n(Dimension)
193	//! c1n(1) .... c1n(Dimension)
194	//! ....
195	//! cmn(1) .... cmn(Dimension)
196	//!
197	//! where the polynomial is defined as :
198	//! 2 m
199	//! c00 + c10 U + c20 U + .... + cm0 U
200	//! 2 m
201	//! + c01 V + c11 UV + c21 U V + .... + cm1 U V
202	//! n m n
203	//! + .... + c0n V + .... + cmn U V
204	//!
205	//! with m = UDegree and n = VDegree
206	//!
207	//! Results stores the result in the following format
208	//!
209	//! f(1) f(2) .... f(Dimension)
210	//!
211	//! Warning: <Results> and <PolynomialCoeff> must be dimensioned properly
212	Standard_EXPORT static void EvalPoly2Var (const Standard_Real U, const Standard_Real V, const Standard_Integer UDerivativeOrder, const Standard_Integer VDerivativeOrder, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, Standard_Real& Results);
213
214	//! Performs the Lagrange Interpolation of
215	//! given series of points with given parameters
216	//! with the requested derivative order
217	//! Results will store things in the following format
218	//! with d = DerivativeOrder
219	//!
220	//! [0], [Dimension-1] : value
221	//! [Dimension], [Dimension + Dimension-1] : first derivative
222	//!
223	//! [d Dimension], [dDimension + Dimension-1]: dth derivative
224	Standard_EXPORT static Standard_Integer EvalLagrange (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& ValueArray, Standard_Real& ParameterArray, Standard_Real& Results);
225
226	//! Performs the Cubic Hermite Interpolation of
227	//! given series of points with given parameters
228	//! with the requested derivative order.
229	//! ValueArray stores the value at the first and
230	//! last parameter. It has the following format :
231	//! [0], [Dimension-1] : value at first param
232	//! [Dimension], [Dimension + Dimension-1] : value at last param
233	//! Derivative array stores the value of the derivatives
234	//! at the first parameter and at the last parameter
235	//! in the following format
236	//! [0], [Dimension-1] : derivative at
237	//! first param
238	//! [Dimension], [Dimension + Dimension-1] : derivative at
239	//! last param
240	//!
241	//! ParameterArray stores the first and last parameter
242	//! in the following format :
243	//! [0] : first parameter
244	//! [1] : last parameter
245	//!
246	//! Results will store things in the following format
247	//! with d = DerivativeOrder
248	//!
249	//! [0], [Dimension-1] : value
250	//! [Dimension], [Dimension + Dimension-1] : first derivative
251	//!
252	//! [d Dimension], [dDimension + Dimension-1]: dth derivative
253	Standard_EXPORT static Standard_Integer EvalCubicHermite (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Dimension, Standard_Real& ValueArray, Standard_Real& DerivativeArray, Standard_Real& ParameterArray, Standard_Real& Results);
254
255	//! This build the coefficient of Hermite's polynomes on
256	//! [FirstParameter, LastParameter]
257	//!
258	//! if j <= FirstOrder+1 then
259	//!
260	//! MatrixCoefs[i, j] = ith coefficient of the polynome H0,j-1
261	//!
262	//! else
263	//!
264	//! MatrixCoefs[i, j] = ith coefficient of the polynome H1,k
265	//! with k = j - FirstOrder - 2
266	//!
267	//! return false if
268	//! - \|FirstParameter\| > 100
269	//! - \|LastParameter\| > 100
270	//! - \|FirstParameter\| +\|LastParameter\| < 1/100
271	//! - \|LastParameter - FirstParameter\|
272	//! / (\|FirstParameter\| +\|LastParameter\|) < 1/100
273	Standard_EXPORT static Standard_Boolean HermiteCoefficients (const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, math_Matrix& MatrixCoefs);
274
275	Standard_EXPORT static void CoefficientsPoles (const TColgp_Array1OfPnt& Coefs, const TColStd_Array1OfReal& WCoefs, TColgp_Array1OfPnt& Poles, TColStd_Array1OfReal& WPoles);
276
277	Standard_EXPORT static void CoefficientsPoles (const TColgp_Array1OfPnt2d& Coefs, const TColStd_Array1OfReal& WCoefs, TColgp_Array1OfPnt2d& Poles, TColStd_Array1OfReal& WPoles);
278
279	Standard_EXPORT static void CoefficientsPoles (const TColStd_Array1OfReal& Coefs, const TColStd_Array1OfReal& WCoefs, TColStd_Array1OfReal& Poles, TColStd_Array1OfReal& WPoles);
280
281	Standard_EXPORT static void CoefficientsPoles (const Standard_Integer dim, const TColStd_Array1OfReal& Coefs, const TColStd_Array1OfReal& WCoefs, TColStd_Array1OfReal& Poles, TColStd_Array1OfReal& WPoles);
282
283	Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt& Coeffs, TColStd_Array1OfReal& WCoeffs);
284
285	Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt2d& Coeffs, TColStd_Array1OfReal& WCoeffs);
286
287	Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal& Coeffs, TColStd_Array1OfReal& WCoeffs);
288
289	Standard_EXPORT static void Trimming (const Standard_Real U1, const Standard_Real U2, const Standard_Integer dim, TColStd_Array1OfReal& Coeffs, TColStd_Array1OfReal& WCoeffs);
290
291	Standard_EXPORT static void CoefficientsPoles (const TColgp_Array2OfPnt& Coefs, const TColStd_Array2OfReal& WCoefs, TColgp_Array2OfPnt& Poles, TColStd_Array2OfReal& WPoles);
292
293	Standard_EXPORT static void UTrimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array2OfPnt& Coeffs, TColStd_Array2OfReal& WCoeffs);
294
295	Standard_EXPORT static void VTrimming (const Standard_Real V1, const Standard_Real V2, TColgp_Array2OfPnt& Coeffs, TColStd_Array2OfReal& WCoeffs);
296
297	//! Compute the coefficients in the canonical base of the
298	//! polynomial satisfying the given constraints
299	//! at the given parameters
300	//! The array FirstContr(i,j) i=1,Dimension j=0,FirstOrder
301	//! contains the values of the constraint at parameter FirstParameter
302	//! idem for LastConstr
303	Standard_EXPORT static Standard_Boolean HermiteInterpolate (const Standard_Integer Dimension, const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, const TColStd_Array2OfReal& FirstConstr, const TColStd_Array2OfReal& LastConstr, TColStd_Array1OfReal& Coefficients);
304
305	//! Compute the number of points used for integral
306	//! computations (NbGaussPoints) and the degree of Jacobi
307	//! Polynomial (WorkDegree).
308	//! ConstraintOrder has to be GeomAbs_C0, GeomAbs_C1 or GeomAbs_C2
309	//! Code: Code d' init. des parametres de discretisation.
310	//! = -5
311	//! = -4
312	//! = -3
313	//! = -2
314	//! = -1
315	//! = 1 calcul rapide avec precision moyenne.
316	//! = 2 calcul rapide avec meilleure precision.
317	//! = 3 calcul un peu plus lent avec bonne precision.
318	//! = 4 calcul lent avec la meilleure precision possible.
319	Standard_EXPORT static void JacobiParameters (const GeomAbs_Shape ConstraintOrder, const Standard_Integer MaxDegree, const Standard_Integer Code, Standard_Integer& NbGaussPoints, Standard_Integer& WorkDegree);
320
321	//! translates from GeomAbs_Shape to Integer
322	Standard_EXPORT static Standard_Integer NivConstr (const GeomAbs_Shape ConstraintOrder);
323
324	//! translates from Integer to GeomAbs_Shape
325	Standard_EXPORT static GeomAbs_Shape ConstraintOrder (const Standard_Integer NivConstr);
326
327	Standard_EXPORT static void EvalLength (const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, const Standard_Real U1, const Standard_Real U2, Standard_Real& Length);
328
329	Standard_EXPORT static void EvalLength (const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real& PolynomialCoeff, const Standard_Real U1, const Standard_Real U2, const Standard_Real Tol, Standard_Real& Length, Standard_Real& Error);
330
331
332
333
334	protected:
335
336
337
338
339
340	private:
341
342
343
344
345	friend class PLib_Base;
346	friend class PLib_JacobiPolynomial;
347	friend class PLib_HermitJacobi;
348	friend class PLib_DoubleJacobiPolynomial;
349
350	};
351
352
353	#include <PLib.lxx>
354
355
356
357
358
359	#endif // _PLib_HeaderFile