+++ /dev/null
--- 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.
-
--- Modified: 28/02/1996 by PMN : HermiteCoefficients added
--- Modified: 19/02/1997 by JCT : EvalPoly2Var added
-
--- Modified: 05/09/97 by JPI for SSV : JacobiPolynomial --
--- DoubleJacobiPolynomial, HermiteInterpolate, JacobiParameters
-
-
-package PLib
-
- ---Purpose: PLib means Polynomial functions library. This pk
- -- provides basic computation functions for
- -- polynomial functions.
- --
-
-uses Standard, math, TColStd, gp, TColgp, GeomAbs
-
-is
- deferred class Base from PLib;
- class JacobiPolynomial from PLib;
- class HermitJacobi from PLib;
- class DoubleJacobiPolynomial from PLib;
-
- NoWeights returns Array1OfReal from TColStd;
- ---Purpose: Used as argument for a non rational functions
- --
- ---C++: return &
- ---C++: inline
-
- NoWeights2 returns Array2OfReal from TColStd;
- ---Purpose: Used as argument for a non rational functions
- --
- ---C++: return &
- ---C++: inline
-
- SetPoles(Poles : Array1OfPnt from TColgp;
- FP : out Array1OfReal from TColStd);
- ---Purpose: Copy in FP the coordinates of the poles.
-
- SetPoles(Poles : Array1OfPnt from TColgp;
- Weights : Array1OfReal from TColStd;
- FP : out Array1OfReal from TColStd);
- ---Purpose: Copy in FP the coordinates of the poles.
-
- GetPoles(FP : Array1OfReal from TColStd;
- Poles : out Array1OfPnt from TColgp);
- ---Purpose: Get from FP the coordinates of the poles.
-
- GetPoles(FP : Array1OfReal from TColStd;
- Poles : out Array1OfPnt from TColgp;
- Weights : out Array1OfReal from TColStd);
- ---Purpose: Get from FP the coordinates of the poles.
-
- SetPoles(Poles : Array1OfPnt2d from TColgp;
- FP : out Array1OfReal from TColStd);
- ---Purpose: Copy in FP the coordinates of the poles.
-
- SetPoles(Poles : Array1OfPnt2d from TColgp;
- Weights : Array1OfReal from TColStd;
- FP : out Array1OfReal from TColStd);
- ---Purpose: Copy in FP the coordinates of the poles.
-
- GetPoles(FP : Array1OfReal from TColStd;
- Poles : out Array1OfPnt2d from TColgp);
- ---Purpose: Get from FP the coordinates of the poles.
-
- GetPoles(FP : Array1OfReal from TColStd;
- Poles : out Array1OfPnt2d from TColgp;
- Weights : out Array1OfReal from TColStd);
- ---Purpose: Get from FP the coordinates of the poles.
-
- Bin(N,P : Integer) returns Real;
- ---Purpose: Returns the Binomial Cnp. N should be <= BSplCLib::MaxDegree().
-
- RationalDerivative(Degree : Integer;
- N : Integer;
- Dimension : Integer;
- Ders : in out Real;
- RDers : in out Real;
- All : Boolean = Standard_True);
- ---Purpose: 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.
-
-
- RationalDerivatives(DerivativesRequest : Integer;
- Dimension : Integer;
- PolesDerivatives : in out Real;
- WeightsDerivatives : in out Real;
- RationalDerivates : in out Real) ;
-
- ---Purpose: 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.
-
-
- EvalPolynomial(U : Real;
- DerivativeOrder : Integer ;
- Degree : Integer ;
- Dimension : Integer ;
- PolynomialCoeff : in out Real ;
- Results : in out Real) ;
-
- ---Purpose: 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
- --
- --
-
- NoDerivativeEvalPolynomial(U : Real;
- Degree : Integer ;
- Dimension : Integer ;
- DegreeDimension : Integer ;
- PolynomialCoeff : in out Real ;
- Results : in out Real) ;
- ---Purpose: Same as above with DerivativeOrder = 0;
-
- EvalPoly2Var(U,V : Real;
- UDerivativeOrder,VDerivativeOrder : Integer ;
- UDegree,VDegree,Dimension : Integer ;
- PolynomialCoeff : in out Real;
- Results : in out Real) ;
-
- ---Purpose: 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
- --
- --
-
-
- EvalLagrange(U : Real ;
- DerivativeOrder : Integer ;
- Degree : Integer ;
- Dimension : Integer ;
- ValueArray : in out Real;
- ParameterArray : in out Real;
- Results : in out Real) returns Integer ;
-
- ---Purpose: 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
-
- EvalCubicHermite(U : Real ;
- DerivativeOrder : Integer ;
- Dimension : Integer ;
- ValueArray : in out Real;
- DerivativeArray : in out Real;
- ParameterArray : in out Real;
- Results : in out Real) returns Integer ;
-
- ---Purpose: 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
-
- HermiteCoefficients(FirstParameter : in Real;
- LastParameter : in Real;
- FirstOrder : in Integer;
- LastOrder : in Integer;
- MatrixCoefs : in out Matrix from math)
-
- ---Purpose: 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
- returns Boolean;
-
-----------------------------------------------------------------
--- The following functions computes poles corresponding to --
--- given coefficients. --
--- PLib::NoWeights() must be given for non rational functions--
-----------------------------------------------------------------
-
- CoefficientsPoles(Coefs : in Array1OfPnt from TColgp;
- WCoefs : in Array1OfReal from TColStd;
- Poles : in out Array1OfPnt from TColgp;
- WPoles : in out Array1OfReal from TColStd);
-
- CoefficientsPoles(Coefs : in Array1OfPnt2d from TColgp;
- WCoefs : in Array1OfReal from TColStd;
- Poles : in out Array1OfPnt2d from TColgp;
- WPoles : in out Array1OfReal from TColStd);
-
- CoefficientsPoles(Coefs : in Array1OfReal from TColStd;
- WCoefs : in Array1OfReal from TColStd;
- Poles : in out Array1OfReal from TColStd;
- WPoles : in out Array1OfReal from TColStd);
-
- CoefficientsPoles(dim : in Integer from Standard;
- Coefs : in Array1OfReal from TColStd;
- WCoefs : in Array1OfReal from TColStd;
- Poles : in out Array1OfReal from TColStd;
- WPoles : in out Array1OfReal from TColStd);
-
-
-----------------------------------------------------------------
--- The following functions trim the Bezier curve between two --
--- parametric values U1, U2. --
--- Can be used to extend the curve : --
--- Parameters U1<0. or U2>1. can be given. --
--- PLib::NoWeights() must be given for non rational functions--
-----------------------------------------------------------------
-
-
- Trimming (U1, U2 : in Real;
- Coeffs : in out Array1OfPnt from TColgp;
- WCoeffs : in out Array1OfReal from TColStd);
-
-
- Trimming (U1, U2 : in Real;
- Coeffs : in out Array1OfPnt2d from TColgp;
- WCoeffs : in out Array1OfReal from TColStd);
-
-
- Trimming (U1, U2 : in Real;
- Coeffs : in out Array1OfReal from TColStd;
- WCoeffs : in out Array1OfReal from TColStd);
-
-
- Trimming (U1, U2 : in Real;
- dim : in Integer;
- Coeffs : in out Array1OfReal from TColStd;
- WCoeffs : in out Array1OfReal from TColStd);
-
-
-
-
-----------------------------------------------------------------
--- The following functions computes poles corresponding to --
--- given coefficients. --
--- PLib::NoWeights2() must be given for non rational --
--- functions. --
-----------------------------------------------------------------
-
- CoefficientsPoles(Coefs : in Array2OfPnt from TColgp;
- WCoefs : in Array2OfReal from TColStd;
- Poles : in out Array2OfPnt from TColgp;
- WPoles : in out Array2OfReal from TColStd);
-
-
-----------------------------------------------------------------
--- The following functions trim the Bezier surface between --
--- two parametric values. --
--- Can be used to extend the surface : --
--- Parameters U1(V1)<0. or U2(V2)>1. can be given. --
--- PLib::NoWeights2() must be given for non rational --
--- functions. --
-----------------------------------------------------------------
-
-
- UTrimming (U1, U2 : in Real;
- Coeffs : in out Array2OfPnt from TColgp;
- WCoeffs : in out Array2OfReal from TColStd);
-
-
- VTrimming (V1, V2 : in Real;
- Coeffs : in out Array2OfPnt from TColgp;
- WCoeffs : in out Array2OfReal from TColStd);
-
-
- HermiteInterpolate(Dimension : in Integer;
- FirstParameter,LastParameter : in Real;
- FirstOrder,LastOrder : in Integer;
- FirstConstr,LastConstr : Array2OfReal from TColStd;
- Coefficients : out Array1OfReal from TColStd)
- returns Boolean from Standard;
- ---Purpose : 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
-
- JacobiParameters (ConstraintOrder: Shape from GeomAbs;
- MaxDegree, Code: in Integer;
- NbGaussPoints: out Integer;
- WorkDegree: out Integer)
----Purpose : 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.
-
- raises ConstructionError from Standard;
--- if ConstraintOrder or Code is not valid
--- MaxDegree < 2*NivConstr+2 or MaxDegree > 50
---
----------- new
- NivConstr(ConstraintOrder : Shape from GeomAbs)
- ---Purpose: translates from GeomAbs_Shape to Integer
- returns Integer
- raises ConstructionError from Standard;
-
- ConstraintOrder(NivConstr : Integer)
- ---Purpose: translates from Integer to GeomAbs_Shape
- returns Shape from GeomAbs
- raises ConstructionError from Standard;
-
-
- EvalLength(Degree : Integer;
- Dimension : Integer;
- PolynomialCoeff : in out Real;
- U1, U2 : Real;
- Length : out Real);
-
- EvalLength(Degree : Integer;
- Dimension : Integer;
- PolynomialCoeff : in out Real;
- U1, U2 : Real;
- Tol : Real;
- Length : out Real;
- Error : out Real);
-
-end PLib;
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