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-- File: PLib.cdl
-- Created: Mon Aug 28 11:17:53 1995
-- Author: Laurent BOURESCHE
-- <lbo@phylox>
-- 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
---Copyright: Matra Datavision 1995
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 , without testing anything.
---C++: inline
Binomial(N : Integer);
---Purpose: test on N > maxbinom and build the PASCAL triangle
-- on size N if necessary.
---C++: inline
InternalBinomial(N : Integer;
maxbinom : out Integer;
binom : out Address);
---Purpose: only called by Binomial(N,P)
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;
|
