OpenCascade/occt
1
0
Fork 0
mirror of https://git.dev.opencascade.org/repos/occt.git synced 2025-06-30 12:14:08 +03:00
Code
occt/src/BSplSLib/BSplSLib.cdl
abv ed4415982c 0024624: Lost word in license statement in source files 
License statement text corrected; compiler warnings caused by Bison 2.41 disabled for MSVC; a few other compiler warnings on 54-bit Windows eliminated by appropriate type cast
Wrong license statements corrected in several files.
Copyright and license statements added in XSD and GLSL files.
Copyright year updated in some files.
Obsolete documentation files removed from DrawResources.
2014-03-25 16:38:55 +04:00

700 lines
32 KiB
Plaintext
Raw Blame History

-- Created on: 1991-08-26
-- Created by: JCV
-- Copyright (c) 1991-1999 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.
package BSplSLib
--- Purpose : BSplSLib B-spline surface Library
-- This package provides an implementation of geometric
-- functions for rational and non rational, periodic and non
-- periodic B-spline surface computation.
--
-- this package uses the multi-dimensions splines methods
-- provided in the package BSplCLib.
--
-- In this package the B-spline surface is defined with :
-- . its control points : Array2OfPnt Poles
-- . its weights : Array2OfReal Weights
-- . its knots and their multiplicity in the two parametric
-- direction U and V : Array1OfReal UKnots, VKnots and
-- Array1OfInteger UMults, VMults.
-- . the degree of the normalized Spline functions :
-- UDegree, VDegree
--
-- . the Booleans URational, VRational to know if the weights
-- are constant in the U or V direction.
--
-- . the Booleans UPeriodic, VRational to know if the the
-- surface is periodic in the U or V direction.
--
-- Warnings : The bounds of UKnots and UMults should be the
-- same, the bounds of VKnots and VMults should be the same,
-- the bounds of Poles and Weights shoud be the same.
--
-- The Control points representation is :
-- Poles(Uorigin,Vorigin) ...................Poles(Uorigin,Vend)
-- . .
-- . .
-- Poles(Uend, Vorigin) .....................Poles(Uend, Vend)
--
-- For the double array the row indice corresponds to the
-- parametric U direction and the columns indice corresponds
-- to the parametric V direction.
--
-- KeyWords :
-- B-spline surface, Functions, Library
--
-- References :
-- . A survey of curve and surface methods in CADG Wolfgang BOHM
-- CAGD 1 (1984)
-- . On de Boor-like algorithms and blossoming Wolfgang BOEHM
-- cagd 5 (1988)
-- . Blossoming and knot insertion algorithms for B-spline curves
-- Ronald N. GOLDMAN
-- . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
-- . Curves and Surfaces for Computer Aided Geometric Design,
-- a practical guide Gerald Farin
uses TColStd, gp, TColgp
is
imported EvaluatorFunction ;
---Purpose:
-- this is a one dimensional function
-- typedef void (*EvaluatorFunction) (
-- Standard_Integer // Derivative Request
-- Standard_Real * // StartEnd[2][2]
-- // [0] = U
-- // [1] = V
-- // [0] = start
-- // [1] = end
-- Standard_Real // UParameter
-- Standard_Real // VParamerer
-- Standard_Real & // Result
-- Standard_Integer &) ;// Error Code
-- serves to multiply a given vectorial BSpline by a function
-------------------------------------------------------------
-------------------------------------------------------------
---------- -----------
---------- Surface Evaluations -----------
---------- -----------
-------------------------------------------------------------
-------------------------------------------------------------
RationalDerivative(UDeg,VDeg : Integer;
N,M : Integer;
Ders : in out Real;
RDers : in out Real;
All : Boolean = Standard_True);
---Purpose: Computes the derivatives of a ratio of
-- two-variables functions x(u,v) / w(u,v) at orders
-- <N,M>, x(u,v) is a vector in dimension
-- <3>.
--
-- <Ders> is an array containing the values of the
-- input derivatives from 0 to Min(<N>,<UDeg>), 0 to
-- Min(<M>,<VDeg>). For orders higher than
-- <UDeg,VDeg> the input derivatives are assumed to
-- be 0.
--
-- The <Ders> is a 2d array and the dimension of the
-- lines is always (<VDeg>+1) * (<3>+1), even
-- if <N> is smaller than <Udeg> (the derivatives
-- higher than <N> are not used).
--
-- Content of <Ders> :
--
-- x(i,j)[k] means : the composant k of x derivated
-- (i) times in u and (j) times in v.
--
-- ... First line ...
--
-- x[1],x[2],...,x[3],w
-- x(0,1)[1],...,x(0,1)[3],w(1,0)
-- ...
-- x(0,VDeg)[1],...,x(0,VDeg)[3],w(0,VDeg)
--
-- ... Then second line ...
--
-- x(1,0)[1],...,x(1,0)[3],w(1,0)
-- x(1,1)[1],...,x(1,1)[3],w(1,1)
-- ...
-- x(1,VDeg)[1],...,x(1,VDeg)[3],w(1,VDeg)
--
-- ...
--
-- ... Last line ...
--
-- x(UDeg,0)[1],...,x(UDeg,0)[3],w(UDeg,0)
-- x(UDeg,1)[1],...,x(UDeg,1)[3],w(UDeg,1)
-- ...
-- x(Udeg,VDeg)[1],...,x(UDeg,VDeg)[3],w(Udeg,VDeg)
--
--
--
-- If <All> is false, only the derivative at order
-- <N,M> is computed. <RDers> is an array of length
-- 3 which will contain the result :
--
-- x(1)/w , x(2)/w , ... derivated <N> <M> times
--
-- If <All> is true multiples derivatives are
-- computed. All the derivatives (i,j) with 0 <= i+j
-- <= Max(N,M) are computed. <RDers> is an array of
-- length 3 * (<N>+1) * (<M>+1) which will
-- contains :
--
-- x(1)/w , x(2)/w , ...
-- x(1)/w , x(2)/w , ... derivated <0,1> times
-- x(1)/w , x(2)/w , ... derivated <0,2> times
-- ...
-- x(1)/w , x(2)/w , ... derivated <0,N> times
--
-- x(1)/w , x(2)/w , ... derivated <1,0> times
-- x(1)/w , x(2)/w , ... derivated <1,1> times
-- ...
-- x(1)/w , x(2)/w , ... derivated <1,N> times
--
-- x(1)/w , x(2)/w , ... derivated <N,0> times
-- ....
-- Warning: <RDers> must be dimensionned properly.
D0 (U, V : in Real;
UIndex, VIndex : in Integer;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
UDegree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
P : out Pnt from gp);
D1 (U, V : in Real;
UIndex, VIndex : in Integer;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
Degree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
P : out Pnt from gp;
Vu, Vv : out Vec from gp);
D2 (U, V : in Real;
UIndex, VIndex : in Integer;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
UDegree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
P : out Pnt from gp;
Vu, Vv : out Vec from gp;
Vuu, Vvv, Vuv : out Vec from gp);
D3 (U, V : in Real;
UIndex, VIndex : in Integer;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
UDegree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
P : out Pnt from gp;
Vu, Vv : out Vec from gp;
Vuu, Vvv, Vuv : out Vec from gp;
Vuuu, Vvvv, Vuuv, Vuvv : out Vec from gp);
DN (U, V : in Real;
Nu, Nv : in Integer;
UIndex, VIndex : in Integer;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
UDegree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
Vn : out Vec from gp);
Iso (Param : in Real;
IsU : in Boolean;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
Degree : in Integer;
Periodic : in Boolean;
CPoles : out Array1OfPnt from TColgp;
CWeights : out Array1OfReal from TColStd);
---Purpose: Computes the poles and weights of an isoparametric
-- curve at parameter <Param> (UIso if <IsU> is True,
-- VIso else).
Reverse (Poles : in out Array2OfPnt from TColgp;
Last : Integer from Standard;
UDirection : Boolean from Standard);
---Purpose: Reverses the array of poles. Last is the Index of
-- the new first Row( Col) of Poles.
-- On a non periodic surface Last is
-- Poles.Upper().
-- On a periodic curve last is
-- (number of flat knots - degree - 1)
-- or
-- (sum of multiplicities(but for the last) + degree
-- - 1)
HomogeneousD0 (U, V : in Real;
UIndex, VIndex : in Integer;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
UDegree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
W : out Real ;
P : out Pnt from gp);
---Purpose: Makes an homogeneous evaluation of Poles and Weights
-- any and returns in P the Numerator value and
-- in W the Denominator value if Weights are present
-- otherwise returns 1.0e0
--
HomogeneousD1 (U, V : in Real;
UIndex, VIndex : in Integer;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
UDegree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
N : out Pnt from gp;
Nu : out Vec from gp;
Nv : out Vec from gp;
D : out Real ;
Du : out Real ;
Dv : out Real) ;
---Purpose: Makes an homogeneous evaluation of Poles and Weights
-- any and returns in P the Numerator value and
-- in W the Denominator value if Weights are present
-- otherwise returns 1.0e0
--
Reverse (Weights : in out Array2OfReal from TColStd;
Last : Integer from Standard;
UDirection : Boolean from Standard);
---Purpose: Reverses the array of weights.
IsRational(Weights : Array2OfReal from TColStd;
I1,I2 : Integer from Standard;
J1,J2 : Integer from Standard;
Epsilon : Real = 0.0) returns Boolean;
---Purpose:
-- Returns False if all the weights of the array <Weights>
-- in the area [I1,I2] * [J1,J2] are identic.
-- Epsilon is used for comparing weights.
-- If Epsilon is 0. the Epsilon of the first weight is used.
SetPoles(Poles : Array2OfPnt from TColgp;
FP : out Array1OfReal from TColStd;
UDirection : Boolean from Standard);
---Purpose: Copy in FP the coordinates of the poles.
SetPoles(Poles : Array2OfPnt from TColgp;
Weights : Array2OfReal from TColStd;
FP : out Array1OfReal from TColStd;
UDirection : Boolean from Standard);
---Purpose: Copy in FP the coordinates of the poles.
GetPoles(FP : Array1OfReal from TColStd;
Poles : out Array2OfPnt from TColgp;
UDirection : Boolean from Standard);
---Purpose: Get from FP the coordinates of the poles.
GetPoles(FP : Array1OfReal from TColStd;
Poles : out Array2OfPnt from TColgp;
Weights : out Array2OfReal from TColStd;
UDirection : Boolean from Standard);
---Purpose: Get from FP the coordinates of the poles.
MovePoint(U, V : Real; -- parameters of the point
Displ : Vec from gp; -- translation vector of the point
UIndex1 : Integer; -- first movable pole in U
UIndex2 : Integer; -- last movable pole in U
VIndex1 : Integer; -- first movable pole in V
VIndex2 : Integer; -- last movable pole in V
UDegree : Integer;
VDegree : Integer;
Rational : Boolean;
Poles : Array2OfPnt from TColgp;
Weights : Array2OfReal from TColStd;
UFlatKnots : Array1OfReal from TColStd;
VFlatKnots : Array1OfReal from TColStd;
UFirstIndex : in out Integer; -- first pole modified in U
ULastIndex : in out Integer; -- last pole modified in U
VFirstIndex : in out Integer; -- first pole modified in V
VLastIndex : in out Integer; -- last pole modified in V
NewPoles : in out Array2OfPnt from TColgp); -- new poles
---Purpose: Find the new poles which allows an old point (with a
-- given u,v as parameters) to reach a new position
-- UIndex1,UIndex2 indicate the range of poles we can
-- move for U
-- (1, UNbPoles-1) or (2, UNbPoles) -> no constraint
-- for one side in U
-- (2, UNbPoles-1) -> the ends are enforced for U
-- don't enter (1,NbPoles) and (1,VNbPoles)
-- -> error: rigid move
-- if problem in BSplineBasis calculation, no change
-- for the curve and
-- UFirstIndex, VLastIndex = 0
-- VFirstIndex, VLastIndex = 0
InsertKnots(UDirection : in Boolean from Standard;
Degree : in Integer from Standard;
Periodic : in Boolean from Standard;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
AddKnots : in Array1OfReal from TColStd;
AddMults : in Array1OfInteger from TColStd;
NewPoles : out Array2OfPnt from TColgp;
NewWeights : out Array2OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Epsilon : in Real from Standard;
Add : in Boolean from Standard = Standard_True);
RemoveKnot(UDirection : in Boolean from Standard;
Index : in Integer from Standard;
Mult : in Integer from Standard;
Degree : in Integer from Standard;
Periodic : in Boolean from Standard;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array2OfPnt from TColgp;
NewWeights : out Array2OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Tolerance : in Real from Standard)
returns Boolean from Standard;
IncreaseDegree(UDirection : in Boolean from Standard;
Degree : in Integer from Standard;
NewDegree : in Integer from Standard;
Periodic : in Boolean from Standard;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array2OfPnt from TColgp;
NewWeights : out Array2OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd);
Unperiodize(UDirection : in Boolean from Standard;
Degree : in Integer from Standard;
Mults : in Array1OfInteger from TColStd;
Knots : in Array1OfReal from TColStd;
Poles : in Array2OfPnt from TColgp;
Weights : in Array2OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewPoles : out Array2OfPnt from TColgp;
NewWeights : out Array2OfReal from TColStd);
NoWeights returns Array2OfReal from TColStd;
---Purpose: Used as argument for a non rational curve.
--
---C++: return &
---C++: inline
BuildCache(U,V : Real;
USpanDomain,VSpanDomain : Real;
UPeriodicFlag,VPeriodicFlag : Boolean ;
UDegree,VDegree : Integer;
UIndex, VIndex : Integer;
UFlatKnots,VFlatKnots : Array1OfReal from TColStd ;
Poles : Array2OfPnt from TColgp;
Weights : Array2OfReal from TColStd ;
CachePoles : in out Array2OfPnt from TColgp;
CacheWeights : in out Array2OfReal from TColStd);
---Purpose: Perform the evaluation of the Taylor expansion
-- of the Bspline normalized between 0 and 1.
-- If rational computes the homogeneous Taylor expension
-- for the numerator and stores it in CachePoles
--
--
CacheD0(U,V : Real;
UDegree,VDegree : Integer;
UCacheParameter,VCacheParameter : Real;
USpanLenght,VSpanLength : Real;
Poles : Array2OfPnt from TColgp ;
Weights : Array2OfReal from TColStd ;
Point : out Pnt from gp) ;
---Purpose: Perform the evaluation of the of the cache
-- the parameter must be normalized between
-- the 0 and 1 for the span.
-- The Cache must be valid when calling this
-- routine. Geom Package will insure that.
-- and then multiplies by the weights
-- this just evaluates the current point
-- the CacheParameter is where the Cache was
-- constructed the SpanLength is to normalize
-- the polynomial in the cache to avoid bad conditioning
-- effects
--
CoefsD0(U,V : Real;
Poles : Array2OfPnt from TColgp ;
Weights : Array2OfReal from TColStd ;
Point : out Pnt from gp) ;
---Purpose: Calls CacheD0 for Bezier Surfaces Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for BezierSurfaces ONLY!!!
---C++: inline
CacheD1(U,V : Real;
UDegree,VDegree : Integer;
UCacheParameter,VCacheParameter : Real;
USpanLenght,VSpanLength : Real;
Poles : Array2OfPnt from TColgp ;
Weights : Array2OfReal from TColStd ;
Point : out Pnt from gp;
VecU, VecV : out Vec from gp) ;
---Purpose: Perform the evaluation of the of the cache
-- the parameter must be normalized between
-- the 0 and 1 for the span.
-- The Cache must be valid when calling this
-- routine. Geom Package will insure that.
-- and then multiplies by the weights
-- this just evaluates the current point
-- the CacheParameter is where the Cache was
-- constructed the SpanLength is to normalize
-- the polynomial in the cache to avoid bad conditioning
-- effects
--
CoefsD1(U,V : Real;
Poles : Array2OfPnt from TColgp;
Weights : Array2OfReal from TColStd;
Point : out Pnt from gp;
VecU, VecV : out Vec from gp) ;
---Purpose: Calls CacheD0 for Bezier Surfaces Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for BezierSurfaces ONLY!!!
---C++: inline
CacheD2(U,V : Real;
UDegree,VDegree : Integer;
UCacheParameter,VCacheParameter : Real;
USpanLenght,VSpanLength : Real;
Poles : Array2OfPnt from TColgp ;
Weights : Array2OfReal from TColStd ;
Point : out Pnt from gp;
VecU, VecV, VecUU, VecUV, VecVV : out Vec from gp) ;
---Purpose: Perform the evaluation of the of the cache
-- the parameter must be normalized between
-- the 0 and 1 for the span.
-- The Cache must be valid when calling this
-- routine. Geom Package will insure that.
-- and then multiplies by the weights
-- this just evaluates the current point
-- the CacheParameter is where the Cache was
-- constructed the SpanLength is to normalize
-- the polynomial in the cache to avoid bad conditioning
-- effects
--
CoefsD2(U,V : Real;
Poles : Array2OfPnt from TColgp ;
Weights : Array2OfReal from TColStd ;
Point : out Pnt from gp;
VecU, VecV, VecUU, VecUV, VecVV : out Vec from gp) ;
---Purpose: Calls CacheD0 for Bezier Surfaces Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for BezierSurfaces ONLY!!!
---C++: inline
PolesCoefficients(Poles : Array2OfPnt from TColgp;
CachePoles : in out Array2OfPnt from TColgp);
---Purpose: Warning! To be used for BezierSurfaces ONLY!!!
---C++: inline
PolesCoefficients(Poles : Array2OfPnt from TColgp;
Weights : Array2OfReal from TColStd ;
CachePoles : in out Array2OfPnt from TColgp;
CacheWeights : in out Array2OfReal from TColStd) ;
---Purpose: Encapsulation of BuildCache to perform the
-- evaluation of the Taylor expansion for beziersurfaces
-- at parameters 0.,0.;
-- Warning: To be used for BezierSurfaces ONLY!!!
--
Resolution(Poles : in Array2OfPnt from TColgp ;
Weights : in Array2OfReal from TColStd;
UKnots, VKnots : in Array1OfReal from TColStd;
UMults, VMults : in Array1OfInteger from TColStd;
UDegree, VDegree : in Integer;
URat,VRat : in Boolean;
UPer,VPer : in Boolean;
Tolerance3D : in Real from Standard ;
UTolerance : in out Real from Standard ;
VTolerance : in out Real from Standard) ;
---Purpose: Given a tolerance in 3D space returns two
-- tolerances, one in U one in V such that for
-- all (u1,v1) and (u0,v0) in the domain of
-- the surface f(u,v) we have :
-- | u1 - u0 | < UTolerance and
-- | v1 - v0 | < VTolerance
-- we have |f (u1,v1) - f (u0,v0)| < Tolerance3D
Interpolate(UDegree, VDegree : Integer ;
UFlatKnots , VFlatKnots : Array1OfReal from TColStd ;
UParameters, VParameters : Array1OfReal from TColStd ;
Poles : in out Array2OfPnt from TColgp ;
Weights : in out Array2OfReal from TColStd ;
InversionProblem : out Integer) ;
---Purpose: Performs the interpolation of the data points given in
-- the Poles array in the form
-- [1,...,RL][1,...,RC][1...PolesDimension] . The
-- ColLength CL and the Length of UParameters must be the
-- same. The length of VFlatKnots is VDegree + CL + 1.
--
-- The RowLength RL and the Length of VParameters must be
-- the same. The length of VFlatKnots is Degree + RL + 1.
--
-- Warning: the method used to do that interpolation
-- is gauss elimination WITHOUT pivoting. Thus if the
-- diagonal is not dominant there is no guarantee that
-- the algorithm will work. Nevertheless for Cubic
-- interpolation at knots or interpolation at Scheonberg
-- points the method will work. The InversionProblem
-- will report 0 if there was no problem else it will
-- give the index of the faulty pivot
--
Interpolate(UDegree, VDegree : Integer ;
UFlatKnots , VFlatKnots : Array1OfReal from TColStd ;
UParameters, VParameters : Array1OfReal from TColStd ;
Poles : in out Array2OfPnt from TColgp ;
InversionProblem : out Integer) ;
---Purpose: Performs the interpolation of the data points given in
-- the Poles array.
-- The ColLength CL and the Length of UParameters must be
-- the same. The length of VFlatKnots is VDegree + CL + 1.
--
-- The RowLength RL and the Length of VParameters must be
-- the same. The length of VFlatKnots is Degree + RL + 1.
--
-- Warning: the method used to do that interpolation
-- is gauss elimination WITHOUT pivoting. Thus if the
-- diagonal is not dominant there is no guarantee that
-- the algorithm will work. Nevertheless for Cubic
-- interpolation at knots or interpolation at Scheonberg
-- points the method will work. The InversionProblem
-- will report 0 if there was no problem else it will
-- give the index of the faulty pivot
--
FunctionMultiply(
Function : EvaluatorFunction from BSplSLib ;
UBSplineDegree : Integer ;
VBSplineDegree : Integer ;
UBSplineKnots : Array1OfReal from TColStd ;
VBSplineKnots : Array1OfReal from TColStd ;
UMults : Array1OfInteger from TColStd ;
VMults : Array1OfInteger from TColStd ;
Poles : Array2OfPnt from TColgp ;
Weights : Array2OfReal from TColStd ;
UFlatKnots : Array1OfReal from TColStd ;
VFlatKnots : Array1OfReal from TColStd ;
UNewDegree : Integer ;
VNewDegree : Integer ;
NewNumerator : in out Array2OfPnt from TColgp ;
NewDenominator : in out Array2OfReal from TColStd ;
Status : in out Integer) ;
---Purpose: this will multiply a given BSpline numerator N(u,v)
-- and denominator D(u,v) defined by its
-- U/VBSplineDegree and U/VBSplineKnots, and
-- U/VMults. Its Poles and Weights are arrays which are
-- coded as array2 of the form
-- [1..UNumPoles][1..VNumPoles] by a function a(u,v)
-- which is assumed to satisfy the following : 1.
-- a(u,v) * N(u,v) and a(u,v) * D(u,v) is a polynomial
-- BSpline that can be expressed exactly as a BSpline of
-- degree U/VNewDegree on the knots U/VFlatKnots 2. the range
-- of a(u,v) is the same as the range of N(u,v)
-- or D(u,v)
-- ---Warning: it is the caller's responsability to
-- insure that conditions 1. and 2. above are satisfied
-- : no check whatsoever is made in this method --
-- Status will return 0 if OK else it will return the
-- pivot index -- of the matrix that was inverted to
-- compute the multiplied -- BSpline : the method used
-- is interpolation at Schoenenberg -- points of
-- a(u,v)* N(u,v) and a(u,v) * D(u,v)
-- Status will return 0 if OK else it will return the pivot index
-- of the matrix that was inverted to compute the multiplied
-- BSpline : the method used is interpolation at Schoenenberg
-- points of a(u,v)*F(u,v)
-- --
--
end BSplSLib;
View Git Blame Copy Permalink