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occt/src/BSplSLib/BSplSLib.hxx
akz 0e14656b30 0026042: OCCT won't work with the latest Xcode 
Dereferenced null pointers was eliminated for PLib, BSplCLib and BSplSLib. All affected code was changed accordingly.
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// 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.
#ifndef _BSplSLib_HeaderFile
#define _BSplSLib_HeaderFile
#include <Standard.hxx>
#include <Standard_DefineAlloc.hxx>
#include <Standard_Handle.hxx>
#include <Standard_Integer.hxx>
#include <Standard_Real.hxx>
#include <Standard_Boolean.hxx>
#include <TColgp_Array2OfPnt.hxx>
#include <TColStd_Array2OfReal.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_Array1OfInteger.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <BSplSLib_EvaluatorFunction.hxx>
class gp_Pnt;
class gp_Vec;
//! 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.
//!
//! Note: weight and multiplicity arrays can be passed by pointer for
//! some functions so that NULL pointer is valid.
//! That means no weights/no multiplicities passed.
//!
//! 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
class BSplSLib
{
public:
DEFINE_STANDARD_ALLOC
//! 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
//! 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.
Standard_EXPORT static void RationalDerivative (const Standard_Integer UDeg, const Standard_Integer VDeg, const Standard_Integer N, const Standard_Integer M, Standard_Real& Ders, Standard_Real& RDers, const Standard_Boolean All = Standard_True);
Standard_EXPORT static void D0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt& P);
Standard_EXPORT static void D1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const Standard_Integer Degree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
Standard_EXPORT static void D2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
Standard_EXPORT static void D3 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
Standard_EXPORT static void DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Vec& Vn);
//! Computes the poles and weights of an isoparametric
//! curve at parameter <Param> (UIso if <IsU> is True,
//! VIso else).
Standard_EXPORT static void Iso (const Standard_Real Param, const Standard_Boolean IsU, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger* Mults, const Standard_Integer Degree, const Standard_Boolean Periodic, TColgp_Array1OfPnt& CPoles, TColStd_Array1OfReal* CWeights);
//! 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)
Standard_EXPORT static void Reverse (TColgp_Array2OfPnt& Poles, const Standard_Integer Last, const Standard_Boolean UDirection);
//! 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
Standard_EXPORT static void HomogeneousD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, Standard_Real& W, gp_Pnt& P);
//! 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
Standard_EXPORT static void HomogeneousD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt& N, gp_Vec& Nu, gp_Vec& Nv, Standard_Real& D, Standard_Real& Du, Standard_Real& Dv);
//! Reverses the array of weights.
Standard_EXPORT static void Reverse (TColStd_Array2OfReal& Weights, const Standard_Integer Last, const Standard_Boolean UDirection);
//! 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.
Standard_EXPORT static Standard_Boolean IsRational (const TColStd_Array2OfReal& Weights, const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer J1, const Standard_Integer J2, const Standard_Real Epsilon = 0.0);
//! Copy in FP the coordinates of the poles.
Standard_EXPORT static void SetPoles (const TColgp_Array2OfPnt& Poles, TColStd_Array1OfReal& FP, const Standard_Boolean UDirection);
//! Copy in FP the coordinates of the poles.
Standard_EXPORT static void SetPoles (const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal& Weights, TColStd_Array1OfReal& FP, const Standard_Boolean UDirection);
//! Get from FP the coordinates of the poles.
Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array2OfPnt& Poles, const Standard_Boolean UDirection);
//! Get from FP the coordinates of the poles.
Standard_EXPORT static void GetPoles (const TColStd_Array1OfReal& FP, TColgp_Array2OfPnt& Poles, TColStd_Array2OfReal& Weights, const Standard_Boolean UDirection);
//! 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
Standard_EXPORT static void MovePoint (const Standard_Real U, const Standard_Real V, const gp_Vec& Displ, const Standard_Integer UIndex1, const Standard_Integer UIndex2, const Standard_Integer VIndex1, const Standard_Integer VIndex2, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean Rational, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal& Weights, const TColStd_Array1OfReal& UFlatKnots, const TColStd_Array1OfReal& VFlatKnots, Standard_Integer& UFirstIndex, Standard_Integer& ULastIndex, Standard_Integer& VFirstIndex, Standard_Integer& VLastIndex, TColgp_Array2OfPnt& NewPoles);
Standard_EXPORT static void InsertKnots (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Mults, const TColStd_Array1OfReal& AddKnots, const TColStd_Array1OfInteger* AddMults, TColgp_Array2OfPnt& NewPoles, TColStd_Array2OfReal* NewWeights, TColStd_Array1OfReal& NewKnots, TColStd_Array1OfInteger& NewMults, const Standard_Real Epsilon, const Standard_Boolean Add = Standard_True);
Standard_EXPORT static Standard_Boolean RemoveKnot (const Standard_Boolean UDirection, const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Mults, TColgp_Array2OfPnt& NewPoles, TColStd_Array2OfReal* NewWeights, TColStd_Array1OfReal& NewKnots, TColStd_Array1OfInteger& NewMults, const Standard_Real Tolerance);
Standard_EXPORT static void IncreaseDegree (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Mults, TColgp_Array2OfPnt& NewPoles, TColStd_Array2OfReal* NewWeights, TColStd_Array1OfReal& NewKnots, TColStd_Array1OfInteger& NewMults);
Standard_EXPORT static void Unperiodize (const Standard_Boolean UDirection, const Standard_Integer Degree, const TColStd_Array1OfInteger& Mults, const TColStd_Array1OfReal& Knots, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, TColStd_Array1OfInteger& NewMults, TColStd_Array1OfReal& NewKnots, TColgp_Array2OfPnt& NewPoles, TColStd_Array2OfReal* NewWeights);
//! Used as argument for a non rational curve.
static TColStd_Array2OfReal* NoWeights();
//! 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
Standard_EXPORT static void BuildCache (const Standard_Real U, const Standard_Real V, const Standard_Real USpanDomain, const Standard_Real VSpanDomain, const Standard_Boolean UPeriodicFlag, const Standard_Boolean VPeriodicFlag, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColStd_Array1OfReal& UFlatKnots, const TColStd_Array1OfReal& VFlatKnots, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, TColgp_Array2OfPnt& CachePoles, TColStd_Array2OfReal* CacheWeights);
//! Perform the evaluation of the Taylor expansion
//! of the Bspline normalized between 0 and 1.
//! Structure of result optimized for BSplSLib_Cache.
Standard_EXPORT static void BuildCache (const Standard_Real theU, const Standard_Real theV, const Standard_Real theUSpanDomain, const Standard_Real theVSpanDomain, const Standard_Boolean theUPeriodic, const Standard_Boolean theVPeriodic, const Standard_Integer theUDegree, const Standard_Integer theVDegree, const Standard_Integer theUIndex, const Standard_Integer theVIndex, const TColStd_Array1OfReal& theUFlatKnots, const TColStd_Array1OfReal& theVFlatKnots, const TColgp_Array2OfPnt& thePoles, const TColStd_Array2OfReal* theWeights, TColStd_Array2OfReal& theCacheArray);
//! 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
Standard_EXPORT static void CacheD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, gp_Pnt& Point);
//! Calls CacheD0 for Bezier Surfaces Arrays computed with
//! the method PolesCoefficients.
//! Warning: To be used for BezierSurfaces ONLY!!!
static void CoefsD0 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, gp_Pnt& Point);
//! 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
Standard_EXPORT static void CacheD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, gp_Pnt& Point, gp_Vec& VecU, gp_Vec& VecV);
//! Calls CacheD0 for Bezier Surfaces Arrays computed with
//! the method PolesCoefficients.
//! Warning: To be used for BezierSurfaces ONLY!!!
static void CoefsD1 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, gp_Pnt& Point, gp_Vec& VecU, gp_Vec& VecV);
//! 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
Standard_EXPORT static void CacheD2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, gp_Pnt& Point, gp_Vec& VecU, gp_Vec& VecV, gp_Vec& VecUU, gp_Vec& VecUV, gp_Vec& VecVV);
//! Calls CacheD0 for Bezier Surfaces Arrays computed with
//! the method PolesCoefficients.
//! Warning: To be used for BezierSurfaces ONLY!!!
static void CoefsD2 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, gp_Pnt& Point, gp_Vec& VecU, gp_Vec& VecV, gp_Vec& VecUU, gp_Vec& VecUV, gp_Vec& VecVV);
//! Warning! To be used for BezierSurfaces ONLY!!!
static void PolesCoefficients (const TColgp_Array2OfPnt& Poles, TColgp_Array2OfPnt& CachePoles);
//! Encapsulation of BuildCache to perform the
//! evaluation of the Taylor expansion for beziersurfaces
//! at parameters 0.,0.;
//! Warning: To be used for BezierSurfaces ONLY!!!
Standard_EXPORT static void PolesCoefficients (const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, TColgp_Array2OfPnt& CachePoles, TColStd_Array2OfReal* CacheWeights);
//! 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
Standard_EXPORT static void Resolution (const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger& UMults, const TColStd_Array1OfInteger& VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, const Standard_Real Tolerance3D, Standard_Real& UTolerance, Standard_Real& VTolerance);
//! 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
Standard_EXPORT static void Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal& UFlatKnots, const TColStd_Array1OfReal& VFlatKnots, const TColStd_Array1OfReal& UParameters, const TColStd_Array1OfReal& VParameters, TColgp_Array2OfPnt& Poles, TColStd_Array2OfReal& Weights, Standard_Integer& InversionProblem);
//! 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
Standard_EXPORT static void Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal& UFlatKnots, const TColStd_Array1OfReal& VFlatKnots, const TColStd_Array1OfReal& UParameters, const TColStd_Array1OfReal& VParameters, TColgp_Array2OfPnt& Poles, Standard_Integer& InversionProblem);
//! 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)
//! --
Standard_EXPORT static void FunctionMultiply (const BSplSLib_EvaluatorFunction& Function, const Standard_Integer UBSplineDegree, const Standard_Integer VBSplineDegree, const TColStd_Array1OfReal& UBSplineKnots, const TColStd_Array1OfReal& VBSplineKnots, const TColStd_Array1OfInteger* UMults, const TColStd_Array1OfInteger* VMults, const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal* Weights, const TColStd_Array1OfReal& UFlatKnots, const TColStd_Array1OfReal& VFlatKnots, const Standard_Integer UNewDegree, const Standard_Integer VNewDegree, TColgp_Array2OfPnt& NewNumerator, TColStd_Array2OfReal& NewDenominator, Standard_Integer& Status);
protected:
private:
};
#include <BSplSLib.lxx>
#endif // _BSplSLib_HeaderFile
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