liboce-foundation-dev 0.17.1-1 / usr / include / oce / BSplSLib.hxx

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#ifndef _BSplSLib_HeaderFile
#define _BSplSLib_HeaderFile

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

#include <Standard_Integer.hxx>
#include <Standard_Real.hxx>
#include <Standard_Boolean.hxx>
#include <BSplSLib_EvaluatorFunction.hxx>
class TColgp_Array2OfPnt;
class TColStd_Array2OfReal;
class TColStd_Array1OfReal;
class TColStd_Array1OfInteger;
class gp_Pnt;
class gp_Vec;
class TColgp_Array1OfPnt;


//! 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
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 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