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// Please do not edit this file; modify original file instead.
// The copyright and license terms as defined for the original file apply to
// this header file considered to be the "object code" form of the original source.
#ifndef _BSplCLib_HeaderFile
#define _BSplCLib_HeaderFile
#ifndef _Standard_HeaderFile
#include <Standard.hxx>
#endif
#ifndef _Standard_DefineAlloc_HeaderFile
#include <Standard_DefineAlloc.hxx>
#endif
#ifndef _Standard_Macro_HeaderFile
#include <Standard_Macro.hxx>
#endif
#ifndef _Standard_Real_HeaderFile
#include <Standard_Real.hxx>
#endif
#ifndef _Standard_Integer_HeaderFile
#include <Standard_Integer.hxx>
#endif
#ifndef _Standard_Boolean_HeaderFile
#include <Standard_Boolean.hxx>
#endif
#ifndef _BSplCLib_KnotDistribution_HeaderFile
#include <BSplCLib_KnotDistribution.hxx>
#endif
#ifndef _BSplCLib_MultDistribution_HeaderFile
#include <BSplCLib_MultDistribution.hxx>
#endif
#ifndef _GeomAbs_BSplKnotDistribution_HeaderFile
#include <GeomAbs_BSplKnotDistribution.hxx>
#endif
#ifndef _Handle_TColStd_HArray1OfReal_HeaderFile
#include <Handle_TColStd_HArray1OfReal.hxx>
#endif
#ifndef _Handle_TColStd_HArray1OfInteger_HeaderFile
#include <Handle_TColStd_HArray1OfInteger.hxx>
#endif
#ifndef _BSplCLib_EvaluatorFunction_HeaderFile
#include <BSplCLib_EvaluatorFunction.hxx>
#endif
class TColStd_Array1OfReal;
class TColStd_Array1OfInteger;
class TColgp_Array1OfPnt;
class TColgp_Array1OfPnt2d;
class gp_Pnt;
class gp_Pnt2d;
class gp_Vec;
class gp_Vec2d;
class math_Matrix;
class TColStd_HArray1OfReal;
class TColStd_HArray1OfInteger;
//! BSplCLib B-spline curve Library. <br>
//! <br>
//! The BSplCLib package is a basic library for BSplines. It <br>
//! provides three categories of functions. <br>
//! <br>
//! * Management methods to process knots and multiplicities. <br>
//! <br>
//! * Multi-Dimensions spline methods. BSpline methods where <br>
//! poles have an arbitrary number of dimensions. They divides <br>
//! in two groups : <br>
//! <br>
//! - Global methods modifying the whole set of poles. The <br>
//! poles are described by an array of Reals and a <br>
//! Dimension. Example : Inserting knots. <br>
//! <br>
//! - Local methods computing points and derivatives. The <br>
//! poles are described by a pointer on a local array of <br>
//! Reals and a Dimension. The local array is modified. <br>
//! <br>
//! * 2D and 3D spline curves methods. <br>
//! <br>
//! Methods for 2d and 3d BSplines curves rational or not <br>
//! rational. <br>
//! <br>
//! Those methods have the following structure : <br>
//! <br>
//! - They extract the pole informations in a working array. <br>
//! <br>
//! - They process the working array with the <br>
//! multi-dimension methods. (for example a 3d rational <br>
//! curve is processed as a 4 dimension curve). <br>
//! <br>
//! - They get back the result in the original dimension. <br>
//! <br>
//! Note that the bspline surface methods found in the <br>
//! package BSplSLib uses the same structure and rely on <br>
//! BSplCLib. <br>
//! <br>
//! In the following list of methods the 2d and 3d curve <br>
//! methods will be described with the corresponding <br>
//! multi-dimension method. <br>
//! <br>
//! The 3d or 2d B-spline curve is defined with : <br>
//! <br>
//! . its control points : TColgp_Array1OfPnt(2d) Poles <br>
//! . its weights : TColStd_Array1OfReal Weights <br>
//! . its knots : TColStd_Array1OfReal Knots <br>
//! . its multiplicities : TColStd_Array1OfInteger Mults <br>
//! . its degree : Standard_Integer Degree <br>
//! . its periodicity : Standard_Boolean Periodic <br>
//! <br>
//! Warnings : <br>
//! The bounds of Poles and Weights should be the same. <br>
//! The bounds of Knots and Mults should be the same. <br>
//! <br>
//! Weights can be a null reference (BSplCLib::NoWeights()) <br>
//! the curve is non rational. <br>
//! <br>
//! Mults can be a null reference (BSplCLib::NoMults()) <br>
//! the knots are "flat" knots. <br>
//! <br>
//! KeyWords : <br>
//! B-spline curve, Functions, Library <br>
//! <br>
//! References : <br>
//! . A survey of curves and surfaces methods in CADG Wolfgang <br>
//! BOHM CAGD 1 (1984) <br>
//! . On de Boor-like algorithms and blossoming Wolfgang BOEHM <br>
//! cagd 5 (1988) <br>
//! . Blossoming and knot insertion algorithms for B-spline curves <br>
//! Ronald N. GOLDMAN <br>
//! . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA <br>
//! . Curves and Surfaces for Computer Aided Geometric Design, <br>
//! a practical guide Gerald Farin <br>
class BSplCLib {
public:
DEFINE_STANDARD_ALLOC
//! This routine searches the position of the real <br>
//! value X in the ordered set of real values XX. <br>
//! <br>
//! The elements in the table XX are either <br>
//! monotonically increasing or monotonically <br>
//! decreasing. <br>
//! <br>
//! The input value Iloc is used to initialize the <br>
//! algorithm : if Iloc is outside of the bounds <br>
//! [XX.Lower(), -- XX.Upper()] the bisection algorithm <br>
//! is used else the routine searches from a previous <br>
//! known position by increasing steps then converges <br>
//! by bisection. <br>
//! <br>
//! This routine is used to locate a knot value in a <br>
//! set of knots. <br>
//! <br>
Standard_EXPORT static void Hunt(const TColStd_Array1OfReal& XX,const Standard_Real X,Standard_Integer& Iloc) ;
//! Computes the index of the knots value which gives <br>
//! the start point of the curve. <br>
Standard_EXPORT static Standard_Integer FirstUKnotIndex(const Standard_Integer Degree,const TColStd_Array1OfInteger& Mults) ;
//! Computes the index of the knots value which gives <br>
//! the end point of the curve. <br>
Standard_EXPORT static Standard_Integer LastUKnotIndex(const Standard_Integer Degree,const TColStd_Array1OfInteger& Mults) ;
//! Computes the index of the flats knots sequence <br>
//! corresponding to <Index> in the knots sequence <br>
//! which multiplicities are <Mults>. <br>
Standard_EXPORT static Standard_Integer FlatIndex(const Standard_Integer Degree,const Standard_Integer Index,const TColStd_Array1OfInteger& Mults,const Standard_Boolean Periodic) ;
//! Locates the parametric value U in the knots <br>
//! sequence between the knot K1 and the knot K2. <br>
//! The value return in Index verifies. <br>
//! <br>
//! Knots(Index) <= U < Knots(Index + 1) <br>
//! if U <= Knots (K1) then Index = K1 <br>
//! if U >= Knots (K2) then Index = K2 - 1 <br>
//! <br>
//! If Periodic is True U may be modified to fit in <br>
//! the range Knots(K1), Knots(K2). In any case the <br>
//! correct value is returned in NewU. <br>
//! <br>
//! Warnings :Index is used as input data to initialize the <br>
//! searching function. <br>
//! Warning: Knots have to be "withe repetitions" <br>
Standard_EXPORT static void LocateParameter(const Standard_Integer Degree,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const Standard_Real U,const Standard_Boolean IsPeriodic,const Standard_Integer FromK1,const Standard_Integer ToK2,Standard_Integer& KnotIndex,Standard_Real& NewU) ;
//! Locates the parametric value U in the knots <br>
//! sequence between the knot K1 and the knot K2. <br>
//! The value return in Index verifies. <br>
//! <br>
//! Knots(Index) <= U < Knots(Index + 1) <br>
//! if U <= Knots (K1) then Index = K1 <br>
//! if U >= Knots (K2) then Index = K2 - 1 <br>
//! <br>
//! If Periodic is True U may be modified to fit in <br>
//! the range Knots(K1), Knots(K2). In any case the <br>
//! correct value is returned in NewU. <br>
//! <br>
//! Warnings :Index is used as input data to initialize the <br>
//! searching function. <br>
//! Warning: Knots have to be "flat" <br>
Standard_EXPORT static void LocateParameter(const Standard_Integer Degree,const TColStd_Array1OfReal& Knots,const Standard_Real U,const Standard_Boolean IsPeriodic,const Standard_Integer FromK1,const Standard_Integer ToK2,Standard_Integer& KnotIndex,Standard_Real& NewU) ;
Standard_EXPORT static void LocateParameter(const Standard_Integer Degree,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const Standard_Real U,const Standard_Boolean Periodic,Standard_Integer& Index,Standard_Real& NewU) ;
//! Finds the greatest multiplicity in a set of knots <br>
//! between K1 and K2. Mults is the multiplicity <br>
//! associated with each knot value. <br>
Standard_EXPORT static Standard_Integer MaxKnotMult(const TColStd_Array1OfInteger& Mults,const Standard_Integer K1,const Standard_Integer K2) ;
//! Finds the lowest multiplicity in a set of knots <br>
//! between K1 and K2. Mults is the multiplicity <br>
//! associated with each knot value. <br>
Standard_EXPORT static Standard_Integer MinKnotMult(const TColStd_Array1OfInteger& Mults,const Standard_Integer K1,const Standard_Integer K2) ;
//! Returns the number of poles of the curve. Returns 0 if <br>
//! one of the multiplicities is incorrect. <br>
//! <br>
//! * Non positive. <br>
//! <br>
//! * Greater than Degree, or Degree+1 at the first and <br>
//! last knot of a non periodic curve. <br>
//! <br>
//! * The last periodicity on a periodic curve is not <br>
//! equal to the first. <br>
Standard_EXPORT static Standard_Integer NbPoles(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfInteger& Mults) ;
//! Returns the length of the sequence of knots with <br>
//! repetition. <br>
//! <br>
//! Periodic : <br>
//! <br>
//! Sum(Mults(i), i = Mults.Lower(); i <= Mults.Upper()); <br>
//! <br>
//! Non Periodic : <br>
//! <br>
//! Sum(Mults(i); i = Mults.Lower(); i < Mults.Upper()) <br>
//! + 2 * Degree <br>
Standard_EXPORT static Standard_Integer KnotSequenceLength(const TColStd_Array1OfInteger& Mults,const Standard_Integer Degree,const Standard_Boolean Periodic) ;
Standard_EXPORT static void KnotSequence(const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColStd_Array1OfReal& KnotSeq) ;
//! Computes the sequence of knots KnotSeq with <br>
//! repetition of the knots of multiplicity greater <br>
//! than 1. <br>
//! <br>
//! Length of KnotSeq must be KnotSequenceLength(Mults,Degree,Periodic) <br>
Standard_EXPORT static void KnotSequence(const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const Standard_Integer Degree,const Standard_Boolean Periodic,TColStd_Array1OfReal& KnotSeq) ;
//! Returns the length of the sequence of knots (and <br>
//! Mults) without repetition. <br>
Standard_EXPORT static Standard_Integer KnotsLength(const TColStd_Array1OfReal& KnotSeq,const Standard_Boolean Periodic = Standard_False) ;
//! Computes the sequence of knots Knots without <br>
//! repetition of the knots of multiplicity greater <br>
//! than 1. <br>
//! <br>
//! Length of <Knots> and <Mults> must be <br>
//! KnotsLength(KnotSequence,Periodic) <br>
Standard_EXPORT static void Knots(const TColStd_Array1OfReal& KnotSeq,TColStd_Array1OfReal& Knots,TColStd_Array1OfInteger& Mults,const Standard_Boolean Periodic = Standard_False) ;
//! Analyses if the knots distribution is "Uniform" <br>
//! or "NonUniform" between the knot FromK1 and the <br>
//! knot ToK2. There is no repetition of knot in the <br>
//! knots'sequence <Knots>. <br>
Standard_EXPORT static BSplCLib_KnotDistribution KnotForm(const TColStd_Array1OfReal& Knots,const Standard_Integer FromK1,const Standard_Integer ToK2) ;
//! Analyses the distribution of multiplicities between <br>
//! the knot FromK1 and the Knot ToK2. <br>
Standard_EXPORT static BSplCLib_MultDistribution MultForm(const TColStd_Array1OfInteger& Mults,const Standard_Integer FromK1,const Standard_Integer ToK2) ;
//! Analyzes the array of knots. <br>
//! Returns the form and the maximum knot multiplicity. <br>
Standard_EXPORT static void KnotAnalysis(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& CKnots,const TColStd_Array1OfInteger& CMults,GeomAbs_BSplKnotDistribution& KnotForm,Standard_Integer& MaxKnotMult) ;
//! Reparametrizes a B-spline curve to [U1, U2]. <br>
//! The knot values are recomputed such that Knots (Lower) = U1 <br>
//! and Knots (Upper) = U2 but the knot form is not modified. <br>
//! Warnings : <br>
//! In the array Knots the values must be in ascending order. <br>
//! U1 must not be equal to U2 to avoid division by zero. <br>
Standard_EXPORT static void Reparametrize(const Standard_Real U1,const Standard_Real U2,TColStd_Array1OfReal& Knots) ;
//! Reverses the array knots to become the knots <br>
//! sequence of the reversed curve. <br>
Standard_EXPORT static void Reverse(TColStd_Array1OfReal& Knots) ;
//! Reverses the array of multiplicities. <br>
Standard_EXPORT static void Reverse(TColStd_Array1OfInteger& Mults) ;
//! Reverses the array of poles. Last is the index of <br>
//! the new first pole. On a non periodic curve last <br>
//! is Poles.Upper(). On a periodic curve last is <br>
//! <br>
//! (number of flat knots - degree - 1) <br>
//! <br>
//! or <br>
//! <br>
//! (sum of multiplicities(but for the last) + degree <br>
//! - 1) <br>
Standard_EXPORT static void Reverse(TColgp_Array1OfPnt& Poles,const Standard_Integer Last) ;
//! Reverses the array of poles. <br>
Standard_EXPORT static void Reverse(TColgp_Array1OfPnt2d& Poles,const Standard_Integer Last) ;
//! Reverses the array of poles. <br>
Standard_EXPORT static void Reverse(TColStd_Array1OfReal& Weights,const Standard_Integer Last) ;
//! Returns False if all the weights of the array <Weights> <br>
//! between I1 an I2 are identic. Epsilon is used for <br>
//! comparing weights. If Epsilon is 0. the Epsilon of the <br>
//! first weight is used. <br>
Standard_EXPORT static Standard_Boolean IsRational(const TColStd_Array1OfReal& Weights,const Standard_Integer I1,const Standard_Integer I2,const Standard_Real Epsilon = 0.0) ;
//! returns the degree maxima for a BSplineCurve. <br>
static Standard_Integer MaxDegree() ;
//! Perform the Boor algorithm to evaluate a point at <br>
//! parameter <U>, with <Degree> and <Dimension>. <br>
//! <br>
//! Poles is an array of Reals of size <br>
//! <br>
//! <Dimension> * <Degree>+1 <br>
//! <br>
//! Containing the poles. At the end <Poles> contains <br>
//! the current point. <br>
Standard_EXPORT static void Eval(const Standard_Real U,const Standard_Integer Degree,Standard_Real& Knots,const Standard_Integer Dimension,Standard_Real& Poles) ;
//! Performs the Boor Algorithm at parameter <U> with <br>
//! the given <Degree> and the array of <Knots> on the <br>
//! poles <Poles> of dimension <Dimension>. The schema <br>
//! is computed until level <Depth> on a basis of <br>
//! <Length+1> poles. <br>
//! <br>
//! * Knots is an array of reals of length : <br>
//! <br>
//! <Length> + <Degree> <br>
//! <br>
//! * Poles is an array of reals of length : <br>
//! <br>
//! (2 * <Length> + 1) * <Dimension> <br>
//! <br>
//! The poles values must be set in the array at the <br>
//! positions. <br>
//! <br>
//! 0..Dimension, <br>
//! <br>
//! 2 * Dimension .. <br>
//! 3 * Dimension <br>
//! <br>
//! 4 * Dimension .. <br>
//! 5 * Dimension <br>
//! <br>
//! ... <br>
//! <br>
//! The results are found in the array poles depending <br>
//! on the Depth. (See the method GetPole). <br>
Standard_EXPORT static void BoorScheme(const Standard_Real U,const Standard_Integer Degree,Standard_Real& Knots,const Standard_Integer Dimension,Standard_Real& Poles,const Standard_Integer Depth,const Standard_Integer Length) ;
//! Compute the content of Pole before the BoorScheme. <br>
//! This method is used to remove poles. <br>
//! <br>
//! U is the poles to remove, Knots should contains the <br>
//! knots of the curve after knot removal. <br>
//! <br>
//! The first and last poles do not change, the other <br>
//! poles are computed by averaging two possible values. <br>
//! The distance between the two possible poles is <br>
//! computed, if it is higher than <Tolerance> False is <br>
//! returned. <br>
Standard_EXPORT static Standard_Boolean AntiBoorScheme(const Standard_Real U,const Standard_Integer Degree,Standard_Real& Knots,const Standard_Integer Dimension,Standard_Real& Poles,const Standard_Integer Depth,const Standard_Integer Length,const Standard_Real Tolerance) ;
//! Computes the poles of the BSpline giving the <br>
//! derivatives of order <Order>. <br>
//! <br>
//! The formula for the first order is <br>
//! <br>
//! Pole(i) = Degree * (Pole(i+1) - Pole(i)) / <br>
//! (Knots(i+Degree+1) - Knots(i+1)) <br>
//! <br>
//! This formula is repeated (Degree is decremented at <br>
//! each step). <br>
Standard_EXPORT static void Derivative(const Standard_Integer Degree,Standard_Real& Knots,const Standard_Integer Dimension,const Standard_Integer Length,const Standard_Integer Order,Standard_Real& Poles) ;
//! Performs the Bohm Algorithm at parameter <U>. This <br>
//! algorithm computes the value and all the derivatives <br>
//! up to order N (N <= Degree). <br>
//! <br>
//! <Poles> is the original array of poles. <br>
//! <br>
//! The result in <Poles> is the value and the <br>
//! derivatives. Poles[0] is the value, Poles[Degree] <br>
//! is the last derivative. <br>
Standard_EXPORT static void Bohm(const Standard_Real U,const Standard_Integer Degree,const Standard_Integer N,Standard_Real& Knots,const Standard_Integer Dimension,Standard_Real& Poles) ;
//! Used as argument for a non rational curve. <br>
//! <br>
static TColStd_Array1OfReal& NoWeights() ;
//! Used as argument for a flatknots evaluation. <br>
//! <br>
static TColStd_Array1OfInteger& NoMults() ;
//! Stores in LK the usefull knots for the BoorSchem <br>
//! on the span Knots(Index) - Knots(Index+1) <br>
Standard_EXPORT static void BuildKnots(const Standard_Integer Degree,const Standard_Integer Index,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,Standard_Real& LK) ;
//! Return the index of the first Pole to use on the <br>
//! span Mults(Index) - Mults(Index+1). This index <br>
//! must be added to Poles.Lower(). <br>
Standard_EXPORT static Standard_Integer PoleIndex(const Standard_Integer Degree,const Standard_Integer Index,const Standard_Boolean Periodic,const TColStd_Array1OfInteger& Mults) ;
Standard_EXPORT static void BuildEval(const Standard_Integer Degree,const Standard_Integer Index,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Weights,Standard_Real& LP) ;
Standard_EXPORT static void BuildEval(const Standard_Integer Degree,const Standard_Integer Index,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,Standard_Real& LP) ;
//! Copy in <LP> the poles and weights for the Eval <br>
//! scheme. starting from Poles(Poles.Lower()+Index) <br>
Standard_EXPORT static void BuildEval(const Standard_Integer Degree,const Standard_Integer Index,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,Standard_Real& LP) ;
//! Copy in <LP> poles for <Dimension> Boor scheme. <br>
//! Starting from <Index> * <Dimension>, copy <br>
//! <Length+1> poles. <br>
Standard_EXPORT static void BuildBoor(const Standard_Integer Index,const Standard_Integer Length,const Standard_Integer Dimension,const TColStd_Array1OfReal& Poles,Standard_Real& LP) ;
//! Returns the index in the Boor result array of the <br>
//! poles <Index>. If the Boor algorithm was perform <br>
//! with <Length> and <Depth>. <br>
Standard_EXPORT static Standard_Integer BoorIndex(const Standard_Integer Index,const Standard_Integer Length,const Standard_Integer Depth) ;
//! Copy the pole at position <Index> in the Boor <br>
//! scheme of dimension <Dimension> to <Position> in <br>
//! the array <Pole>. <Position> is updated. <br>
Standard_EXPORT static void GetPole(const Standard_Integer Index,const Standard_Integer Length,const Standard_Integer Depth,const Standard_Integer Dimension,Standard_Real& LocPoles,Standard_Integer& Position,TColStd_Array1OfReal& Pole) ;
//! Returns in <NbPoles, NbKnots> the new number of poles <br>
//! and knots if the sequence of knots <AddKnots, <br>
//! AddMults> is inserted in the sequence <Knots, Mults>. <br>
//! <br>
//! Epsilon is used to compare knots for equality. <br>
//! <br>
//! If Add is True the multiplicities on equal knots are <br>
//! added. <br>
//! <br>
//! If Add is False the max value of the multiplicities is <br>
//! kept. <br>
//! <br>
//! Return False if : <br>
//! The knew knots are knot increasing. <br>
//! The new knots are not in the range. <br>
Standard_EXPORT static Standard_Boolean PrepareInsertKnots(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& AddKnots,const TColStd_Array1OfInteger& AddMults,Standard_Integer& NbPoles,Standard_Integer& NbKnots,const Standard_Real Epsilon,const Standard_Boolean Add = Standard_True) ;
Standard_EXPORT static void InsertKnots(const Standard_Integer Degree,const Standard_Boolean Periodic,const Standard_Integer Dimension,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& AddKnots,const TColStd_Array1OfInteger& AddMults,TColStd_Array1OfReal& NewPoles,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,const Standard_Real Epsilon,const Standard_Boolean Add = Standard_True) ;
Standard_EXPORT static void InsertKnots(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& AddKnots,const TColStd_Array1OfInteger& AddMults,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,const Standard_Real Epsilon,const Standard_Boolean Add = Standard_True) ;
//! Insert a sequence of knots <AddKnots> with <br>
//! multiplicities <AddMults>. <AddKnots> must be a non <br>
//! decreasing sequence and verifies : <br>
//! <br>
//! Knots(Knots.Lower()) <= AddKnots(AddKnots.Lower()) <br>
//! Knots(Knots.Upper()) >= AddKnots(AddKnots.Upper()) <br>
//! <br>
//! The NewPoles and NewWeights arrays must have a length : <br>
//! Poles.Length() + Sum(AddMults()) <br>
//! <br>
//! When a knot to insert is identic to an existing knot the <br>
//! multiplicities are added. <br>
//! <br>
//! Epsilon is used to test knots for equality. <br>
//! <br>
//! When AddMult is negative or null the knot is not inserted. <br>
//! No multiplicity will becomes higher than the degree. <br>
//! <br>
//! The new Knots and Multiplicities are copied in <NewKnots> <br>
//! and <NewMults>. <br>
//! <br>
//! All the New arrays should be correctly dimensioned. <br>
//! <br>
//! When all the new knots are existing knots, i.e. only the <br>
//! multiplicities will change it is safe to use the same <br>
//! arrays as input and output. <br>
Standard_EXPORT static void InsertKnots(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& AddKnots,const TColStd_Array1OfInteger& AddMults,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,const Standard_Real Epsilon,const Standard_Boolean Add = Standard_True) ;
Standard_EXPORT static void InsertKnot(const Standard_Integer UIndex,const Standard_Real U,const Standard_Integer UMult,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights) ;
//! Insert a new knot U of multiplicity UMult in the <br>
//! knot sequence. <br>
//! <br>
//! The location of the new Knot should be given as an input <br>
//! data. UIndex locates the new knot U in the knot sequence <br>
//! and Knots (UIndex) < U < Knots (UIndex + 1). <br>
//! <br>
//! The new control points corresponding to this insertion are <br>
//! returned. Knots and Mults are not updated. <br>
Standard_EXPORT static void InsertKnot(const Standard_Integer UIndex,const Standard_Real U,const Standard_Integer UMult,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights) ;
Standard_EXPORT static void RaiseMultiplicity(const Standard_Integer KnotIndex,const Standard_Integer Mult,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights) ;
//! Raise the multiplicity of knot to <UMult>. <br>
//! <br>
//! The new control points are returned. Knots and Mults are <br>
//! not updated. <br>
Standard_EXPORT static void RaiseMultiplicity(const Standard_Integer KnotIndex,const Standard_Integer Mult,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights) ;
Standard_EXPORT static Standard_Boolean RemoveKnot(const Standard_Integer Index,const Standard_Integer Mult,const Standard_Integer Degree,const Standard_Boolean Periodic,const Standard_Integer Dimension,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColStd_Array1OfReal& NewPoles,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,const Standard_Real Tolerance) ;
Standard_EXPORT static Standard_Boolean RemoveKnot(const Standard_Integer Index,const Standard_Integer Mult,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,const Standard_Real Tolerance) ;
//! Decrement the multiplicity of <Knots(Index)> <br>
//! to <Mult>. If <Mult> is null the knot is <br>
//! removed. <br>
//! <br>
//! As there are two ways to compute the new poles <br>
//! the midlle will be used as long as the <br>
//! distance is lower than Tolerance. <br>
//! <br>
//! If a distance is bigger than tolerance the <br>
//! methods returns False and the new arrays are <br>
//! not modified. <br>
//! <br>
//! A low tolerance can be used to test if the <br>
//! knot can be removed without modifying the <br>
//! curve. <br>
//! <br>
//! A high tolerance can be used to "smooth" the <br>
//! curve. <br>
Standard_EXPORT static Standard_Boolean RemoveKnot(const Standard_Integer Index,const Standard_Integer Mult,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,const Standard_Real Tolerance) ;
//! Returns the number of knots of a curve with <br>
//! multiplicities <Mults> after elevating the degree from <br>
//! <Degree> to <NewDegree>. See the IncreaseDegree method <br>
//! for more comments. <br>
Standard_EXPORT static Standard_Integer IncreaseDegreeCountKnots(const Standard_Integer Degree,const Standard_Integer NewDegree,const Standard_Boolean Periodic,const TColStd_Array1OfInteger& Mults) ;
Standard_EXPORT static void IncreaseDegree(const Standard_Integer Degree,const Standard_Integer NewDegree,const Standard_Boolean Periodic,const Standard_Integer Dimension,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColStd_Array1OfReal& NewPoles,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults) ;
Standard_EXPORT static void IncreaseDegree(const Standard_Integer Degree,const Standard_Integer NewDegree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults) ;
Standard_EXPORT static void IncreaseDegree(const Standard_Integer Degree,const Standard_Integer NewDegree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults) ;
Standard_EXPORT static void IncreaseDegree(const Standard_Integer NewDegree,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights) ;
//! Increase the degree of a bspline (or bezier) curve <br>
//! of dimension <Dimension> form <Degree> to <br>
//! <NewDegree>. <br>
//! <br>
//! The number of poles in the new curve is : <br>
//! <br>
//! Poles.Length() + (NewDegree - Degree) * Number of spans <br>
//! <br>
//! Where the number of spans is : <br>
//! <br>
//! LastUKnotIndex(Mults) - FirstUKnotIndex(Mults) + 1 <br>
//! <br>
//! for a non-periodic curve <br>
//! <br>
//! And Knots.Length() - 1 for a periodic curve. <br>
//! <br>
//! The multiplicities of all knots are increased by <br>
//! the degree elevation. <br>
//! <br>
//! The new knots are usually the same knots with the <br>
//! exception of a non-periodic curve with the first <br>
//! and last multiplicity not equal to Degree+1 where <br>
//! knots are removed form the start and the bottom <br>
//! untils the sum of the multiplicities is equal to <br>
//! NewDegree+1 at the knots corresponding to the <br>
//! first and last parameters of the curve. <br>
//! <br>
//! Example : Suppose a curve of degree 3 starting <br>
//! with following knots and multiplicities : <br>
//! <br>
//! knot : 0. 1. 2. <br>
//! mult : 1 2 1 <br>
//! <br>
//! The FirstUKnot is 2. because the sum of <br>
//! multiplicities is Degree+1 : 1 + 2 + 1 = 4 = 3 + 1 <br>
//! <br>
//! i.e. the first parameter of the curve is 2. and <br>
//! will still be 2. after degree elevation. Let <br>
//! raises this curve to degree 4. The multiplicities <br>
//! are increased by 2. <br>
//! <br>
//! They become 2 3 2. But we need a sum of <br>
//! multiplicities of 5 at knot 2. So the first knot <br>
//! is removed and the new knots are : <br>
//! <br>
//! knot : 1. 2. <br>
//! mult : 3 2 <br>
//! <br>
//! The multipicity of the first knot may also be <br>
//! reduced if the sum is still to big. <br>
//! <br>
//! In the most common situations (periodic curve or <br>
//! curve with first and last multiplicities equals to <br>
//! Degree+1) the knots are knot changes. <br>
//! <br>
//! The method IncreaseDegreeCountKnots can be used to <br>
//! compute the new number of knots.\ <br>
//! <br>
Standard_EXPORT static void IncreaseDegree(const Standard_Integer NewDegree,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights) ;
//! Set in <NbKnots> and <NbPolesToAdd> the number of Knots and <br>
//! Poles of the NotPeriodic Curve identical at the <br>
//! periodic curve with a degree <Degree> , a <br>
//! knots-distribution with Multiplicities <Mults>. <br>
Standard_EXPORT static void PrepareUnperiodize(const Standard_Integer Degree,const TColStd_Array1OfInteger& Mults,Standard_Integer& NbKnots,Standard_Integer& NbPoles) ;
Standard_EXPORT static void Unperiodize(const Standard_Integer Degree,const Standard_Integer Dimension,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfReal& Poles,TColStd_Array1OfInteger& NewMults,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfReal& NewPoles) ;
Standard_EXPORT static void Unperiodize(const Standard_Integer Degree,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& Knots,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,TColStd_Array1OfInteger& NewMults,TColStd_Array1OfReal& NewKnots,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights) ;
Standard_EXPORT static void Unperiodize(const Standard_Integer Degree,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& Knots,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,TColStd_Array1OfInteger& NewMults,TColStd_Array1OfReal& NewKnots,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights) ;
//! Set in <NbKnots> and <NbPoles> the number of Knots and <br>
//! Poles of the curve resulting of the trimming of the <br>
//! BSplinecurve definded with <degree>, <knots>, <mults> <br>
Standard_EXPORT static void PrepareTrimming(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const Standard_Real U1,const Standard_Real U2,Standard_Integer& NbKnots,Standard_Integer& NbPoles) ;
Standard_EXPORT static void Trimming(const Standard_Integer Degree,const Standard_Boolean Periodic,const Standard_Integer Dimension,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const TColStd_Array1OfReal& Poles,const Standard_Real U1,const Standard_Real U2,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,TColStd_Array1OfReal& NewPoles) ;
Standard_EXPORT static void Trimming(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const Standard_Real U1,const Standard_Real U2,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,TColgp_Array1OfPnt& NewPoles,TColStd_Array1OfReal& NewWeights) ;
Standard_EXPORT static void Trimming(const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const Standard_Real U1,const Standard_Real U2,TColStd_Array1OfReal& NewKnots,TColStd_Array1OfInteger& NewMults,TColgp_Array1OfPnt2d& NewPoles,TColStd_Array1OfReal& NewWeights) ;
Standard_EXPORT static void D0(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,Standard_Real& P) ;
Standard_EXPORT static void D0(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt& P) ;
Standard_EXPORT static void D0(const Standard_Real U,const Standard_Integer UIndex,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt2d& P) ;
Standard_EXPORT static void D0(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& P) ;
Standard_EXPORT static void D0(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& P) ;
Standard_EXPORT static void D1(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,Standard_Real& P,Standard_Real& V) ;
Standard_EXPORT static void D1(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt& P,gp_Vec& V) ;
Standard_EXPORT static void D1(const Standard_Real U,const Standard_Integer UIndex,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt2d& P,gp_Vec2d& V) ;
Standard_EXPORT static void D1(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& P,gp_Vec& V) ;
Standard_EXPORT static void D1(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& P,gp_Vec2d& V) ;
Standard_EXPORT static void D2(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,Standard_Real& P,Standard_Real& V1,Standard_Real& V2) ;
Standard_EXPORT static void D2(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2) ;
Standard_EXPORT static void D2(const Standard_Real U,const Standard_Integer UIndex,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt2d& P,gp_Vec2d& V1,gp_Vec2d& V2) ;
Standard_EXPORT static void D2(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2) ;
Standard_EXPORT static void D2(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& P,gp_Vec2d& V1,gp_Vec2d& V2) ;
Standard_EXPORT static void D3(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,Standard_Real& P,Standard_Real& V1,Standard_Real& V2,Standard_Real& V3) ;
Standard_EXPORT static void D3(const Standard_Real U,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2,gp_Vec& V3) ;
Standard_EXPORT static void D3(const Standard_Real U,const Standard_Integer UIndex,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Pnt2d& P,gp_Vec2d& V1,gp_Vec2d& V2,gp_Vec2d& V3) ;
Standard_EXPORT static void D3(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& P,gp_Vec& V1,gp_Vec& V2,gp_Vec& V3) ;
Standard_EXPORT static void D3(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& P,gp_Vec2d& V1,gp_Vec2d& V2,gp_Vec2d& V3) ;
Standard_EXPORT static void DN(const Standard_Real U,const Standard_Integer N,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,Standard_Real& VN) ;
Standard_EXPORT static void DN(const Standard_Real U,const Standard_Integer N,const Standard_Integer Index,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Vec& VN) ;
Standard_EXPORT static void DN(const Standard_Real U,const Standard_Integer N,const Standard_Integer UIndex,const Standard_Integer Degree,const Standard_Boolean Periodic,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& Knots,const TColStd_Array1OfInteger& Mults,gp_Vec2d& V) ;
Standard_EXPORT static void DN(const Standard_Real U,const Standard_Integer N,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& P,gp_Vec& VN) ;
//! The above functions compute values and <br>
//! derivatives in the following situations : <br>
//! <br>
//! * 3D, 2D and 1D <br>
//! <br>
//! * Rational or not Rational. <br>
//! <br>
//! * Knots and multiplicities or "flat knots" without <br>
//! multiplicities. <br>
//! <br>
//! * The <Index> is the the localization of the <br>
//! parameter in the knot sequence. If <Index> is out <br>
//! of range the correct value will be searched. <br>
//! <br>
//! <br>
//! VERY IMPORTANT!!! <br>
//! USE BSplCLib::NoWeights() as Weights argument for non <br>
//! rational curves computations. <br>
Standard_EXPORT static void DN(const Standard_Real U,const Standard_Integer N,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& P,gp_Vec2d& VN) ;
//! This evaluates the Bspline Basis at a <br>
//! given parameter Parameter up to the <br>
//! requested DerivativeOrder and store the <br>
//! result in the array BsplineBasis in the <br>
//! following fashion <br>
//! BSplineBasis(1,1) = <br>
//! value of first non vanishing <br>
//! Bspline function which has Index FirstNonZeroBsplineIndex <br>
//! BsplineBasis(1,2) = <br>
//! value of second non vanishing <br>
//! Bspline function which has Index <br>
//! FirstNonZeroBsplineIndex + 1 <br>
//! BsplineBasis(1,n) = <br>
//! value of second non vanishing non vanishing <br>
//! Bspline function which has Index <br>
//! FirstNonZeroBsplineIndex + n (n <= Order) <br>
//! BSplineBasis(2,1) = <br>
//! value of derivative of first non vanishing <br>
//! Bspline function which has Index FirstNonZeroBsplineIndex <br>
//! BSplineBasis(N,1) = <br>
//! value of Nth derivative of first non vanishing <br>
//! Bspline function which has Index FirstNonZeroBsplineIndex <br>
//! if N <= DerivativeOrder + 1 <br>
Standard_EXPORT static Standard_Integer EvalBsplineBasis(const Standard_Integer Side,const Standard_Integer DerivativeOrder,const Standard_Integer Order,const TColStd_Array1OfReal& FlatKnots,const Standard_Real Parameter,Standard_Integer& FirstNonZeroBsplineIndex,math_Matrix& BsplineBasis) ;
//! This Builds a fully blown Matrix of <br>
//! (ni) <br>
//! Bi (tj) <br>
//! <br>
//! with i and j within 1..Order + NumPoles <br>
//! The integer ni is the ith slot of the <br>
//! array OrderArray, tj is the jth slot of <br>
//! the array Parameters <br>
Standard_EXPORT static Standard_Integer BuildBSpMatrix(const TColStd_Array1OfReal& Parameters,const TColStd_Array1OfInteger& OrderArray,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer Degree,math_Matrix& Matrix,Standard_Integer& UpperBandWidth,Standard_Integer& LowerBandWidth) ;
//! this factors the Banded Matrix in <br>
//! the LU form with a Banded storage of <br>
//! components of the L matrix <br>
//! WARNING : do not use if the Matrix is <br>
//! totally positive (It is the case for <br>
//! Bspline matrices build as above with <br>
//! parameters being the Schoenberg points <br>
Standard_EXPORT static Standard_Integer FactorBandedMatrix(math_Matrix& Matrix,const Standard_Integer UpperBandWidth,const Standard_Integer LowerBandWidth,Standard_Integer& PivotIndexProblem) ;
//! This solves the system Matrix.X = B <br>
//! with when Matrix is factored in LU form <br>
//! The Array is an seen as an <br>
//! Array[1..N][1..ArrayDimension] with N = <br>
//! the rank of the matrix Matrix. The <br>
//! result is stored in Array when each <br>
//! coordinate is solved that is B is the <br>
//! array whose values are <br>
//! B[i] = Array[i][p] for each p in 1..ArrayDimension <br>
Standard_EXPORT static Standard_Integer SolveBandedSystem(const math_Matrix& Matrix,const Standard_Integer UpperBandWidth,const Standard_Integer LowerBandWidth,const Standard_Integer ArrayDimension,Standard_Real& Array) ;
//! This solves the system Matrix.X = B <br>
//! with when Matrix is factored in LU form <br>
//! The Array has the length of <br>
//! the rank of the matrix Matrix. The <br>
//! result is stored in Array when each <br>
//! coordinate is solved that is B is the <br>
//! array whose values are <br>
//! B[i] = Array[i][p] for each p in 1..ArrayDimension <br>
Standard_EXPORT static Standard_Integer SolveBandedSystem(const math_Matrix& Matrix,const Standard_Integer UpperBandWidth,const Standard_Integer LowerBandWidth,TColgp_Array1OfPnt2d& Array) ;
//! This solves the system Matrix.X = B <br>
//! with when Matrix is factored in LU form <br>
//! The Array has the length of <br>
//! the rank of the matrix Matrix. The <br>
//! result is stored in Array when each <br>
//! coordinate is solved that is B is the <br>
//! array whose values are <br>
//! B[i] = Array[i][p] for each p in 1..ArrayDimension <br>
Standard_EXPORT static Standard_Integer SolveBandedSystem(const math_Matrix& Matrix,const Standard_Integer UpperBandWidth,const Standard_Integer LowerBandWidth,TColgp_Array1OfPnt& Array) ;
Standard_EXPORT static Standard_Integer SolveBandedSystem(const math_Matrix& Matrix,const Standard_Integer UpperBandWidth,const Standard_Integer LowerBandWidth,const Standard_Boolean HomogenousFlag,const Standard_Integer ArrayDimension,Standard_Real& Array,Standard_Real& Weights) ;
//! This solves the system Matrix.X = B <br>
//! with when Matrix is factored in LU form <br>
//! The Array is an seen as an <br>
//! Array[1..N][1..ArrayDimension] with N = <br>
//! the rank of the matrix Matrix. The <br>
//! result is stored in Array when each <br>
//! coordinate is solved that is B is the <br>
//! array whose values are B[i] = <br>
//! Array[i][p] for each p in <br>
//! 1..ArrayDimension. If HomogeneousFlag == <br>
//! 0 the Poles are multiplied by the <br>
//! Weights uppon Entry and once <br>
//! interpolation is carried over the <br>
//! result of the poles are divided by the <br>
//! result of the interpolation of the <br>
//! weights. Otherwise if HomogenousFlag == 1 <br>
//! the Poles and Weigths are treated homogenously <br>
//! that is that those are interpolated as they <br>
//! are and result is returned without division <br>
//! by the interpolated weigths. <br>
Standard_EXPORT static Standard_Integer SolveBandedSystem(const math_Matrix& Matrix,const Standard_Integer UpperBandWidth,const Standard_Integer LowerBandWidth,const Standard_Boolean HomogenousFlag,TColgp_Array1OfPnt2d& Array,TColStd_Array1OfReal& Weights) ;
//! This solves the system Matrix.X = B <br>
//! with when Matrix is factored in LU form <br>
//! The Array is an seen as an <br>
//! Array[1..N][1..ArrayDimension] with N = <br>
//! the rank of the matrix Matrix. The <br>
//! result is stored in Array when each <br>
//! coordinate is solved that is B is the <br>
//! array whose values are <br>
//! B[i] = Array[i][p] for each p in 1..ArrayDimension <br>
//! If HomogeneousFlag == <br>
//! 0 the Poles are multiplied by the <br>
//! Weights uppon Entry and once <br>
//! interpolation is carried over the <br>
//! result of the poles are divided by the <br>
//! result of the interpolation of the <br>
//! weights. Otherwise if HomogenousFlag == 1 <br>
//! the Poles and Weigths are treated homogenously <br>
//! that is that those are interpolated as they <br>
//! are and result is returned without division <br>
//! by the interpolated weigths. <br>
Standard_EXPORT static Standard_Integer SolveBandedSystem(const math_Matrix& Matrix,const Standard_Integer UpperBandWidth,const Standard_Integer LowerBandWidth,const Standard_Boolean HomogeneousFlag,TColgp_Array1OfPnt& Array,TColStd_Array1OfReal& Weights) ;
//! Merges two knot vector by setting the starting and <br>
//! ending values to StartValue and EndValue <br>
Standard_EXPORT static void MergeBSplineKnots(const Standard_Real Tolerance,const Standard_Real StartValue,const Standard_Real EndValue,const Standard_Integer Degree1,const TColStd_Array1OfReal& Knots1,const TColStd_Array1OfInteger& Mults1,const Standard_Integer Degree2,const TColStd_Array1OfReal& Knots2,const TColStd_Array1OfInteger& Mults2,Standard_Integer& NumPoles,Handle(TColStd_HArray1OfReal)& NewKnots,Handle(TColStd_HArray1OfInteger)& NewMults) ;
//! This function will compose a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] with a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following: <br>
//! <br>
//! 1. F(a(t)) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots <br>
//! <br>
//! 2. a(t) defines a differentiable <br>
//! isomorphism between the range of FlatKnots to the range <br>
//! of BSplineFlatKnots which is the <br>
//! same as the range of F(t) <br>
//! <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of F(a(t)) <br>
Standard_EXPORT static void FunctionReparameterise(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const Standard_Integer PolesDimension,Standard_Real& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,Standard_Real& NewPoles,Standard_Integer& Status) ;
//! This function will compose a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] with a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following: <br>
//! <br>
//! 1. F(a(t)) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots <br>
//! <br>
//! 2. a(t) defines a differentiable <br>
//! isomorphism between the range of FlatKnots to the range <br>
//! of BSplineFlatKnots which is the <br>
//! same as the range of F(t) <br>
//! <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of F(a(t)) <br>
Standard_EXPORT static void FunctionReparameterise(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,TColStd_Array1OfReal& NewPoles,Standard_Integer& Status) ;
//! this will compose a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] with a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following : 1. F(a(t)) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots <br>
//! 2. a(t) defines a differentiable <br>
//! isomorphism between the range of FlatKnots to the range <br>
//! of BSplineFlatKnots which is the <br>
//! same as the range of F(t) <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of F(a(t)) <br>
Standard_EXPORT static void FunctionReparameterise(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,TColgp_Array1OfPnt& NewPoles,Standard_Integer& Status) ;
//! this will compose a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] with a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following : 1. F(a(t)) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots <br>
//! 2. a(t) defines a differentiable <br>
//! isomorphism between the range of FlatKnots to the range <br>
//! of BSplineFlatKnots which is the <br>
//! same as the range of F(t) <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of F(a(t)) <br>
Standard_EXPORT static void FunctionReparameterise(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,TColgp_Array1OfPnt2d& NewPoles,Standard_Integer& Status) ;
//! this will multiply a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] by a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following : 1. a(t) * F(t) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots 2. the range of a(t) <br>
//! is the same as the range of F(t) <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of a(t)*F(t) <br>
Standard_EXPORT static void FunctionMultiply(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const Standard_Integer PolesDimension,Standard_Real& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,Standard_Real& NewPoles,Standard_Integer& Status) ;
//! this will multiply a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] by a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following : 1. a(t) * F(t) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots 2. the range of a(t) <br>
//! is the same as the range of F(t) <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of a(t)*F(t) <br>
Standard_EXPORT static void FunctionMultiply(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const TColStd_Array1OfReal& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,TColStd_Array1OfReal& NewPoles,Standard_Integer& Status) ;
//! this will multiply a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] by a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following : 1. a(t) * F(t) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots 2. the range of a(t) <br>
//! is the same as the range of F(t) <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of a(t)*F(t) <br>
Standard_EXPORT static void FunctionMultiply(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,TColgp_Array1OfPnt2d& NewPoles,Standard_Integer& Status) ;
//! this will multiply a given Vectorial BSpline F(t) <br>
//! defined by its BSplineDegree and BSplineFlatKnotsl, <br>
//! its Poles array which are coded as an array of Real <br>
//! of the form [1..NumPoles][1..PolesDimension] by a <br>
//! function a(t) which is assumed to satisfy the <br>
//! following : 1. a(t) * F(t) is a polynomial BSpline <br>
//! that can be expressed exactly as a BSpline of degree <br>
//! NewDegree on the knots FlatKnots 2. the range of a(t) <br>
//! is the same as the range of F(t) <br>
//! Warning: it is <br>
//! the caller's responsability to insure that conditions <br>
//! 1. and 2. above are satisfied : no check whatsoever <br>
//! is made in this method <br>
//! Status will return 0 if OK else it will return the pivot index <br>
//! of the matrix that was inverted to compute the multiplied <br>
//! BSpline : the method used is interpolation at Schoenenberg <br>
//! points of a(t)*F(t) <br>
Standard_EXPORT static void FunctionMultiply(const BSplCLib_EvaluatorFunction& Function,const Standard_Integer BSplineDegree,const TColStd_Array1OfReal& BSplineFlatKnots,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer NewDegree,TColgp_Array1OfPnt& NewPoles,Standard_Integer& Status) ;
//! Perform the De Boor algorithm to evaluate a point at <br>
//! parameter <U>, with <Degree> and <Dimension>. <br>
//! <br>
//! Poles is an array of Reals of size <br>
//! <br>
//! <Dimension> * <Degree>+1 <br>
//! <br>
//! Containing the poles. At the end <Poles> contains <br>
//! the current point. Poles Contain all the poles of <br>
//! the BsplineCurve, Knots also Contains all the knots <br>
//! of the BsplineCurve. ExtrapMode has two slots [0] = <br>
//! Degree used to extrapolate before the first knot [1] <br>
//! = Degre used to extrapolate after the last knot has <br>
//! to be between 1 and Degree <br>
Standard_EXPORT static void Eval(const Standard_Real U,const Standard_Boolean PeriodicFlag,const Standard_Integer DerivativeRequest,Standard_Integer& ExtrapMode,const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer ArrayDimension,Standard_Real& Poles,Standard_Real& Result) ;
//! Perform the De Boor algorithm to evaluate a point at <br>
//! parameter <U>, with <Degree> and <Dimension>. <br>
//! Evaluates by multiplying the Poles by the Weights and <br>
//! gives the homogeneous result in PolesResult that is <br>
//! the results of the evaluation of the numerator once it <br>
//! has been multiplied by the weights and in <br>
//! WeightsResult one has the result of the evaluation of <br>
//! the denominator <br>
//! <br>
//! Warning: <PolesResult> and <WeightsResult> must be dimensionned <br>
//! properly. <br>
Standard_EXPORT static void Eval(const Standard_Real U,const Standard_Boolean PeriodicFlag,const Standard_Integer DerivativeRequest,Standard_Integer& ExtrapMode,const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer ArrayDimension,Standard_Real& Poles,Standard_Real& Weights,Standard_Real& PolesResult,Standard_Real& WeightsResult) ;
//! Perform the evaluation of the Bspline Basis <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
Standard_EXPORT static void Eval(const Standard_Real U,const Standard_Boolean PeriodicFlag,const Standard_Boolean HomogeneousFlag,Standard_Integer& ExtrapMode,const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point,Standard_Real& Weight) ;
//! Perform the evaluation of the Bspline Basis <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! <br>
Standard_EXPORT static void Eval(const Standard_Real U,const Standard_Boolean PeriodicFlag,const Standard_Boolean HomogeneousFlag,Standard_Integer& ExtrapMode,const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point,Standard_Real& Weight) ;
//! Extend a BSpline nD using the tangency map <br>
//! <C1Coefficient> is the coefficient of reparametrisation <br>
//! <Continuity> must be equal to 1, 2 or 3. <br>
//! <Degree> must be greater or equal than <Continuity> + 1. <br>
//! <br>
//! Warning: <KnotsResult> and <PolesResult> must be dimensionned <br>
//! properly. <br>
Standard_EXPORT static void TangExtendToConstraint(const TColStd_Array1OfReal& FlatKnots,const Standard_Real C1Coefficient,const Standard_Integer NumPoles,Standard_Real& Poles,const Standard_Integer Dimension,const Standard_Integer Degree,const TColStd_Array1OfReal& ConstraintPoint,const Standard_Integer Continuity,const Standard_Boolean After,Standard_Integer& NbPolesResult,Standard_Integer& NbKnotsRsult,Standard_Real& KnotsResult,Standard_Real& PolesResult) ;
//! Perform the evaluation of the of the cache <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effects <br>
Standard_EXPORT static void CacheD0(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point) ;
//! Perform the evaluation of the Bspline Basis <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! ththe CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effectsis just evaluates the current point <br>
Standard_EXPORT static void CacheD0(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point) ;
//! Calls CacheD0 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD0(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point) ;
//! Calls CacheD0 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD0(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point) ;
//! Perform the evaluation of the of the cache <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effects <br>
Standard_EXPORT static void CacheD1(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point,gp_Vec& Vec) ;
//! Perform the evaluation of the Bspline Basis <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! ththe CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effectsis just evaluates the current point <br>
Standard_EXPORT static void CacheD1(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point,gp_Vec2d& Vec) ;
//! Calls CacheD1 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD1(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point,gp_Vec& Vec) ;
//! Calls CacheD1 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD1(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point,gp_Vec2d& Vec) ;
//! Perform the evaluation of the of the cache <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effects <br>
Standard_EXPORT static void CacheD2(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point,gp_Vec& Vec1,gp_Vec& Vec2) ;
//! Perform the evaluation of the Bspline Basis <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! ththe CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effectsis just evaluates the current point <br>
Standard_EXPORT static void CacheD2(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point,gp_Vec2d& Vec1,gp_Vec2d& Vec2) ;
//! Calls CacheD1 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD2(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point,gp_Vec& Vec1,gp_Vec& Vec2) ;
//! Calls CacheD1 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD2(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point,gp_Vec2d& Vec1,gp_Vec2d& Vec2) ;
//! Perform the evaluation of the of the cache <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effects <br>
Standard_EXPORT static void CacheD3(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point,gp_Vec& Vec1,gp_Vec& Vec2,gp_Vec& Vec3) ;
//! Perform the evaluation of the Bspline Basis <br>
//! and then multiplies by the weights <br>
//! this just evaluates the current point <br>
//! the parameter must be normalized between <br>
//! the 0 and 1 for the span. <br>
//! The Cache must be valid when calling this <br>
//! routine. Geom Package will insure that. <br>
//! and then multiplies by the weights <br>
//! ththe CacheParameter is where the Cache was <br>
//! constructed the SpanLength is to normalize <br>
//! the polynomial in the cache to avoid bad conditioning <br>
//! effectsis just evaluates the current point <br>
Standard_EXPORT static void CacheD3(const Standard_Real U,const Standard_Integer Degree,const Standard_Real CacheParameter,const Standard_Real SpanLenght,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point,gp_Vec2d& Vec1,gp_Vec2d& Vec2,gp_Vec2d& Vec3) ;
//! Calls CacheD1 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD3(const Standard_Real U,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt& Point,gp_Vec& Vec1,gp_Vec& Vec2,gp_Vec& Vec3) ;
//! Calls CacheD1 for Bezier Curves Arrays computed with <br>
//! the method PolesCoefficients. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
static void CoefsD3(const Standard_Real U,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,gp_Pnt2d& Point,gp_Vec2d& Vec1,gp_Vec2d& Vec2,gp_Vec2d& Vec3) ;
//! Perform the evaluation of the Taylor expansion <br>
//! of the Bspline normalized between 0 and 1. <br>
//! If rational computes the homogeneous Taylor expension <br>
//! for the numerator and stores it in CachePoles <br>
Standard_EXPORT static void BuildCache(const Standard_Real U,const Standard_Real InverseOfSpanDomain,const Standard_Boolean PeriodicFlag,const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,TColgp_Array1OfPnt& CachePoles,TColStd_Array1OfReal& CacheWeights) ;
//! Perform the evaluation of the Taylor expansion <br>
//! of the Bspline normalized between 0 and 1. <br>
//! If rational computes the homogeneous Taylor expension <br>
//! for the numerator and stores it in CachePoles <br>
Standard_EXPORT static void BuildCache(const Standard_Real U,const Standard_Real InverseOfSpanDomain,const Standard_Boolean PeriodicFlag,const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,TColgp_Array1OfPnt2d& CachePoles,TColStd_Array1OfReal& CacheWeights) ;
static void PolesCoefficients(const TColgp_Array1OfPnt2d& Poles,TColgp_Array1OfPnt2d& CachePoles) ;
Standard_EXPORT static void PolesCoefficients(const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,TColgp_Array1OfPnt2d& CachePoles,TColStd_Array1OfReal& CacheWeights) ;
static void PolesCoefficients(const TColgp_Array1OfPnt& Poles,TColgp_Array1OfPnt& CachePoles) ;
//! Encapsulation of BuildCache to perform the <br>
//! evaluation of the Taylor expansion for beziercurves <br>
//! at parameter 0. <br>
//! Warning: To be used for Beziercurves ONLY!!! <br>
Standard_EXPORT static void PolesCoefficients(const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,TColgp_Array1OfPnt& CachePoles,TColStd_Array1OfReal& CacheWeights) ;
//! Returns pointer to statically allocated array representing <br>
//! flat knots for bezier curve of the specified degree. <br>
//! Raises OutOfRange if Degree > MaxDegree() <br>
Standard_EXPORT static const Standard_Real& FlatBezierKnots(const Standard_Integer Degree) ;
//! builds the Schoenberg points from the flat knot <br>
//! used to interpolate a BSpline since the <br>
//! BSpline matrix is invertible. <br>
Standard_EXPORT static void BuildSchoenbergPoints(const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,TColStd_Array1OfReal& Parameters) ;
//! Performs the interpolation of the data given in <br>
//! the Poles array according to the requests in <br>
//! ContactOrderArray that is : if <br>
//! ContactOrderArray(i) has value d it means that <br>
//! Poles(i) containes the dth derivative of the <br>
//! function to be interpolated. The length L of the <br>
//! following arrays must be the same : <br>
//! Parameters, ContactOrderArray, Poles, <br>
//! The length of FlatKnots is Degree + L + 1 <br>
//! Warning: <br>
//! the method used to do that interpolation is <br>
//! gauss elimination WITHOUT pivoting. Thus if the <br>
//! diagonal is not dominant there is no guarantee <br>
//! that the algorithm will work. Nevertheless for <br>
//! Cubic interpolation or interpolation at Scheonberg <br>
//! points the method will work <br>
//! The InversionProblem will report 0 if there was no <br>
//! problem else it will give the index of the faulty <br>
//! pivot <br>
Standard_EXPORT static void Interpolate(const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColStd_Array1OfReal& Parameters,const TColStd_Array1OfInteger& ContactOrderArray,TColgp_Array1OfPnt& Poles,Standard_Integer& InversionProblem) ;
//! Performs the interpolation of the data given in <br>
//! the Poles array according to the requests in <br>
//! ContactOrderArray that is : if <br>
//! ContactOrderArray(i) has value d it means that <br>
//! Poles(i) containes the dth derivative of the <br>
//! function to be interpolated. The length L of the <br>
//! following arrays must be the same : <br>
//! Parameters, ContactOrderArray, Poles, <br>
//! The length of FlatKnots is Degree + L + 1 <br>
//! Warning: <br>
//! the method used to do that interpolation is <br>
//! gauss elimination WITHOUT pivoting. Thus if the <br>
//! diagonal is not dominant there is no guarantee <br>
//! that the algorithm will work. Nevertheless for <br>
//! Cubic interpolation at knots or interpolation at Scheonberg <br>
//! points the method will work. <br>
//! The InversionProblem w <br>
//! ll report 0 if there was no <br>
//! problem else it will give the index of the faulty <br>
//! pivot <br>
Standard_EXPORT static void Interpolate(const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColStd_Array1OfReal& Parameters,const TColStd_Array1OfInteger& ContactOrderArray,TColgp_Array1OfPnt2d& Poles,Standard_Integer& InversionProblem) ;
//! Performs the interpolation of the data given in <br>
//! the Poles array according to the requests in <br>
//! ContactOrderArray that is : if <br>
//! ContactOrderArray(i) has value d it means that <br>
//! Poles(i) containes the dth derivative of the <br>
//! function to be interpolated. The length L of the <br>
//! following arrays must be the same : <br>
//! Parameters, ContactOrderArray, Poles, <br>
//! The length of FlatKnots is Degree + L + 1 <br>
//! Warning: <br>
//! the method used to do that interpolation is <br>
//! gauss elimination WITHOUT pivoting. Thus if the <br>
//! diagonal is not dominant there is no guarantee <br>
//! that the algorithm will work. Nevertheless for <br>
//! Cubic interpolation at knots or interpolation at Scheonberg <br>
//! points the method will work. <br>
//! The InversionProblem will report 0 if there was no <br>
//! problem else it will give the index of the faulty <br>
//! pivot <br>
//! <br>
//! <br>
Standard_EXPORT static void Interpolate(const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColStd_Array1OfReal& Parameters,const TColStd_Array1OfInteger& ContactOrderArray,TColgp_Array1OfPnt& Poles,TColStd_Array1OfReal& Weights,Standard_Integer& InversionProblem) ;
//! Performs the interpolation of the data given in <br>
//! the Poles array according to the requests in <br>
//! ContactOrderArray that is : if <br>
//! ContactOrderArray(i) has value d it means that <br>
//! Poles(i) containes the dth derivative of the <br>
//! function to be interpolated. The length L of the <br>
//! following arrays must be the same : <br>
//! Parameters, ContactOrderArray, Poles, <br>
//! The length of FlatKnots is Degree + L + 1 <br>
//! Warning: <br>
//! the method used to do that interpolation is <br>
//! gauss elimination WITHOUT pivoting. Thus if the <br>
//! diagonal is not dominant there is no guarantee <br>
//! that the algorithm will work. Nevertheless for <br>
//! Cubic interpolation at knots or interpolation at Scheonberg <br>
//! points the method will work. <br>
//! The InversionProblem w <br>
//! ll report 0 if there was no <br>
//! problem else it will give the i <br>
Standard_EXPORT static void Interpolate(const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColStd_Array1OfReal& Parameters,const TColStd_Array1OfInteger& ContactOrderArray,TColgp_Array1OfPnt2d& Poles,TColStd_Array1OfReal& Weights,Standard_Integer& InversionProblem) ;
//! Performs the interpolation of the data given in <br>
//! the Poles array according to the requests in <br>
//! ContactOrderArray that is : if <br>
//! ContactOrderArray(i) has value d it means that <br>
//! Poles(i) containes the dth derivative of the <br>
//! function to be interpolated. The length L of the <br>
//! following arrays must be the same : <br>
//! Parameters, ContactOrderArray <br>
//! The length of FlatKnots is Degree + L + 1 <br>
//! The PolesArray is an seen as an <br>
//! Array[1..N][1..ArrayDimension] with N = tge length <br>
//! of the parameters array <br>
//! Warning: <br>
//! the method used to do that interpolation is <br>
//! gauss elimination WITHOUT pivoting. Thus if the <br>
//! diagonal is not dominant there is no guarantee <br>
//! that the algorithm will work. Nevertheless for <br>
//! Cubic interpolation or interpolation at Scheonberg <br>
//! points the method will work <br>
//! The InversionProblem will report 0 if there was no <br>
//! problem else it will give the index of the faulty <br>
//! pivot <br>
//! <br>
Standard_EXPORT static void Interpolate(const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColStd_Array1OfReal& Parameters,const TColStd_Array1OfInteger& ContactOrderArray,const Standard_Integer ArrayDimension,Standard_Real& Poles,Standard_Integer& InversionProblem) ;
Standard_EXPORT static void Interpolate(const Standard_Integer Degree,const TColStd_Array1OfReal& FlatKnots,const TColStd_Array1OfReal& Parameters,const TColStd_Array1OfInteger& ContactOrderArray,const Standard_Integer ArrayDimension,Standard_Real& Poles,Standard_Real& Weights,Standard_Integer& InversionProblem) ;
//! Find the new poles which allows an old point (with a <br>
//! given u as parameter) to reach a new position <br>
//! Index1 and Index2 indicate the range of poles we can move <br>
//! (1, NbPoles-1) or (2, NbPoles) -> no constraint for one side <br>
//! don't enter (1,NbPoles) -> error: rigid move <br>
//! (2, NbPoles-1) -> the ends are enforced <br>
//! (3, NbPoles-2) -> the ends and the tangency are enforced <br>
//! if Problem in BSplineBasis calculation, no change for the curve <br>
//! and FirstIndex, LastIndex = 0 <br>
Standard_EXPORT static void MovePoint(const Standard_Real U,const gp_Vec2d& Displ,const Standard_Integer Index1,const Standard_Integer Index2,const Standard_Integer Degree,const Standard_Boolean Rational,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& FlatKnots,Standard_Integer& FirstIndex,Standard_Integer& LastIndex,TColgp_Array1OfPnt2d& NewPoles) ;
//! Find the new poles which allows an old point (with a <br>
//! given u as parameter) to reach a new position <br>
//! Index1 and Index2 indicate the range of poles we can move <br>
//! (1, NbPoles-1) or (2, NbPoles) -> no constraint for one side <br>
//! don't enter (1,NbPoles) -> error: rigid move <br>
//! (2, NbPoles-1) -> the ends are enforced <br>
//! (3, NbPoles-2) -> the ends and the tangency are enforced <br>
//! if Problem in BSplineBasis calculation, no change for the curve <br>
//! and FirstIndex, LastIndex = 0 <br>
Standard_EXPORT static void MovePoint(const Standard_Real U,const gp_Vec& Displ,const Standard_Integer Index1,const Standard_Integer Index2,const Standard_Integer Degree,const Standard_Boolean Rational,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& FlatKnots,Standard_Integer& FirstIndex,Standard_Integer& LastIndex,TColgp_Array1OfPnt& NewPoles) ;
//! This is the dimension free version of the utility <br>
//! U is the parameter must be within the first FlatKnots and the <br>
//! last FlatKnots Delta is the amount the curve has to be moved <br>
//! DeltaDerivative is the amount the derivative has to be moved. <br>
//! Delta and DeltaDerivative must be array of dimension <br>
//! ArrayDimension Degree is the degree of the BSpline and the <br>
//! FlatKnots are the knots of the BSpline Starting Condition if = <br>
//! -1 means the starting point of the curve can move <br>
//! = 0 means the <br>
//! starting point of the cuve cannot move but tangen starting <br>
//! point of the curve cannot move <br>
//! = 1 means the starting point and tangents cannot move <br>
//! = 2 means the starting point tangent and curvature cannot move <br>
//! = ... <br>
//! Same holds for EndingCondition <br>
//! Poles are the poles of the curve <br>
//! Weights are the weights of the curve if Rational = Standard_True <br>
//! NewPoles are the poles of the deformed curve <br>
//! ErrorStatus will be 0 if no error happened <br>
//! 1 if there are not enough knots/poles <br>
//! the imposed conditions <br>
//! The way to solve this problem is to add knots to the BSpline <br>
//! If StartCondition = 1 and EndCondition = 1 then you need at least <br>
//! 4 + 2 = 6 poles so for example to have a C1 cubic you will need <br>
//! have at least 2 internal knots. <br>
Standard_EXPORT static void MovePointAndTangent(const Standard_Real U,const Standard_Integer ArrayDimension,Standard_Real& Delta,Standard_Real& DeltaDerivative,const Standard_Real Tolerance,const Standard_Integer Degree,const Standard_Boolean Rational,const Standard_Integer StartingCondition,const Standard_Integer EndingCondition,Standard_Real& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& FlatKnots,Standard_Real& NewPoles,Standard_Integer& ErrorStatus) ;
//! This is the dimension free version of the utility <br>
//! U is the parameter must be within the first FlatKnots and the <br>
//! last FlatKnots Delta is the amount the curve has to be moved <br>
//! DeltaDerivative is the amount the derivative has to be moved. <br>
//! Delta and DeltaDerivative must be array of dimension <br>
//! ArrayDimension Degree is the degree of the BSpline and the <br>
//! FlatKnots are the knots of the BSpline Starting Condition if = <br>
//! -1 means the starting point of the curve can move <br>
//! = 0 means the <br>
//! starting point of the cuve cannot move but tangen starting <br>
//! point of the curve cannot move <br>
//! = 1 means the starting point and tangents cannot move <br>
//! = 2 means the starting point tangent and curvature cannot move <br>
//! = ... <br>
//! Same holds for EndingCondition <br>
//! Poles are the poles of the curve <br>
//! Weights are the weights of the curve if Rational = Standard_True <br>
//! NewPoles are the poles of the deformed curve <br>
//! ErrorStatus will be 0 if no error happened <br>
//! 1 if there are not enough knots/poles <br>
//! the imposed conditions <br>
//! The way to solve this problem is to add knots to the BSpline <br>
//! If StartCondition = 1 and EndCondition = 1 then you need at least <br>
//! 4 + 2 = 6 poles so for example to have a C1 cubic you will need <br>
//! have at least 2 internal knots. <br>
Standard_EXPORT static void MovePointAndTangent(const Standard_Real U,const gp_Vec& Delta,const gp_Vec& DeltaDerivative,const Standard_Real Tolerance,const Standard_Integer Degree,const Standard_Boolean Rational,const Standard_Integer StartingCondition,const Standard_Integer EndingCondition,const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& FlatKnots,TColgp_Array1OfPnt& NewPoles,Standard_Integer& ErrorStatus) ;
//! This is the dimension free version of the utility <br>
//! U is the parameter must be within the first FlatKnots and the <br>
//! last FlatKnots Delta is the amount the curve has to be moved <br>
//! DeltaDerivative is the amount the derivative has to be moved. <br>
//! Delta and DeltaDerivative must be array of dimension <br>
//! ArrayDimension Degree is the degree of the BSpline and the <br>
//! FlatKnots are the knots of the BSpline Starting Condition if = <br>
//! -1 means the starting point of the curve can move <br>
//! = 0 means the <br>
//! starting point of the cuve cannot move but tangen starting <br>
//! point of the curve cannot move <br>
//! = 1 means the starting point and tangents cannot move <br>
//! = 2 means the starting point tangent and curvature cannot move <br>
//! = ... <br>
//! Same holds for EndingCondition <br>
//! Poles are the poles of the curve <br>
//! Weights are the weights of the curve if Rational = Standard_True <br>
//! NewPoles are the poles of the deformed curve <br>
//! ErrorStatus will be 0 if no error happened <br>
//! 1 if there are not enough knots/poles <br>
//! the imposed conditions <br>
//! The way to solve this problem is to add knots to the BSpline <br>
//! If StartCondition = 1 and EndCondition = 1 then you need at least <br>
//! 4 + 2 = 6 poles so for example to have a C1 cubic you will need <br>
//! have at least 2 internal knots. <br>
Standard_EXPORT static void MovePointAndTangent(const Standard_Real U,const gp_Vec2d& Delta,const gp_Vec2d& DeltaDerivative,const Standard_Real Tolerance,const Standard_Integer Degree,const Standard_Boolean Rational,const Standard_Integer StartingCondition,const Standard_Integer EndingCondition,const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& FlatKnots,TColgp_Array1OfPnt2d& NewPoles,Standard_Integer& ErrorStatus) ;
//! given a tolerance in 3D space returns a <br>
//! tolerance in U parameter space such that <br>
//! all u1 and u0 in the domain of the curve f(u) <br>
//! | u1 - u0 | < UTolerance and <br>
//! we have |f (u1) - f (u0)| < Tolerance3D <br>
Standard_EXPORT static void Resolution(Standard_Real& PolesArray,const Standard_Integer ArrayDimension,const Standard_Integer NumPoles,const TColStd_Array1OfReal& Weights,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer Degree,const Standard_Real Tolerance3D,Standard_Real& UTolerance) ;
//! given a tolerance in 3D space returns a <br>
//! tolerance in U parameter space such that <br>
//! all u1 and u0 in the domain of the curve f(u) <br>
//! | u1 - u0 | < UTolerance and <br>
//! we have |f (u1) - f (u0)| < Tolerance3D <br>
Standard_EXPORT static void Resolution(const TColgp_Array1OfPnt& Poles,const TColStd_Array1OfReal& Weights,const Standard_Integer NumPoles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer Degree,const Standard_Real Tolerance3D,Standard_Real& UTolerance) ;
//! given a tolerance in 3D space returns a <br>
//! tolerance in U parameter space such that <br>
//! all u1 and u0 in the domain of the curve f(u) <br>
//! | u1 - u0 | < UTolerance and <br>
//! we have |f (u1) - f (u0)| < Tolerance3D <br>
Standard_EXPORT static void Resolution(const TColgp_Array1OfPnt2d& Poles,const TColStd_Array1OfReal& Weights,const Standard_Integer NumPoles,const TColStd_Array1OfReal& FlatKnots,const Standard_Integer Degree,const Standard_Real Tolerance3D,Standard_Real& UTolerance) ;
protected:
private:
Standard_EXPORT static void LocateParameter(const TColStd_Array1OfReal& Knots,const Standard_Real U,const Standard_Boolean Periodic,const Standard_Integer K1,const Standard_Integer K2,Standard_Integer& Index,Standard_Real& NewU,const Standard_Real Uf,const Standard_Real Ue) ;
};
#include <BSplCLib.lxx>
// other Inline functions and methods (like "C++: function call" methods)
#endif
|