// Created on: 1991-08-09 // Created by: Jean Claude VAUTHIER // Copyright (c) 1991-1999 Matra Datavision // Copyright (c) 1999-2014 OPEN CASCADE SAS // // This file is part of Open CASCADE Technology software library. // // This library is free software; you can redistribute it and/or modify it under // the terms of the GNU Lesser General Public License version 2.1 as published // by the Free Software Foundation, with special exception defined in the file // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT // distribution for complete text of the license and disclaimer of any warranty. // // Alternatively, this file may be used under the terms of Open CASCADE // commercial license or contractual agreement. #ifndef _BSplCLib_HeaderFile #define _BSplCLib_HeaderFile #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include class gp_Pnt; class gp_Pnt2d; class gp_Vec; class gp_Vec2d; class math_Matrix; //! BSplCLib B-spline curve Library. //! //! The BSplCLib package is a basic library for BSplines. It //! provides three categories of functions. //! //! * Management methods to process knots and multiplicities. //! //! * Multi-Dimensions spline methods. BSpline methods where //! poles have an arbitrary number of dimensions. They divides //! in two groups : //! //! - Global methods modifying the whole set of poles. The //! poles are described by an array of Reals and a //! Dimension. Example : Inserting knots. //! //! - Local methods computing points and derivatives. The //! poles are described by a pointer on a local array of //! Reals and a Dimension. The local array is modified. //! //! * 2D and 3D spline curves methods. //! //! Methods for 2d and 3d BSplines curves rational or not //! rational. //! //! Those methods have the following structure : //! //! - They extract the pole information in a working array. //! //! - They process the working array with the //! multi-dimension methods. (for example a 3d rational //! curve is processed as a 4 dimension curve). //! //! - They get back the result in the original dimension. //! //! Note that the bspline surface methods found in the //! package BSplSLib uses the same structure and rely on //! BSplCLib. //! //! In the following list of methods the 2d and 3d curve //! methods will be described with the corresponding //! multi-dimension method. //! //! The 3d or 2d B-spline curve is defined with : //! //! . its control points : TColgp_Array1OfPnt(2d) Poles //! . its weights : TColStd_Array1OfReal Weights //! . its knots : TColStd_Array1OfReal Knots //! . its multiplicities : TColStd_Array1OfInteger Mults //! . its degree : Standard_Integer Degree //! . its periodicity : Standard_Boolean Periodic //! //! Warnings : //! The bounds of Poles and Weights should be the same. //! The bounds of Knots and Mults should be the same. //! //! Note: weight and multiplicity arrays can be passed by pointer for //! some functions so that NULL pointer is valid. //! That means no weights/no multiplicities passed. //! //! No weights (BSplCLib::NoWeights()) means the curve is non rational. //! No mults (BSplCLib::NoMults()) means the knots are "flat" knots. //! //! KeyWords : //! B-spline curve, Functions, Library //! //! References : //! . A survey of curves and surfaces 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 BSplCLib { public: DEFINE_STANDARD_ALLOC //! This routine searches the position of the real value theX //! in the monotonically increasing set of real values theArray using bisection algorithm. //! //! If the given value is out of range or array values, algorithm returns either //! theArray.Lower()-1 or theArray.Upper()+1 depending on theX position in the ordered set. //! //! This routine is used to locate a knot value in a set of knots. Standard_EXPORT static void Hunt (const TColStd_Array1OfReal& theArray, const Standard_Real theX, Standard_Integer& theXPos); //! Computes the index of the knots value which gives //! the start point of the curve. Standard_EXPORT static Standard_Integer FirstUKnotIndex (const Standard_Integer Degree, const TColStd_Array1OfInteger& Mults); //! Computes the index of the knots value which gives //! the end point of the curve. Standard_EXPORT static Standard_Integer LastUKnotIndex (const Standard_Integer Degree, const TColStd_Array1OfInteger& Mults); //! Computes the index of the flats knots sequence //! corresponding to in the knots sequence //! which multiplicities are . 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 //! sequence between the knot K1 and the knot K2. //! The value return in Index verifies. //! //! Knots(Index) <= U < Knots(Index + 1) //! if U <= Knots (K1) then Index = K1 //! if U >= Knots (K2) then Index = K2 - 1 //! //! If Periodic is True U may be modified to fit in //! the range Knots(K1), Knots(K2). In any case the //! correct value is returned in NewU. //! //! Warnings :Index is used as input data to initialize the //! searching function. //! Warning: Knots have to be "withe repetitions" 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 //! sequence between the knot K1 and the knot K2. //! The value return in Index verifies. //! //! Knots(Index) <= U < Knots(Index + 1) //! if U <= Knots (K1) then Index = K1 //! if U >= Knots (K2) then Index = K2 - 1 //! //! If Periodic is True U may be modified to fit in //! the range Knots(K1), Knots(K2). In any case the //! correct value is returned in NewU. //! //! Warnings :Index is used as input data to initialize the //! searching function. //! Warning: Knots have to be "flat" 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 //! between K1 and K2. Mults is the multiplicity //! associated with each knot value. 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 //! between K1 and K2. Mults is the multiplicity //! associated with each knot value. 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 //! one of the multiplicities is incorrect. //! //! * Non positive. //! //! * Greater than Degree, or Degree+1 at the first and //! last knot of a non periodic curve. //! //! * The last periodicity on a periodic curve is not //! equal to the first. 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 //! repetition. //! //! Periodic : //! //! Sum(Mults(i), i = Mults.Lower(); i <= Mults.Upper()); //! //! Non Periodic : //! //! Sum(Mults(i); i = Mults.Lower(); i < Mults.Upper()) //! + 2 * Degree 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, const Standard_Boolean Periodic = Standard_False); //! Computes the sequence of knots KnotSeq with //! repetition of the knots of multiplicity greater //! than 1. //! //! Length of KnotSeq must be KnotSequenceLength(Mults,Degree,Periodic) 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 //! Mults) without repetition. Standard_EXPORT static Standard_Integer KnotsLength (const TColStd_Array1OfReal& KnotSeq, const Standard_Boolean Periodic = Standard_False); //! Computes the sequence of knots Knots without //! repetition of the knots of multiplicity greater //! than 1. //! //! Length of and must be //! KnotsLength(KnotSequence,Periodic) 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" //! or "NonUniform" between the knot FromK1 and the //! knot ToK2. There is no repetition of knot in the //! knots'sequence . Standard_EXPORT static BSplCLib_KnotDistribution KnotForm (const TColStd_Array1OfReal& Knots, const Standard_Integer FromK1, const Standard_Integer ToK2); //! Analyses the distribution of multiplicities between //! the knot FromK1 and the Knot ToK2. Standard_EXPORT static BSplCLib_MultDistribution MultForm (const TColStd_Array1OfInteger& Mults, const Standard_Integer FromK1, const Standard_Integer ToK2); //! Analyzes the array of knots. //! Returns the form and the maximum knot multiplicity. 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]. //! The knot values are recomputed such that Knots (Lower) = U1 //! and Knots (Upper) = U2 but the knot form is not modified. //! Warnings : //! In the array Knots the values must be in ascending order. //! U1 must not be equal to U2 to avoid division by zero. Standard_EXPORT static void Reparametrize (const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal& Knots); //! Reverses the array knots to become the knots //! sequence of the reversed curve. Standard_EXPORT static void Reverse (TColStd_Array1OfReal& Knots); //! Reverses the array of multiplicities. Standard_EXPORT static void Reverse (TColStd_Array1OfInteger& Mults); //! Reverses the array of poles. Last is the index of //! the new first pole. On a non periodic curve 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_Array1OfPnt& Poles, const Standard_Integer Last); //! Reverses the array of poles. Standard_EXPORT static void Reverse (TColgp_Array1OfPnt2d& Poles, const Standard_Integer Last); //! Reverses the array of poles. Standard_EXPORT static void Reverse (TColStd_Array1OfReal& Weights, const Standard_Integer Last); //! Returns False if all the weights of the array //! between I1 an I2 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_Array1OfReal& Weights, const Standard_Integer I1, const Standard_Integer I2, const Standard_Real Epsilon = 0.0); //! returns the degree maxima for a BSplineCurve. static Standard_Integer MaxDegree(); //! Perform the Boor algorithm to evaluate a point at //! parameter , with and . //! //! Poles is an array of Reals of size //! //! * +1 //! //! Containing the poles. At the end contains //! the current point. 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 with //! the given and the array of on the //! poles of dimension . The schema //! is computed until level on a basis of //! poles. //! //! * Knots is an array of reals of length : //! //! + //! //! * Poles is an array of reals of length : //! //! (2 * + 1) * //! //! The poles values must be set in the array at the //! positions. //! //! 0..Dimension, //! //! 2 * Dimension .. //! 3 * Dimension //! //! 4 * Dimension .. //! 5 * Dimension //! //! ... //! //! The results are found in the array poles depending //! on the Depth. (See the method GetPole). 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. //! This method is used to remove poles. //! //! U is the poles to remove, Knots should contains the //! knots of the curve after knot removal. //! //! The first and last poles do not change, the other //! poles are computed by averaging two possible values. //! The distance between the two possible poles is //! computed, if it is higher than False is //! returned. 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 //! derivatives of order . //! //! The formula for the first order is //! //! Pole(i) = Degree * (Pole(i+1) - Pole(i)) / //! (Knots(i+Degree+1) - Knots(i+1)) //! //! This formula is repeated (Degree is decremented at //! each step). 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 . This //! algorithm computes the value and all the derivatives //! up to order N (N <= Degree). //! //! is the original array of poles. //! //! The result in is the value and the //! derivatives. Poles[0] is the value, Poles[Degree] //! is the last derivative. 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. static TColStd_Array1OfReal* NoWeights(); //! Used as argument for a flatknots evaluation. static TColStd_Array1OfInteger* NoMults(); //! Stores in LK the useful knots for the BoorSchem //! on the span Knots(Index) - Knots(Index+1) 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 //! span Mults(Index) - Mults(Index+1). This index //! must be added to Poles.Lower(). 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 the poles and weights for the Eval //! scheme. starting from Poles(Poles.Lower()+Index) 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 poles for Boor scheme. //! Starting from * , copy //! poles. 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 //! poles . If the Boor algorithm was perform //! with and . Standard_EXPORT static Standard_Integer BoorIndex (const Standard_Integer Index, const Standard_Integer Length, const Standard_Integer Depth); //! Copy the pole at position in the Boor //! scheme of dimension to in //! the array . is updated. 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 the new number of poles //! and knots if the sequence of knots is inserted in the sequence . //! //! Epsilon is used to compare knots for equality. //! //! If Add is True the multiplicities on equal knots are //! added. //! //! If Add is False the max value of the multiplicities is //! kept. //! //! Return False if : //! The knew knots are knot increasing. //! The new knots are not in the range. 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 with //! multiplicities . must be a non //! decreasing sequence and verifies : //! //! Knots(Knots.Lower()) <= AddKnots(AddKnots.Lower()) //! Knots(Knots.Upper()) >= AddKnots(AddKnots.Upper()) //! //! The NewPoles and NewWeights arrays must have a length : //! Poles.Length() + Sum(AddMults()) //! //! When a knot to insert is identic to an existing knot the //! multiplicities are added. //! //! Epsilon is used to test knots for equality. //! //! When AddMult is negative or null the knot is not inserted. //! No multiplicity will becomes higher than the degree. //! //! The new Knots and Multiplicities are copied in //! and . //! //! All the New arrays should be correctly dimensioned. //! //! When all the new knots are existing knots, i.e. only the //! multiplicities will change it is safe to use the same //! arrays as input and output. 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 //! knot sequence. //! //! The location of the new Knot should be given as an input //! data. UIndex locates the new knot U in the knot sequence //! and Knots (UIndex) < U < Knots (UIndex + 1). //! //! The new control points corresponding to this insertion are //! returned. Knots and Mults are not updated. 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 . //! //! The new control points are returned. Knots and Mults are //! not updated. 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 //! to . If is null the knot is //! removed. //! //! As there are two ways to compute the new poles //! the midlle will be used as long as the //! distance is lower than Tolerance. //! //! If a distance is bigger than tolerance the //! methods returns False and the new arrays are //! not modified. //! //! A low tolerance can be used to test if the //! knot can be removed without modifying the //! curve. //! //! A high tolerance can be used to "smooth" the //! curve. 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 //! multiplicities after elevating the degree from //! to . See the IncreaseDegree method //! for more comments. 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 //! of dimension theDimension form theDegree to theNewDegree. //! //! The number of poles in the new curve is: //! @code //! Poles.Length() + (NewDegree - Degree) * Number of spans //! @endcode //! Where the number of spans is: //! @code //! LastUKnotIndex(Mults) - FirstUKnotIndex(Mults) + 1 //! @endcode //! for a non-periodic curve, and //! @code //! Knots.Length() - 1 //! @endcode //! for a periodic curve. //! //! The multiplicities of all knots are increased by the degree elevation. //! //! The new knots are usually the same knots with the //! exception of a non-periodic curve with the first //! and last multiplicity not equal to Degree+1 where //! knots are removed form the start and the bottom //! until the sum of the multiplicities is equal to //! NewDegree+1 at the knots corresponding to the //! first and last parameters of the curve. //! //! Example: Suppose a curve of degree 3 starting //! with following knots and multiplicities: //! @code //! knot : 0. 1. 2. //! mult : 1 2 1 //! @endcode //! //! The FirstUKnot is 2.0 because the sum of multiplicities is //! @code //! Degree+1 : 1 + 2 + 1 = 4 = 3 + 1 //! @endcode //! i.e. the first parameter of the curve is 2.0 and //! will still be 2.0 after degree elevation. //! Let raise this curve to degree 4. //! The multiplicities are increased by 2. //! //! They become 2 3 2. //! But we need a sum of multiplicities of 5 at knot 2. //! So the first knot is removed and the new knots are: //! @code //! knot : 1. 2. //! mult : 3 2 //! @endcode //! The multipicity of the first knot may also be reduced if the sum is still to big. //! //! In the most common situations (periodic curve or curve with first //! and last multiplicities equals to Degree+1) the knots are knot changes. //! //! The method IncreaseDegreeCountKnots can be used to compute the new number of knots. Standard_EXPORT static void IncreaseDegree (const Standard_Integer theNewDegree, const TColgp_Array1OfPnt2d& thePoles, const TColStd_Array1OfReal* theWeights, TColgp_Array1OfPnt2d& theNewPoles, TColStd_Array1OfReal* theNewWeights); //! Set in and the number of Knots and //! Poles of the NotPeriodic Curve identical at the //! periodic curve with a degree , a //! knots-distribution with Multiplicities . 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 and the number of Knots and //! Poles of the curve resulting from the trimming of the //! BSplinecurve defined with , , 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 //! derivatives in the following situations : //! //! * 3D, 2D and 1D //! //! * Rational or not Rational. //! //! * Knots and multiplicities or "flat knots" without //! multiplicities. //! //! * The is the localization of the //! parameter in the knot sequence. If is out //! of range the correct value will be searched. //! //! VERY IMPORTANT!!! //! USE BSplCLib::NoWeights() as Weights argument for non //! rational curves computations. 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 //! given parameter Parameter up to the //! requested DerivativeOrder and store the //! result in the array BsplineBasis in the //! following fashion //! BSplineBasis(1,1) = //! value of first non vanishing //! Bspline function which has Index FirstNonZeroBsplineIndex //! BsplineBasis(1,2) = //! value of second non vanishing //! Bspline function which has Index //! FirstNonZeroBsplineIndex + 1 //! BsplineBasis(1,n) = //! value of second non vanishing non vanishing //! Bspline function which has Index //! FirstNonZeroBsplineIndex + n (n <= Order) //! BSplineBasis(2,1) = //! value of derivative of first non vanishing //! Bspline function which has Index FirstNonZeroBsplineIndex //! BSplineBasis(N,1) = //! value of Nth derivative of first non vanishing //! Bspline function which has Index FirstNonZeroBsplineIndex //! if N <= DerivativeOrder + 1 Standard_EXPORT static Standard_Integer EvalBsplineBasis (const Standard_Integer DerivativeOrder, const Standard_Integer Order, const TColStd_Array1OfReal& FlatKnots, const Standard_Real Parameter, Standard_Integer& FirstNonZeroBsplineIndex, math_Matrix& BsplineBasis, const Standard_Boolean isPeriodic = Standard_False); //! This Builds a fully blown Matrix of //! (ni) //! Bi (tj) //! //! with i and j within 1..Order + NumPoles //! The integer ni is the ith slot of the //! array OrderArray, tj is the jth slot of //! the array Parameters 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 //! the LU form with a Banded storage of //! components of the L matrix //! WARNING : do not use if the Matrix is //! totally positive (It is the case for //! Bspline matrices build as above with //! parameters being the Schoenberg points 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 //! with when Matrix is factored in LU form //! The Array is an seen as an //! Array[1..N][1..ArrayDimension] with N = //! the rank of the matrix Matrix. The //! result is stored in Array when each //! coordinate is solved that is B is the //! array whose values are //! B[i] = Array[i][p] for each p in 1..ArrayDimension 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 //! with when Matrix is factored in LU form //! The Array has the length of //! the rank of the matrix Matrix. The //! result is stored in Array when each //! coordinate is solved that is B is the //! array whose values are //! B[i] = Array[i][p] for each p in 1..ArrayDimension 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 //! with when Matrix is factored in LU form //! The Array has the length of //! the rank of the matrix Matrix. The //! result is stored in Array when each //! coordinate is solved that is B is the //! array whose values are //! B[i] = Array[i][p] for each p in 1..ArrayDimension 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 //! with when Matrix is factored in LU form //! The Array is an seen as an //! Array[1..N][1..ArrayDimension] with N = //! the rank of the matrix Matrix. The //! result is stored in Array when each //! coordinate is solved that is B is the //! array whose values are B[i] = //! Array[i][p] for each p in //! 1..ArrayDimension. If HomogeneousFlag == //! 0 the Poles are multiplied by the //! Weights upon Entry and once //! interpolation is carried over the //! result of the poles are divided by the //! result of the interpolation of the //! weights. Otherwise if HomogenousFlag == 1 //! the Poles and Weigths are treated homogeneously //! that is that those are interpolated as they //! are and result is returned without division //! by the interpolated weigths. 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 //! with when Matrix is factored in LU form //! The Array is an seen as an //! Array[1..N][1..ArrayDimension] with N = //! the rank of the matrix Matrix. The //! result is stored in Array when each //! coordinate is solved that is B is the //! array whose values are //! B[i] = Array[i][p] for each p in 1..ArrayDimension //! If HomogeneousFlag == //! 0 the Poles are multiplied by the //! Weights upon Entry and once //! interpolation is carried over the //! result of the poles are divided by the //! result of the interpolation of the //! weights. Otherwise if HomogenousFlag == 1 //! the Poles and Weigths are treated homogeneously //! that is that those are interpolated as they //! are and result is returned without division //! by the interpolated weigths. 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 //! ending values to StartValue and EndValue 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) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] with a //! function a(t) which is assumed to satisfy the //! following: //! //! 1. F(a(t)) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots //! //! 2. a(t) defines a differentiable //! isomorphism between the range of FlatKnots to the range //! of BSplineFlatKnots which is the //! same as the range of F(t) //! //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! //! theStatus 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 F(a(t)) 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& theStatus); //! This function will compose a given Vectorial BSpline F(t) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] with a //! function a(t) which is assumed to satisfy the //! following: //! //! 1. F(a(t)) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots //! //! 2. a(t) defines a differentiable //! isomorphism between the range of FlatKnots to the range //! of BSplineFlatKnots which is the //! same as the range of F(t) //! //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! //! theStatus 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 F(a(t)) 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& theStatus); //! this will compose a given Vectorial BSpline F(t) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] with a //! function a(t) which is assumed to satisfy the //! following : 1. F(a(t)) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots //! 2. a(t) defines a differentiable //! isomorphism between the range of FlatKnots to the range //! of BSplineFlatKnots which is the //! same as the range of F(t) //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! theStatus 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 F(a(t)) 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& theStatus); //! this will compose a given Vectorial BSpline F(t) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] with a //! function a(t) which is assumed to satisfy the //! following : 1. F(a(t)) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots //! 2. a(t) defines a differentiable //! isomorphism between the range of FlatKnots to the range //! of BSplineFlatKnots which is the //! same as the range of F(t) //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! theStatus 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 F(a(t)) 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& theStatus); //! this will multiply a given Vectorial BSpline F(t) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] by a //! function a(t) which is assumed to satisfy the //! following : 1. a(t) * F(t) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots 2. the range of a(t) //! is the same as the range of F(t) //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! theStatus 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(t)*F(t) 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& theStatus); //! this will multiply a given Vectorial BSpline F(t) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] by a //! function a(t) which is assumed to satisfy the //! following : 1. a(t) * F(t) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots 2. the range of a(t) //! is the same as the range of F(t) //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! theStatus 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(t)*F(t) 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& theStatus); //! this will multiply a given Vectorial BSpline F(t) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] by a //! function a(t) which is assumed to satisfy the //! following : 1. a(t) * F(t) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots 2. the range of a(t) //! is the same as the range of F(t) //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! theStatus 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(t)*F(t) 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& theStatus); //! this will multiply a given Vectorial BSpline F(t) //! defined by its BSplineDegree and BSplineFlatKnotsl, //! its Poles array which are coded as an array of Real //! of the form [1..NumPoles][1..PolesDimension] by a //! function a(t) which is assumed to satisfy the //! following : 1. a(t) * F(t) is a polynomial BSpline //! that can be expressed exactly as a BSpline of degree //! NewDegree on the knots FlatKnots 2. the range of a(t) //! is the same as the range of F(t) //! Warning: it is //! the caller's responsibility to insure that conditions //! 1. and 2. above are satisfied : no check whatsoever //! is made in this method //! theStatus 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(t)*F(t) 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& theStatus); //! Perform the De Boor algorithm to evaluate a point at //! parameter , with and . //! //! Poles is an array of Reals of size //! //! * +1 //! //! Containing the poles. At the end contains //! the current point. Poles Contain all the poles of //! the BsplineCurve, Knots also Contains all the knots //! of the BsplineCurve. ExtrapMode has two slots [0] = //! Degree used to extrapolate before the first knot [1] //! = Degre used to extrapolate after the last knot has //! to be between 1 and Degree 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 //! parameter , with and . //! Evaluates by multiplying the Poles by the Weights and //! gives the homogeneous result in PolesResult that is //! the results of the evaluation of the numerator once it //! has been multiplied by the weights and in //! WeightsResult one has the result of the evaluation of //! the denominator //! //! Warning: and must be dimensionned //! properly. 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 //! and then multiplies by the weights //! this just evaluates the current point 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 //! and then multiplies by the weights //! this just evaluates the current point 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 //! is the coefficient of reparametrisation //! must be equal to 1, 2 or 3. //! must be greater or equal than + 1. //! //! Warning: and must be dimensionned //! properly. 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 //! 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_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 //! and then multiplies by the weights //! this just evaluates the current point //! 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 //! ththe CacheParameter is where the Cache was //! constructed the SpanLength is to normalize //! the polynomial in the cache to avoid bad conditioning //! effectsis just evaluates the current point 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! 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_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 //! and then multiplies by the weights //! this just evaluates the current point //! 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 //! ththe CacheParameter is where the Cache was //! constructed the SpanLength is to normalize //! the polynomial in the cache to avoid bad conditioning //! effectsis just evaluates the current point 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! 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_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 //! and then multiplies by the weights //! this just evaluates the current point //! 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 //! ththe CacheParameter is where the Cache was //! constructed the SpanLength is to normalize //! the polynomial in the cache to avoid bad conditioning //! effectsis just evaluates the current point 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! 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 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 //! and then multiplies by the weights //! this just evaluates the current point //! 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 //! ththe CacheParameter is where the Cache was //! constructed the SpanLength is to normalize //! the polynomial in the cache to avoid bad conditioning //! effectsis just evaluates the current point 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! the method PolesCoefficients. //! Warning: To be used for Beziercurves ONLY!!! 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 //! 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 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 //! 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 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); //! Perform the evaluation of the Taylor expansion //! of the Bspline normalized between 0 and 1. //! Structure of result optimized for BSplCLib_Cache. Standard_EXPORT static void BuildCache (const Standard_Real theParameter, const Standard_Real theSpanDomain, const Standard_Boolean thePeriodicFlag, const Standard_Integer theDegree, const Standard_Integer theSpanIndex, const TColStd_Array1OfReal& theFlatKnots, const TColgp_Array1OfPnt& thePoles, const TColStd_Array1OfReal* theWeights, TColStd_Array2OfReal& theCacheArray); //! Perform the evaluation of the Taylor expansion //! of the Bspline normalized between 0 and 1. //! Structure of result optimized for BSplCLib_Cache. Standard_EXPORT static void BuildCache (const Standard_Real theParameter, const Standard_Real theSpanDomain, const Standard_Boolean thePeriodicFlag, const Standard_Integer theDegree, const Standard_Integer theSpanIndex, const TColStd_Array1OfReal& theFlatKnots, const TColgp_Array1OfPnt2d& thePoles, const TColStd_Array1OfReal* theWeights, TColStd_Array2OfReal& theCacheArray); 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 //! evaluation of the Taylor expansion for beziercurves //! at parameter 0. //! Warning: To be used for Beziercurves ONLY!!! 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 //! flat knots for bezier curve of the specified degree. //! Raises OutOfRange if Degree > MaxDegree() Standard_EXPORT static const Standard_Real& FlatBezierKnots (const Standard_Integer Degree); //! builds the Schoenberg points from the flat knot //! used to interpolate a BSpline since the //! BSpline matrix is invertible. Standard_EXPORT static void BuildSchoenbergPoints (const Standard_Integer Degree, const TColStd_Array1OfReal& FlatKnots, TColStd_Array1OfReal& Parameters); //! Performs the interpolation of the data given in //! the Poles array according to the requests in //! ContactOrderArray that is : if //! ContactOrderArray(i) has value d it means that //! Poles(i) contains the dth derivative of the //! function to be interpolated. The length L of the //! following arrays must be the same : //! Parameters, ContactOrderArray, Poles, //! The length of FlatKnots is Degree + L + 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 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 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 //! the Poles array according to the requests in //! ContactOrderArray that is : if //! ContactOrderArray(i) has value d it means that //! Poles(i) contains the dth derivative of the //! function to be interpolated. The length L of the //! following arrays must be the same : //! Parameters, ContactOrderArray, Poles, //! The length of FlatKnots is Degree + L + 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 w //! ll 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 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 //! the Poles array according to the requests in //! ContactOrderArray that is : if //! ContactOrderArray(i) has value d it means that //! Poles(i) contains the dth derivative of the //! function to be interpolated. The length L of the //! following arrays must be the same : //! Parameters, ContactOrderArray, Poles, //! The length of FlatKnots is Degree + L + 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 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 //! the Poles array according to the requests in //! ContactOrderArray that is : if //! ContactOrderArray(i) has value d it means that //! Poles(i) contains the dth derivative of the //! function to be interpolated. The length L of the //! following arrays must be the same : //! Parameters, ContactOrderArray, Poles, //! The length of FlatKnots is Degree + L + 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 w //! ll report 0 if there was no //! problem else it will give the i 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 //! the Poles array according to the requests in //! ContactOrderArray that is : if //! ContactOrderArray(i) has value d it means that //! Poles(i) contains the dth derivative of the //! function to be interpolated. The length L of the //! following arrays must be the same : //! Parameters, ContactOrderArray //! The length of FlatKnots is Degree + L + 1 //! The PolesArray is an seen as an //! Array[1..N][1..ArrayDimension] with N = tge length //! of the parameters array //! 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 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 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 //! given u as parameter) to reach a new position //! Index1 and Index2 indicate the range of poles we can move //! (1, NbPoles-1) or (2, NbPoles) -> no constraint for one side //! don't enter (1,NbPoles) -> error: rigid move //! (2, NbPoles-1) -> the ends are enforced //! (3, NbPoles-2) -> the ends and the tangency are enforced //! if Problem in BSplineBasis calculation, no change for the curve //! and FirstIndex, LastIndex = 0 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 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 //! given u as parameter) to reach a new position //! Index1 and Index2 indicate the range of poles we can move //! (1, NbPoles-1) or (2, NbPoles) -> no constraint for one side //! don't enter (1,NbPoles) -> error: rigid move //! (2, NbPoles-1) -> the ends are enforced //! (3, NbPoles-2) -> the ends and the tangency are enforced //! if Problem in BSplineBasis calculation, no change for the curve //! and FirstIndex, LastIndex = 0 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 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 //! U is the parameter must be within the first FlatKnots and the //! last FlatKnots Delta is the amount the curve has to be moved //! DeltaDerivative is the amount the derivative has to be moved. //! Delta and DeltaDerivative must be array of dimension //! ArrayDimension Degree is the degree of the BSpline and the //! FlatKnots are the knots of the BSpline Starting Condition if = //! -1 means the starting point of the curve can move //! = 0 means the //! starting point of the curve cannot move but tangent starting //! point of the curve cannot move //! = 1 means the starting point and tangents cannot move //! = 2 means the starting point tangent and curvature cannot move //! = ... //! Same holds for EndingCondition //! Poles are the poles of the curve //! Weights are the weights of the curve if not NULL //! NewPoles are the poles of the deformed curve //! ErrorStatus will be 0 if no error happened //! 1 if there are not enough knots/poles //! the imposed conditions //! The way to solve this problem is to add knots to the BSpline //! If StartCondition = 1 and EndCondition = 1 then you need at least //! 4 + 2 = 6 poles so for example to have a C1 cubic you will need //! have at least 2 internal knots. 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_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 //! U is the parameter must be within the first FlatKnots and the //! last FlatKnots Delta is the amount the curve has to be moved //! DeltaDerivative is the amount the derivative has to be moved. //! Delta and DeltaDerivative must be array of dimension //! ArrayDimension Degree is the degree of the BSpline and the //! FlatKnots are the knots of the BSpline Starting Condition if = //! -1 means the starting point of the curve can move //! = 0 means the //! starting point of the curve cannot move but tangent starting //! point of the curve cannot move //! = 1 means the starting point and tangents cannot move //! = 2 means the starting point tangent and curvature cannot move //! = ... //! Same holds for EndingCondition //! Poles are the poles of the curve //! Weights are the weights of the curve if not NULL //! NewPoles are the poles of the deformed curve //! ErrorStatus will be 0 if no error happened //! 1 if there are not enough knots/poles //! the imposed conditions //! The way to solve this problem is to add knots to the BSpline //! If StartCondition = 1 and EndCondition = 1 then you need at least //! 4 + 2 = 6 poles so for example to have a C1 cubic you will need //! have at least 2 internal knots. 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_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 //! U is the parameter must be within the first FlatKnots and the //! last FlatKnots Delta is the amount the curve has to be moved //! DeltaDerivative is the amount the derivative has to be moved. //! Delta and DeltaDerivative must be array of dimension //! ArrayDimension Degree is the degree of the BSpline and the //! FlatKnots are the knots of the BSpline Starting Condition if = //! -1 means the starting point of the curve can move //! = 0 means the //! starting point of the curve cannot move but tangent starting //! point of the curve cannot move //! = 1 means the starting point and tangents cannot move //! = 2 means the starting point tangent and curvature cannot move //! = ... //! Same holds for EndingCondition //! Poles are the poles of the curve //! Weights are the weights of the curve if not NULL //! NewPoles are the poles of the deformed curve //! ErrorStatus will be 0 if no error happened //! 1 if there are not enough knots/poles //! the imposed conditions //! The way to solve this problem is to add knots to the BSpline //! If StartCondition = 1 and EndCondition = 1 then you need at least //! 4 + 2 = 6 poles so for example to have a C1 cubic you will need //! have at least 2 internal knots. 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_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 //! tolerance in U parameter space such that //! all u1 and u0 in the domain of the curve f(u) //! | u1 - u0 | < UTolerance and //! we have |f (u1) - f (u0)| < Tolerance3D 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 //! tolerance in U parameter space such that //! all u1 and u0 in the domain of the curve f(u) //! | u1 - u0 | < UTolerance and //! we have |f (u1) - f (u0)| < Tolerance3D 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 //! tolerance in U parameter space such that //! all u1 and u0 in the domain of the curve f(u) //! | u1 - u0 | < UTolerance and //! we have |f (u1) - f (u0)| < Tolerance3D 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 #endif // _BSplCLib_HeaderFile