--- /dev/null
+// 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 <Standard.hxx>
+#include <Standard_DefineAlloc.hxx>
+#include <Standard_Handle.hxx>
+
+#include <TColStd_Array1OfReal.hxx>
+#include <Standard_Real.hxx>
+#include <Standard_Integer.hxx>
+#include <TColStd_Array1OfInteger.hxx>
+#include <Standard_Boolean.hxx>
+#include <BSplCLib_KnotDistribution.hxx>
+#include <BSplCLib_MultDistribution.hxx>
+#include <GeomAbs_BSplKnotDistribution.hxx>
+#include <TColgp_Array1OfPnt.hxx>
+#include <TColgp_Array1OfPnt2d.hxx>
+#include <TColStd_HArray1OfReal.hxx>
+#include <TColStd_HArray1OfInteger.hxx>
+#include <BSplCLib_EvaluatorFunction.hxx>
+#include <TColStd_Array2OfReal.hxx>
+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 informations 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.
+//!
+//! Weights can be a null reference (BSplCLib::NoWeights())
+//! the curve is non rational.
+//!
+//! Mults can be a null reference (BSplCLib::NoMults())
+//! 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 X in the ordered set of real values XX.
+ //!
+ //! The elements in the table XX are either
+ //! monotonically increasing or monotonically
+ //! decreasing.
+ //!
+ //! The input value Iloc is used to initialize the
+ //! algorithm : if Iloc is outside of the bounds
+ //! [XX.Lower(), -- XX.Upper()] the bisection algorithm
+ //! is used else the routine searches from a previous
+ //! known position by increasing steps then converges
+ //! by bisection.
+ //!
+ //! This routine is used to locate a knot value in a
+ //! set of knots.
+ 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
+ //! 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 <Index> in the knots sequence
+ //! which multiplicities are <Mults>.
+ 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 <Knots> and <Mults> 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 <Knots>.
+ 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 <Weights>
+ //! 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 <U>, with <Degree> and <Dimension>.
+ //!
+ //! Poles is an array of Reals of size
+ //!
+ //! <Dimension> * <Degree>+1
+ //!
+ //! Containing the poles. At the end <Poles> 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 <U> with
+ //! the given <Degree> and the array of <Knots> on the
+ //! poles <Poles> of dimension <Dimension>. The schema
+ //! is computed until level <Depth> on a basis of
+ //! <Length+1> poles.
+ //!
+ //! * Knots is an array of reals of length :
+ //!
+ //! <Length> + <Degree>
+ //!
+ //! * Poles is an array of reals of length :
+ //!
+ //! (2 * <Length> + 1) * <Dimension>
+ //!
+ //! 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 <Tolerance> 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 <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 <U>. This
+ //! algorithm computes the value and all the derivatives
+ //! up to order N (N <= Degree).
+ //!
+ //! <Poles> is the original array of poles.
+ //!
+ //! The result in <Poles> 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 usefull 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 <LP> 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 <LP> poles for <Dimension> Boor scheme.
+ //! Starting from <Index> * <Dimension>, copy
+ //! <Length+1> 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 <Index>. If the Boor algorithm was perform
+ //! with <Length> and <Depth>.
+ 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
+ //! scheme of dimension <Dimension> to <Position> in
+ //! the array <Pole>. <Position> 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 <NbPoles, NbKnots> the new number of poles
+ //! and knots if the sequence of knots <AddKnots,
+ //! AddMults> is inserted in the sequence <Knots, Mults>.
+ //!
+ //! 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 <AddKnots> with
+ //! multiplicities <AddMults>. <AddKnots> 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 <NewKnots>
+ //! and <NewMults>.
+ //!
+ //! 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 <UMult>.
+ //!
+ //! 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 <Knots(Index)>
+ //! to <Mult>. If <Mult> 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 <Mults> after elevating the degree from
+ //! <Degree> to <NewDegree>. 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 <Dimension> form <Degree> to
+ //! <NewDegree>.
+ //!
+ //! The number of poles in the new curve is :
+ //!
+ //! Poles.Length() + (NewDegree - Degree) * Number of spans
+ //!
+ //! Where the number of spans is :
+ //!
+ //! LastUKnotIndex(Mults) - FirstUKnotIndex(Mults) + 1
+ //!
+ //! for a non-periodic curve
+ //!
+ //! And Knots.Length() - 1 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
+ //! untils 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 :
+ //!
+ //! knot : 0. 1. 2.
+ //! mult : 1 2 1
+ //!
+ //! The FirstUKnot is 2. because the sum of
+ //! multiplicities is Degree+1 : 1 + 2 + 1 = 4 = 3 + 1
+ //!
+ //! i.e. the first parameter of the curve is 2. and
+ //! will still be 2. after degree elevation. Let
+ //! raises 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 :
+ //!
+ //! knot : 1. 2.
+ //! mult : 3 2
+ //!
+ //! 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 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
+ //! Poles of the NotPeriodic Curve identical at the
+ //! periodic curve with a degree <Degree> , a
+ //! knots-distribution with Multiplicities <Mults>.
+ 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
+ //! Poles of the curve resulting of the trimming of the
+ //! BSplinecurve definded with <degree>, <knots>, <mults>
+ 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 <Index> is the the localization of the
+ //! parameter in the knot sequence. If <Index> 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 Side, 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 uppon 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 homogenously
+ //! 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 uppon 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 homogenously
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //!
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of 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& Status);
+
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //!
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of 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& Status);
+
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of 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& Status);
+
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of 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& Status);
+
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of a(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& Status);
+
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of a(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& Status);
+
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of a(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& Status);
+
+ //! 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 responsability to insure that conditions
+ //! 1. and 2. above are satisfied : no check whatsoever
+ //! is made in this method
+ //! Status will return 0 if OK else it will return the pivot index
+ //! of the matrix that was inverted to compute the multiplied
+ //! BSpline : the method used is interpolation at Schoenenberg
+ //! points of a(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& Status);
+
+ //! Perform the De Boor algorithm to evaluate a point at
+ //! parameter <U>, with <Degree> and <Dimension>.
+ //!
+ //! Poles is an array of Reals of size
+ //!
+ //! <Dimension> * <Degree>+1
+ //!
+ //! Containing the poles. At the end <Poles> 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 <U>, with <Degree> and <Dimension>.
+ //! 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: <PolesResult> and <WeightsResult> 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
+ //! <C1Coefficient> is the coefficient of reparametrisation
+ //! <Continuity> must be equal to 1, 2 or 3.
+ //! <Degree> must be greater or equal than <Continuity> + 1.
+ //!
+ //! Warning: <KnotsResult> and <PolesResult> 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 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 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) containes 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) containes 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) containes 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) containes 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) containes 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 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
+ //! 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 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
+ //! 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 cuve cannot move but tangen 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 Rational = Standard_True
+ //! 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_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
+ //! 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 cuve cannot move but tangen 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 Rational = Standard_True
+ //! 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_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
+ //! 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 cuve cannot move but tangen 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 Rational = Standard_True
+ //! 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_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
+ //! 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 <BSplCLib.lxx>
+
+
+
+
+
+#endif // _BSplCLib_HeaderFile
projects / occt.git / blobdiff