BSplCLib Class Reference

BSplCLib B-spline curve Library. More...

#include <BSplCLib.hxx>

Static Public Member Functions
static void	Hunt (const NCollection_Array1< double > &theArray, const double theX, int &theXPos)
	This routine searches the position of the real value theX in the monotonically increasing set of real values theArray using bisection algorithm.
static int	FirstUKnotIndex (const int Degree, const NCollection_Array1< int > &Mults)
	Computes the index of the knots value which gives the start point of the curve.
static int	LastUKnotIndex (const int Degree, const NCollection_Array1< int > &Mults)
	Computes the index of the knots value which gives the end point of the curve.
static int	FlatIndex (const int Degree, const int Index, const NCollection_Array1< int > &Mults, const bool Periodic)
	Computes the index of the flats knots sequence corresponding to <Index> in the knots sequence which multiplicities are <Mults>.
static void	LocateParameter (const int Degree, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const double U, const bool IsPeriodic, const int FromK1, const int ToK2, int &KnotIndex, double &NewU)
	Locates the parametric value U in the knots sequence between the knot K1 and the knot K2. The value return in Index verifies.
static void	LocateParameter (const int Degree, const NCollection_Array1< double > &Knots, const double U, const bool IsPeriodic, const int FromK1, const int ToK2, int &KnotIndex, double &NewU)
	Locates the parametric value U in the knots sequence between the knot K1 and the knot K2. The value return in Index verifies.
static void	LocateParameter (const int Degree, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, const double U, const bool Periodic, int &Index, double &NewU)
static int	MaxKnotMult (const NCollection_Array1< int > &Mults, const int K1, const int K2)
	Finds the greatest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.
static int	MinKnotMult (const NCollection_Array1< int > &Mults, const int K1, const int K2)
	Finds the lowest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.
static int	NbPoles (const int Degree, const bool Periodic, const NCollection_Array1< int > &Mults)
	Returns the number of poles of the curve. Returns 0 if one of the multiplicities is incorrect.
static int	KnotSequenceLength (const NCollection_Array1< int > &Mults, const int Degree, const bool Periodic)
	Returns the length of the sequence of knots with repetition.
static void	KnotSequence (const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< double > &KnotSeq, const bool Periodic=false)
static void	KnotSequence (const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const int Degree, const bool Periodic, NCollection_Array1< double > &KnotSeq)
	Computes the sequence of knots KnotSeq with repetition of the knots of multiplicity greater than 1.
static int	KnotsLength (const NCollection_Array1< double > &KnotSeq, const bool Periodic=false)
	Returns thelength of the sequence of knots (and Mults) without repetition.
static void	Knots (const NCollection_Array1< double > &KnotSeq, NCollection_Array1< double > &Knots, NCollection_Array1< int > &Mults, const bool Periodic=false)
	Computes the sequence of knots Knots without repetition of the knots of multiplicity greater than 1.
static BSplCLib_KnotDistribution	KnotForm (const NCollection_Array1< double > &Knots, const int FromK1, const int ToK2)
	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>.
static BSplCLib_MultDistribution	MultForm (const NCollection_Array1< int > &Mults, const int FromK1, const int ToK2)
	Analyses the distribution of multiplicities between the knot FromK1 and the Knot ToK2.
static void	KnotAnalysis (const int Degree, const bool Periodic, const NCollection_Array1< double > &CKnots, const NCollection_Array1< int > &CMults, GeomAbs_BSplKnotDistribution &KnotForm, int &MaxKnotMult)
	Analyzes the array of knots. Returns the form and the maximum knot multiplicity.
static void	Reparametrize (const double U1, const double U2, NCollection_Array1< double > &Knots)
	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.
static void	Reverse (NCollection_Array1< double > &Knots)
	Reverses the array knots to become the knots sequence of the reversed curve.
static void	Reverse (NCollection_Array1< int > &Mults)
	Reverses the array of multiplicities.
static void	Reverse (NCollection_Array1< gp_Pnt > &Poles, const int Last)
	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.
static void	Reverse (NCollection_Array1< gp_Pnt2d > &Poles, const int Last)
	Reverses the array of poles.
static void	Reverse (NCollection_Array1< double > &Weights, const int Last)
	Reverses the array of poles.
static bool	IsRational (const NCollection_Array1< double > &Weights, const int I1, const int I2, const double Epsilon=0.0)
	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.
static constexpr int	MaxDegree ()
	returns the degree maxima for a BSplineCurve.
static void	Eval (const double U, const int Degree, double &Knots, const int Dimension, double &Poles)
	Perform the Boor algorithm to evaluate a point at parameter , with <Degree> and <Dimension>.
static void	BoorScheme (const double U, const int Degree, double &Knots, const int Dimension, double &Poles, const int Depth, const int Length)
	Performs the Boor Algorithm at parameter 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.
static bool	AntiBoorScheme (const double U, const int Degree, double &Knots, const int Dimension, double &Poles, const int Depth, const int Length, const double Tolerance)
	Compute the content of Pole before the BoorScheme. This method is used to remove poles.
static void	Derivative (const int Degree, double &Knots, const int Dimension, const int Length, const int Order, double &Poles)
	Computes the poles of the BSpline giving the derivatives of order <Order>.
static void	Bohm (const double U, const int Degree, const int N, double &Knots, const int Dimension, double &Poles)
	Performs the Bohm Algorithm at parameter . This algorithm computes the value and all the derivatives up to order N (N <= Degree).
static NCollection_Array1< double > *	NoWeights ()
	Used as argument for a non rational curve.
static NCollection_Array1< int > *	NoMults ()
	Used as argument for a flatknots evaluation.
static constexpr int	MaxUnitWeightsSize ()
	Returns the maximum number of elements supported by the pre-allocated unit weights array (2049). For sizes larger than this, UnitWeights() will allocate a new array.
static NCollection_Array1< double >	UnitWeights (const int theNbElems)
	Returns an NCollection_Array1<double> filled with 1.0 values. If theNbElems <= MaxUnitWeightsSize(), references a pre-allocated global array (zero allocation). Otherwise, allocates a new array and fills with 1.0.
static const double *	UnitWeightsData ()
	Returns a pointer to the pre-allocated unit weights static array. The array contains MaxUnitWeightsSize() elements, all equal to 1.0.
static void	BuildKnots (const int Degree, const int Index, const bool Periodic, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, double &LK)
	Stores in LK the useful knots for the BoorSchem on the span Knots(Index) - Knots(Index+1)
static int	PoleIndex (const int Degree, const int Index, const bool Periodic, const NCollection_Array1< int > &Mults)
	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().
static void	BuildEval (const int Degree, const int Index, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > *Weights, double &LP)
static void	BuildEval (const int Degree, const int Index, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, double &LP)
static void	BuildEval (const int Degree, const int Index, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, double &LP)
	Copy in <LP> the poles and weights for the Eval scheme. starting from Poles(Poles.Lower()+Index)
static void	BuildBoor (const int Index, const int Length, const int Dimension, const NCollection_Array1< double > &Poles, double &LP)
	Copy in <LP> poles for <Dimension> Boor scheme. Starting from <Index> * <Dimension>, copy <Length+1> poles.
static int	BoorIndex (const int Index, const int Length, const int Depth)
	Returns the index in the Boor result array of the poles <Index>. If the Boor algorithm was perform with <Length> and <Depth>.
static void	GetPole (const int Index, const int Length, const int Depth, const int Dimension, double &LocPoles, int &Position, NCollection_Array1< double > &Pole)
	Copy the pole at position <Index> in the Boor scheme of dimension <Dimension> to <Position> in the array <Pole>. <Position> is updated.
static bool	PrepareInsertKnots (const int Degree, const bool Periodic, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &AddKnots, const NCollection_Array1< int > *AddMults, int &NbPoles, int &NbKnots, const double Epsilon, const bool Add=true)
	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>.
static void	InsertKnots (const int Degree, const bool Periodic, const int Dimension, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &AddKnots, const NCollection_Array1< int > *AddMults, NCollection_Array1< double > &NewPoles, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Epsilon, const bool Add=true)
static void	InsertKnots (const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &AddKnots, const NCollection_Array1< int > *AddMults, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Epsilon, const bool Add=true)
static void	InsertKnots (const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &AddKnots, const NCollection_Array1< int > *AddMults, NCollection_Array1< gp_Pnt2d > &NewPoles, NCollection_Array1< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Epsilon, const bool Add=true)
	Insert a sequence of knots <AddKnots> with multiplicities <AddMults>. <AddKnots> must be a non decreasing sequence and verifies:
static void	InsertKnot (const int UIndex, const double U, const int UMult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights)
static void	InsertKnot (const int UIndex, const double U, const int UMult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt2d > &NewPoles, NCollection_Array1< double > *NewWeights)
	Insert a new knot U of multiplicity UMult in the knot sequence.
static void	RaiseMultiplicity (const int KnotIndex, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights)
static void	RaiseMultiplicity (const int KnotIndex, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt2d > &NewPoles, NCollection_Array1< double > *NewWeights)
	Raise the multiplicity of knot to <UMult>.
static bool	RemoveKnot (const int Index, const int Mult, const int Degree, const bool Periodic, const int Dimension, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< double > &NewPoles, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Tolerance)
static bool	RemoveKnot (const int Index, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Tolerance)
static bool	RemoveKnot (const int Index, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt2d > &NewPoles, NCollection_Array1< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, const double Tolerance)
	Decrement the multiplicity of <Knots(Index)> to <Mult>. If <Mult> is null the knot is removed.
static int	IncreaseDegreeCountKnots (const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array1< int > &Mults)
	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.
static void	IncreaseDegree (const int Degree, const int NewDegree, const bool Periodic, const int Dimension, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< double > &NewPoles, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults)
static void	IncreaseDegree (const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults)
static void	IncreaseDegree (const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, NCollection_Array1< gp_Pnt2d > &NewPoles, NCollection_Array1< double > *NewWeights, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults)
static void	IncreaseDegree (const int NewDegree, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights)
static void	IncreaseDegree (const int theNewDegree, const NCollection_Array1< gp_Pnt2d > &thePoles, const NCollection_Array1< double > *theWeights, NCollection_Array1< gp_Pnt2d > &theNewPoles, NCollection_Array1< double > *theNewWeights)
	Increase the degree of a bspline (or bezier) curve of dimension theDimension form theDegree to theNewDegree.
static void	PrepareUnperiodize (const int Degree, const NCollection_Array1< int > &Mults, int &NbKnots, int &NbPoles)
	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>.
static void	Unperiodize (const int Degree, const int Dimension, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &Knots, const NCollection_Array1< double > &Poles, NCollection_Array1< int > &NewMults, NCollection_Array1< double > &NewKnots, NCollection_Array1< double > &NewPoles)
static void	Unperiodize (const int Degree, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &Knots, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, NCollection_Array1< int > &NewMults, NCollection_Array1< double > &NewKnots, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights)
static void	Unperiodize (const int Degree, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &Knots, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, NCollection_Array1< int > &NewMults, NCollection_Array1< double > &NewKnots, NCollection_Array1< gp_Pnt2d > &NewPoles, NCollection_Array1< double > *NewWeights)
static void	PrepareTrimming (const int Degree, const bool Periodic, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const double U1, const double U2, int &NbKnots, int &NbPoles)
	Set in <NbKnots> and <NbPoles> the number of Knots and Poles of the curve resulting from the trimming of the BSplinecurve defined with <degree>, <knots>, <mults>
static void	Trimming (const int Degree, const bool Periodic, const int Dimension, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< double > &Poles, const double U1, const double U2, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, NCollection_Array1< double > &NewPoles)
static void	Trimming (const int Degree, const bool Periodic, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const double U1, const double U2, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, NCollection_Array1< gp_Pnt > &NewPoles, NCollection_Array1< double > *NewWeights)
static void	Trimming (const int Degree, const bool Periodic, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const double U1, const double U2, NCollection_Array1< double > &NewKnots, NCollection_Array1< int > &NewMults, NCollection_Array1< gp_Pnt2d > &NewPoles, NCollection_Array1< double > *NewWeights)
static void	D0 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, double &P)
static void	D0 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt &P)
static void	D0 (const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt2d &P)
static void	D0 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &P)
static void	D0 (const double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &P)
static void	D1 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, double &P, double &V)
static void	D1 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt &P, gp_Vec &V)
static void	D1 (const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt2d &P, gp_Vec2d &V)
static void	D1 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &P, gp_Vec &V)
static void	D1 (const double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &P, gp_Vec2d &V)
static void	D2 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, double &P, double &V1, double &V2)
static void	D2 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)
static void	D2 (const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)
static void	D2 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)
static void	D2 (const double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)
static void	D3 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, double &P, double &V1, double &V2, double &V3)
static void	D3 (const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)
static void	D3 (const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)
static void	D3 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)
static void	D3 (const double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)
static void	DN (const double U, const int N, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, double &VN)
static void	DN (const double U, const int N, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Vec &VN)
static void	DN (const double U, const int N, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &Knots, const NCollection_Array1< int > *Mults, gp_Vec2d &V)
static void	DN (const double U, const int N, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > &Weights, gp_Pnt &P, gp_Vec &VN)
static void	DN (const double U, const int N, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > &Weights, gp_Pnt2d &P, gp_Vec2d &VN)
	The above functions compute values and derivatives in the following situations:
static int	EvalBsplineBasis (const int DerivativeOrder, const int Order, const NCollection_Array1< double > &FlatKnots, const double Parameter, int &FirstNonZeroBsplineIndex, math_Matrix &BsplineBasis, const bool isPeriodic=false)
	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.
static int	BuildBSpMatrix (const NCollection_Array1< double > &Parameters, const NCollection_Array1< int > &OrderArray, const NCollection_Array1< double > &FlatKnots, const int Degree, math_Matrix &Matrix, int &UpperBandWidth, int &LowerBandWidth)
	This Builds a fully blown Matrix of (ni) Bi (tj)
static int	FactorBandedMatrix (math_Matrix &Matrix, const int UpperBandWidth, const int LowerBandWidth, int &PivotIndexProblem)
	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
static int	SolveBandedSystem (const math_Matrix &Matrix, const int UpperBandWidth, const int LowerBandWidth, const int ArrayDimension, double &Array)
	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.
static int	SolveBandedSystem (const math_Matrix &Matrix, const int UpperBandWidth, const int LowerBandWidth, NCollection_Array1< gp_Pnt2d > &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.
static int	SolveBandedSystem (const math_Matrix &Matrix, const int UpperBandWidth, const int LowerBandWidth, NCollection_Array1< gp_Pnt > &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.
static int	SolveBandedSystem (const math_Matrix &Matrix, const int UpperBandWidth, const int LowerBandWidth, const bool HomogenousFlag, const int ArrayDimension, double &Array, double &Weights)
static int	SolveBandedSystem (const math_Matrix &Matrix, const int UpperBandWidth, const int LowerBandWidth, const bool HomogenousFlag, NCollection_Array1< gp_Pnt2d > &Array, NCollection_Array1< double > &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 Weights are treated homogeneously that is that those are interpolated as they are and result is returned without division by the interpolated weights.
static int	SolveBandedSystem (const math_Matrix &Matrix, const int UpperBandWidth, const int LowerBandWidth, const bool HomogeneousFlag, NCollection_Array1< gp_Pnt > &Array, NCollection_Array1< double > &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 Weights are treated homogeneously that is that those are interpolated as they are and result is returned without division by the interpolated weights.
static void	MergeBSplineKnots (const double Tolerance, const double StartValue, const double EndValue, const int Degree1, const NCollection_Array1< double > &Knots1, const NCollection_Array1< int > &Mults1, const int Degree2, const NCollection_Array1< double > &Knots2, const NCollection_Array1< int > &Mults2, int &NumPoles, occ::handle< NCollection_HArray1< double > > &NewKnots, occ::handle< NCollection_HArray1< int > > &NewMults)
	Merges two knot vector by setting the starting and ending values to StartValue and EndValue.
static void	FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const int PolesDimension, double &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, double &NewPoles, int &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:
static void	FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, NCollection_Array1< double > &NewPoles, int &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:
static void	FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt > &NewPoles, int &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
static void	FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt2d > &NewPoles, int &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
static void	FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const int PolesDimension, double &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, double &NewPoles, int &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
static void	FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const NCollection_Array1< double > &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, NCollection_Array1< double > &NewPoles, int &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
static void	FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt2d > &NewPoles, int &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
static void	FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const int BSplineDegree, const NCollection_Array1< double > &BSplineFlatKnots, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > &FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt > &NewPoles, int &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
static void	Eval (const double U, const bool PeriodicFlag, const int DerivativeRequest, int &ExtrapMode, const int Degree, const NCollection_Array1< double > &FlatKnots, const int ArrayDimension, double &Poles, double &Result)
	Perform the De Boor algorithm to evaluate a point at parameter , with <Degree> and <Dimension>.
static void	Eval (const double U, const bool PeriodicFlag, const int DerivativeRequest, int &ExtrapMode, const int Degree, const NCollection_Array1< double > &FlatKnots, const int ArrayDimension, double &Poles, double &Weights, double &PolesResult, double &WeightsResult)
	Perform the De Boor algorithm to evaluate a point at parameter , 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.
static void	Eval (const double U, const bool PeriodicFlag, const bool HomogeneousFlag, int &ExtrapMode, const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > &Weights, gp_Pnt &Point, double &Weight)
	Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point.
static void	Eval (const double U, const bool PeriodicFlag, const bool HomogeneousFlag, int &ExtrapMode, const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > &Weights, gp_Pnt2d &Point, double &Weight)
	Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point.
static void	TangExtendToConstraint (const NCollection_Array1< double > &FlatKnots, const double C1Coefficient, const int NumPoles, double &Poles, const int Dimension, const int Degree, const NCollection_Array1< double > &ConstraintPoint, const int Continuity, const bool After, int &NbPolesResult, int &NbKnotsRsult, double &KnotsResult, double &PolesResult)
	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.
static void	CacheD0 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &Point)
	Perform the evaluation of the of the cache the parameter must be normalized between the 0 and 1 for the span. The Cache must be valid when calling this routine. Geom Package will insure that. and then multiplies by the weights this just evaluates the current point the CacheParameter is where the Cache was constructed the SpanLength is to normalize the polynomial in the cache to avoid bad conditioning effects.
static void	CacheD0 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &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.
static void	CoefsD0 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *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 double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &Point)
	Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
static void	CacheD1 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &Point, gp_Vec &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.
static void	CacheD1 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &Point, gp_Vec2d &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.
static void	CoefsD1 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *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 double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *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	CacheD2 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &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.
static void	CacheD2 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &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.
static void	CoefsD2 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *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 double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *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	CacheD3 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2, gp_Vec &Vec3)
	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.
static void	CacheD3 (const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2, gp_Vec2d &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.
static void	CoefsD3 (const double U, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *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 double U, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *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	BuildCache (const double U, const double InverseOfSpanDomain, const bool PeriodicFlag, const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, NCollection_Array1< gp_Pnt > &CachePoles, NCollection_Array1< double > *CacheWeights)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expansion for the numerator and stores it in CachePoles.
static void	BuildCache (const double U, const double InverseOfSpanDomain, const bool PeriodicFlag, const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, NCollection_Array1< gp_Pnt2d > &CachePoles, NCollection_Array1< double > *CacheWeights)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expansion for the numerator and stores it in CachePoles.
static void	BuildCache (const double theParameter, const double theSpanDomain, const bool thePeriodicFlag, const int theDegree, const int theSpanIndex, const NCollection_Array1< double > &theFlatKnots, const NCollection_Array1< gp_Pnt > &thePoles, const NCollection_Array1< double > *theWeights, NCollection_Array2< double > &theCacheArray)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplCLib_Cache.
static void	BuildCache (const double theParameter, const double theSpanDomain, const bool thePeriodicFlag, const int theDegree, const int theSpanIndex, const NCollection_Array1< double > &theFlatKnots, const NCollection_Array1< gp_Pnt2d > &thePoles, const NCollection_Array1< double > *theWeights, NCollection_Array2< double > &theCacheArray)
	Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplCLib_Cache.
static void	PolesCoefficients (const NCollection_Array1< gp_Pnt2d > &Poles, NCollection_Array1< gp_Pnt2d > &CachePoles)
static void	PolesCoefficients (const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, NCollection_Array1< gp_Pnt2d > &CachePoles, NCollection_Array1< double > *CacheWeights)
static void	PolesCoefficients (const NCollection_Array1< gp_Pnt > &Poles, NCollection_Array1< gp_Pnt > &CachePoles)
static void	PolesCoefficients (const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, NCollection_Array1< gp_Pnt > &CachePoles, NCollection_Array1< double > *CacheWeights)
	Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziercurves at parameter 0. Warning: To be used for Beziercurves ONLY!!!
static const double &	FlatBezierKnots (const int Degree)
	Returns pointer to statically allocated array representing flat knots for bezier curve of the specified degree. Raises OutOfRange if Degree > MaxDegree()
static void	BuildSchoenbergPoints (const int Degree, const NCollection_Array1< double > &FlatKnots, NCollection_Array1< double > &Parameters)
	builds the Schoenberg points from the flat knot used to interpolate a BSpline since the BSpline matrix is invertible.
static void	Interpolate (const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< double > &Parameters, const NCollection_Array1< int > &ContactOrderArray, NCollection_Array1< gp_Pnt > &Poles, int &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 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.
static void	Interpolate (const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< double > &Parameters, const NCollection_Array1< int > &ContactOrderArray, NCollection_Array1< gp_Pnt2d > &Poles, int &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.
static void	Interpolate (const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< double > &Parameters, const NCollection_Array1< int > &ContactOrderArray, NCollection_Array1< gp_Pnt > &Poles, NCollection_Array1< double > &Weights, int &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.
static void	Interpolate (const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< double > &Parameters, const NCollection_Array1< int > &ContactOrderArray, NCollection_Array1< gp_Pnt2d > &Poles, NCollection_Array1< double > &Weights, int &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 i.
static void	Interpolate (const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< double > &Parameters, const NCollection_Array1< int > &ContactOrderArray, const int ArrayDimension, double &Poles, int &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.
static void	Interpolate (const int Degree, const NCollection_Array1< double > &FlatKnots, const NCollection_Array1< double > &Parameters, const NCollection_Array1< int > &ContactOrderArray, const int ArrayDimension, double &Poles, double &Weights, int &InversionProblem)
static void	MovePoint (const double U, const gp_Vec2d &Displ, const int Index1, const int Index2, const int Degree, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &FlatKnots, int &FirstIndex, int &LastIndex, NCollection_Array1< gp_Pnt2d > &NewPoles)
	Find the new poles which allows an old point (with a given 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.
static void	MovePoint (const double U, const gp_Vec &Displ, const int Index1, const int Index2, const int Degree, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &FlatKnots, int &FirstIndex, int &LastIndex, NCollection_Array1< gp_Pnt > &NewPoles)
	Find the new poles which allows an old point (with a given 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.
static void	MovePointAndTangent (const double U, const int ArrayDimension, double &Delta, double &DeltaDerivative, const double Tolerance, const int Degree, const int StartingCondition, const int EndingCondition, double &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &FlatKnots, double &NewPoles, int &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.
static void	MovePointAndTangent (const double U, const gp_Vec &Delta, const gp_Vec &DeltaDerivative, const double Tolerance, const int Degree, const int StartingCondition, const int EndingCondition, const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &FlatKnots, NCollection_Array1< gp_Pnt > &NewPoles, int &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.
static void	MovePointAndTangent (const double U, const gp_Vec2d &Delta, const gp_Vec2d &DeltaDerivative, const double Tolerance, const int Degree, const int StartingCondition, const int EndingCondition, const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &FlatKnots, NCollection_Array1< gp_Pnt2d > &NewPoles, int &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.
static void	Resolution (double &PolesArray, const int ArrayDimension, const int NumPoles, const NCollection_Array1< double > *Weights, const NCollection_Array1< double > &FlatKnots, const int Degree, const double Tolerance3D, double &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
static void	Resolution (const NCollection_Array1< gp_Pnt > &Poles, const NCollection_Array1< double > *Weights, const int NumPoles, const NCollection_Array1< double > &FlatKnots, const int Degree, const double Tolerance3D, double &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
static void	Resolution (const NCollection_Array1< gp_Pnt2d > &Poles, const NCollection_Array1< double > *Weights, const int NumPoles, const NCollection_Array1< double > &FlatKnots, const int Degree, const double Tolerance3D, double &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
static int	Intervals (const NCollection_Array1< double > &theKnots, const NCollection_Array1< int > &theMults, int theDegree, bool isPeriodic, int theContinuity, double theFirst, double theLast, double theTolerance, NCollection_Array1< double > *theIntervals)
	Splits the given range to BSpline intervals of given continuity.

Detailed Description

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 : NCollection_Array1<gp_Pnt>(2d) Poles . its weights : NCollection_Array1<double> Weights . its knots : NCollection_Array1<double> Knots . its multiplicities : NCollection_Array1<int> Mults . its degree : int Degree . its periodicity : bool 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

Member Function Documentation

AntiBoorScheme()

static bool BSplCLib::AntiBoorScheme ( const double U, const int Degree, double & Knots, const int Dimension, double & Poles, const int Depth, const int Length, const double Tolerance )

static

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.

Bohm()

static void BSplCLib::Bohm ( const double U, const int Degree, const int N, double & Knots, const int Dimension, double & Poles )

static

Performs the Bohm Algorithm at parameter . 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.

BoorIndex()

static int BSplCLib::BoorIndex ( const int Index, const int Length, const int Depth )

static

Returns the index in the Boor result array of the poles <Index>. If the Boor algorithm was perform with <Length> and <Depth>.

BoorScheme()

static void BSplCLib::BoorScheme ( const double U, const int Degree, double & Knots, const int Dimension, double & Poles, const int Depth, const int Length )

static

Performs the Boor Algorithm at parameter 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).

BuildBoor()

static void BSplCLib::BuildBoor ( const int Index, const int Length, const int Dimension, const NCollection_Array1< double > & Poles, double & LP )

static

Copy in <LP> poles for <Dimension> Boor scheme. Starting from <Index> * <Dimension>, copy <Length+1> poles.

BuildBSpMatrix()

static int BSplCLib::BuildBSpMatrix ( const NCollection_Array1< double > & Parameters, const NCollection_Array1< int > & OrderArray, const NCollection_Array1< double > & FlatKnots, const int Degree, math_Matrix & Matrix, int & UpperBandWidth, int & LowerBandWidth )

static

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

BuildCache() [1/4]

static void BSplCLib::BuildCache ( const double theParameter, const double theSpanDomain, const bool thePeriodicFlag, const int theDegree, const int theSpanIndex, const NCollection_Array1< double > & theFlatKnots, const NCollection_Array1< gp_Pnt > & thePoles, const NCollection_Array1< double > * theWeights, NCollection_Array2< double > & theCacheArray )

static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplCLib_Cache.

BuildCache() [2/4]

static void BSplCLib::BuildCache ( const double theParameter, const double theSpanDomain, const bool thePeriodicFlag, const int theDegree, const int theSpanIndex, const NCollection_Array1< double > & theFlatKnots, const NCollection_Array1< gp_Pnt2d > & thePoles, const NCollection_Array1< double > * theWeights, NCollection_Array2< double > & theCacheArray )

static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplCLib_Cache.

BuildCache() [3/4]

static void BSplCLib::BuildCache ( const double U, const double InverseOfSpanDomain, const bool PeriodicFlag, const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, NCollection_Array1< gp_Pnt > & CachePoles, NCollection_Array1< double > * CacheWeights )

static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expansion for the numerator and stores it in CachePoles.

BuildCache() [4/4]

static void BSplCLib::BuildCache ( const double U, const double InverseOfSpanDomain, const bool PeriodicFlag, const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, NCollection_Array1< gp_Pnt2d > & CachePoles, NCollection_Array1< double > * CacheWeights )

static

Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expansion for the numerator and stores it in CachePoles.

BuildEval() [1/3]

static void BSplCLib::BuildEval ( const int Degree, const int Index, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > * Weights, double & LP )

static

BuildEval() [2/3]

static void BSplCLib::BuildEval ( const int Degree, const int Index, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, double & LP )

static

BuildEval() [3/3]

static void BSplCLib::BuildEval ( const int Degree, const int Index, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, double & LP )

static

Copy in <LP> the poles and weights for the Eval scheme. starting from Poles(Poles.Lower()+Index)

BuildKnots()

static void BSplCLib::BuildKnots ( const int Degree, const int Index, const bool Periodic, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, double & LK )

static

Stores in LK the useful knots for the BoorSchem on the span Knots(Index) - Knots(Index+1)

BuildSchoenbergPoints()

static void BSplCLib::BuildSchoenbergPoints ( const int Degree, const NCollection_Array1< double > & FlatKnots, NCollection_Array1< double > & Parameters )

static

builds the Schoenberg points from the flat knot used to interpolate a BSpline since the BSpline matrix is invertible.

CacheD0() [1/2]

static void BSplCLib::CacheD0 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point )

static

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.

CacheD0() [2/2]

static void BSplCLib::CacheD0 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point )

static

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.

CacheD1() [1/2]

static void BSplCLib::CacheD1 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point, gp_Vec & Vec )

static

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.

CacheD1() [2/2]

static void BSplCLib::CacheD1 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point, gp_Vec2d & Vec )

static

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.

CacheD2() [1/2]

static void BSplCLib::CacheD2 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point, gp_Vec & Vec1, gp_Vec & Vec2 )

static

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.

CacheD2() [2/2]

static void BSplCLib::CacheD2 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point, gp_Vec2d & Vec1, gp_Vec2d & Vec2 )

static

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.

CacheD3() [1/2]

static void BSplCLib::CacheD3 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point, gp_Vec & Vec1, gp_Vec & Vec2, gp_Vec & Vec3 )

static

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.

CacheD3() [2/2]

static void BSplCLib::CacheD3 ( const double U, const int Degree, const double CacheParameter, const double SpanLenght, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point, gp_Vec2d & Vec1, gp_Vec2d & Vec2, gp_Vec2d & Vec3 )

static

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.

CoefsD0() [1/2]

static void BSplCLib::CoefsD0 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point )

static

Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

CoefsD0() [2/2]

static void BSplCLib::CoefsD0 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point )

static

Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

CoefsD1() [1/2]

static void BSplCLib::CoefsD1 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point, gp_Vec & Vec )

static

Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

CoefsD1() [2/2]

static void BSplCLib::CoefsD1 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point, gp_Vec2d & Vec )

static

Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

CoefsD2() [1/2]

static void BSplCLib::CoefsD2 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point, gp_Vec & Vec1, gp_Vec & Vec2 )

static

Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

CoefsD2() [2/2]

static void BSplCLib::CoefsD2 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point, gp_Vec2d & Vec1, gp_Vec2d & Vec2 )

static

Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

CoefsD3() [1/2]

static void BSplCLib::CoefsD3 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & Point, gp_Vec & Vec1, gp_Vec & Vec2, gp_Vec & Vec3 )

static

Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

CoefsD3() [2/2]

static void BSplCLib::CoefsD3 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & Point, gp_Vec2d & Vec1, gp_Vec2d & Vec2, gp_Vec2d & Vec3 )

static

Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

D0() [1/5]

static void BSplCLib::D0 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, double & P )

static

D0() [2/5]

static void BSplCLib::D0 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt & P )

static

D0() [3/5]

static void BSplCLib::D0 ( const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt2d & P )

static

D0() [4/5]

static void BSplCLib::D0 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & P )

static

D0() [5/5]

static void BSplCLib::D0 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & P )

static

D1() [1/5]

static void BSplCLib::D1 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, double & P, double & V )

static

D1() [2/5]

static void BSplCLib::D1 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt & P, gp_Vec & V )

static

D1() [3/5]

static void BSplCLib::D1 ( const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt2d & P, gp_Vec2d & V )

static

D1() [4/5]

static void BSplCLib::D1 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & P, gp_Vec & V )

static

D1() [5/5]

static void BSplCLib::D1 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & P, gp_Vec2d & V )

static

D2() [1/5]

static void BSplCLib::D2 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, double & P, double & V1, double & V2 )

static

D2() [2/5]

static void BSplCLib::D2 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )

static

D2() [3/5]

static void BSplCLib::D2 ( const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )

static

D2() [4/5]

static void BSplCLib::D2 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )

static

D2() [5/5]

static void BSplCLib::D2 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )

static

D3() [1/5]

static void BSplCLib::D3 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, double & P, double & V1, double & V2, double & V3 )

static

D3() [2/5]

static void BSplCLib::D3 ( const double U, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )

static

D3() [3/5]

static void BSplCLib::D3 ( const double U, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )

static

D3() [4/5]

static void BSplCLib::D3 ( const double U, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )

static

D3() [5/5]

static void BSplCLib::D3 ( const double U, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )

static

Derivative()

static void BSplCLib::Derivative ( const int Degree, double & Knots, const int Dimension, const int Length, const int Order, double & Poles )

static

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).

DN() [1/5]

static void BSplCLib::DN ( const double U, const int N, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, double & VN )

static

DN() [2/5]

static void BSplCLib::DN ( const double U, const int N, const int Index, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Vec & VN )

static

DN() [3/5]

static void BSplCLib::DN ( const double U, const int N, const int UIndex, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, gp_Vec2d & V )

static

DN() [4/5]

static void BSplCLib::DN ( const double U, const int N, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > & Weights, gp_Pnt & P, gp_Vec & VN )

static

DN() [5/5]

static void BSplCLib::DN ( const double U, const int N, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > & Weights, gp_Pnt2d & P, gp_Vec2d & VN )

static

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 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.

Eval() [1/5]

static void BSplCLib::Eval ( const double U, const bool PeriodicFlag, const bool HomogeneousFlag, int & ExtrapMode, const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > & Weights, gp_Pnt & Point, double & Weight )

static

Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point.

Eval() [2/5]

static void BSplCLib::Eval ( const double U, const bool PeriodicFlag, const bool HomogeneousFlag, int & ExtrapMode, const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > & Weights, gp_Pnt2d & Point, double & Weight )

static

Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point.

Eval() [3/5]

static void BSplCLib::Eval ( const double U, const bool PeriodicFlag, const int DerivativeRequest, int & ExtrapMode, const int Degree, const NCollection_Array1< double > & FlatKnots, const int ArrayDimension, double & Poles, double & Result )

static

Perform the De Boor algorithm to evaluate a point at parameter , 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

Eval() [4/5]

static void BSplCLib::Eval ( const double U, const bool PeriodicFlag, const int DerivativeRequest, int & ExtrapMode, const int Degree, const NCollection_Array1< double > & FlatKnots, const int ArrayDimension, double & Poles, double & Weights, double & PolesResult, double & WeightsResult )

static

Perform the De Boor algorithm to evaluate a point at parameter , 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 dimensioned properly.

Eval() [5/5]

static void BSplCLib::Eval ( const double U, const int Degree, double & Knots, const int Dimension, double & Poles )

static

Perform the Boor algorithm to evaluate a point at parameter , 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.

EvalBsplineBasis()

static int BSplCLib::EvalBsplineBasis ( const int DerivativeOrder, const int Order, const NCollection_Array1< double > & FlatKnots, const double Parameter, int & FirstNonZeroBsplineIndex, math_Matrix & BsplineBasis, const bool isPeriodic = false )

static

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.

FactorBandedMatrix()

static int BSplCLib::FactorBandedMatrix ( math_Matrix & Matrix, const int UpperBandWidth, const int LowerBandWidth, int & PivotIndexProblem )

static

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

FirstUKnotIndex()

static int BSplCLib::FirstUKnotIndex ( const int Degree, const NCollection_Array1< int > & Mults )

static

Computes the index of the knots value which gives the start point of the curve.

FlatBezierKnots()

static const double & BSplCLib::FlatBezierKnots ( const int Degree )

static

Returns pointer to statically allocated array representing flat knots for bezier curve of the specified degree. Raises OutOfRange if Degree > MaxDegree()

FlatIndex()

static int BSplCLib::FlatIndex ( const int Degree, const int Index, const NCollection_Array1< int > & Mults, const bool Periodic )

static

Computes the index of the flats knots sequence corresponding to <Index> in the knots sequence which multiplicities are <Mults>.

FunctionMultiply() [1/4]

static void BSplCLib::FunctionMultiply ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const int PolesDimension, double & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, double & NewPoles, int & theStatus )

static

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)

FunctionMultiply() [2/4]

static void BSplCLib::FunctionMultiply ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, NCollection_Array1< double > & NewPoles, int & theStatus )

static

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)

FunctionMultiply() [3/4]

static void BSplCLib::FunctionMultiply ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt > & NewPoles, int & theStatus )

static

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)

FunctionMultiply() [4/4]

static void BSplCLib::FunctionMultiply ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt2d > & NewPoles, int & theStatus )

static

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)

FunctionReparameterise() [1/4]

static void BSplCLib::FunctionReparameterise ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const int PolesDimension, double & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, double & NewPoles, int & theStatus )

static

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))

FunctionReparameterise() [2/4]

static void BSplCLib::FunctionReparameterise ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, NCollection_Array1< double > & NewPoles, int & theStatus )

static

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))

FunctionReparameterise() [3/4]

static void BSplCLib::FunctionReparameterise ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt > & NewPoles, int & theStatus )

static

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

1. 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))

FunctionReparameterise() [4/4]

static void BSplCLib::FunctionReparameterise ( const BSplCLib_EvaluatorFunction & Function, const int BSplineDegree, const NCollection_Array1< double > & BSplineFlatKnots, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > & FlatKnots, const int NewDegree, NCollection_Array1< gp_Pnt2d > & NewPoles, int & theStatus )

static

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

1. 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))

GetPole()

static void BSplCLib::GetPole ( const int Index, const int Length, const int Depth, const int Dimension, double & LocPoles, int & Position, NCollection_Array1< double > & Pole )

static

Copy the pole at position <Index> in the Boor scheme of dimension <Dimension> to <Position> in the array <Pole>. <Position> is updated.

Hunt()

static void BSplCLib::Hunt ( const NCollection_Array1< double > & theArray, const double theX, int & theXPos )

static

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.

IncreaseDegree() [1/5]

static void BSplCLib::IncreaseDegree ( const int Degree, const int NewDegree, const bool Periodic, const int Dimension, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< double > & NewPoles, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults )

static

IncreaseDegree() [2/5]

static void BSplCLib::IncreaseDegree ( const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults )

static

IncreaseDegree() [3/5]

static void BSplCLib::IncreaseDegree ( const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt2d > & NewPoles, NCollection_Array1< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults )

static

IncreaseDegree() [4/5]

static void BSplCLib::IncreaseDegree ( const int NewDegree, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights )

static

IncreaseDegree() [5/5]

static void BSplCLib::IncreaseDegree ( const int theNewDegree, const NCollection_Array1< gp_Pnt2d > & thePoles, const NCollection_Array1< double > * theWeights, NCollection_Array1< gp_Pnt2d > & theNewPoles, NCollection_Array1< double > * theNewWeights )

static

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:

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 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:

knot : 0.  1.  2.
mult : 1   2   1

The FirstUKnot is 2.0 because the sum of multiplicities is

Degree+1 : 1 + 2 + 1 = 4 = 3 + 1

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:

knot : 1.  2.
mult : 3   2

The multiplicity of the first knot may also be reduced if the sum is still too 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.

IncreaseDegreeCountKnots()

static int BSplCLib::IncreaseDegreeCountKnots ( const int Degree, const int NewDegree, const bool Periodic, const NCollection_Array1< int > & Mults )

static

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.

InsertKnot() [1/2]

static void BSplCLib::InsertKnot ( const int UIndex, const double U, const int UMult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights )

static

InsertKnot() [2/2]

static void BSplCLib::InsertKnot ( const int UIndex, const double U, const int UMult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt2d > & NewPoles, NCollection_Array1< double > * NewWeights )

static

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.

InsertKnots() [1/3]

static void BSplCLib::InsertKnots ( const int Degree, const bool Periodic, const int Dimension, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & AddKnots, const NCollection_Array1< int > * AddMults, NCollection_Array1< double > & NewPoles, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Epsilon, const bool Add = true )

static

InsertKnots() [2/3]

static void BSplCLib::InsertKnots ( const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & AddKnots, const NCollection_Array1< int > * AddMults, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Epsilon, const bool Add = true )

static

InsertKnots() [3/3]

static void BSplCLib::InsertKnots ( const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & AddKnots, const NCollection_Array1< int > * AddMults, NCollection_Array1< gp_Pnt2d > & NewPoles, NCollection_Array1< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Epsilon, const bool Add = true )

static

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.

Interpolate() [1/6]

static void BSplCLib::Interpolate ( const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< double > & Parameters, const NCollection_Array1< int > & ContactOrderArray, const int ArrayDimension, double & Poles, double & Weights, int & InversionProblem )

static

Interpolate() [2/6]

static void BSplCLib::Interpolate ( const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< double > & Parameters, const NCollection_Array1< int > & ContactOrderArray, const int ArrayDimension, double & Poles, int & InversionProblem )

static

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.

Interpolate() [3/6]

static void BSplCLib::Interpolate ( const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< double > & Parameters, const NCollection_Array1< int > & ContactOrderArray, NCollection_Array1< gp_Pnt > & Poles, int & InversionProblem )

static

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.

Interpolate() [4/6]

static void BSplCLib::Interpolate ( const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< double > & Parameters, const NCollection_Array1< int > & ContactOrderArray, NCollection_Array1< gp_Pnt > & Poles, NCollection_Array1< double > & Weights, int & InversionProblem )

static

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.

Interpolate() [5/6]

static void BSplCLib::Interpolate ( const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< double > & Parameters, const NCollection_Array1< int > & ContactOrderArray, NCollection_Array1< gp_Pnt2d > & Poles, int & InversionProblem )

static

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.

Interpolate() [6/6]

static void BSplCLib::Interpolate ( const int Degree, const NCollection_Array1< double > & FlatKnots, const NCollection_Array1< double > & Parameters, const NCollection_Array1< int > & ContactOrderArray, NCollection_Array1< gp_Pnt2d > & Poles, NCollection_Array1< double > & Weights, int & InversionProblem )

static

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 i.

Intervals()

static int BSplCLib::Intervals ( const NCollection_Array1< double > & theKnots, const NCollection_Array1< int > & theMults, int theDegree, bool isPeriodic, int theContinuity, double theFirst, double theLast, double theTolerance, NCollection_Array1< double > * theIntervals )

static

Splits the given range to BSpline intervals of given continuity.

Parameters

[in]	theKnots	the knots of BSpline
[in]	theMults	the knots' multiplicities
[in]	theDegree	the degree of BSpline
[in]	isPeriodic	the periodicity of BSpline
[in]	theContinuity	the target interval's continuity
[in]	theFirst	the begin of the target range
[in]	theLast	the end of the target range
[in]	theTolerance	the tolerance
[in,out]	theIntervals	the array to store intervals if isn't nullptr

Returns

the number of intervals

IsRational()

static bool BSplCLib::IsRational ( const NCollection_Array1< double > & Weights, const int I1, const int I2, const double Epsilon = 0.0 )

static

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.

KnotAnalysis()

static void BSplCLib::KnotAnalysis ( const int Degree, const bool Periodic, const NCollection_Array1< double > & CKnots, const NCollection_Array1< int > & CMults, GeomAbs_BSplKnotDistribution & KnotForm, int & MaxKnotMult )

static

Analyzes the array of knots. Returns the form and the maximum knot multiplicity.

KnotForm()

static BSplCLib_KnotDistribution BSplCLib::KnotForm ( const NCollection_Array1< double > & Knots, const int FromK1, const int ToK2 )

static

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>.

Knots()

static void BSplCLib::Knots ( const NCollection_Array1< double > & KnotSeq, NCollection_Array1< double > & Knots, NCollection_Array1< int > & Mults, const bool Periodic = false )

static

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)

KnotSequence() [1/2]

static void BSplCLib::KnotSequence ( const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const int Degree, const bool Periodic, NCollection_Array1< double > & KnotSeq )

static

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)

KnotSequence() [2/2]

static void BSplCLib::KnotSequence ( const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< double > & KnotSeq, const bool Periodic = false )

static

KnotSequenceLength()

static int BSplCLib::KnotSequenceLength ( const NCollection_Array1< int > & Mults, const int Degree, const bool Periodic )

static

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

KnotsLength()

static int BSplCLib::KnotsLength ( const NCollection_Array1< double > & KnotSeq, const bool Periodic = false )

static

Returns thelength of the sequence of knots (and Mults) without repetition.

LastUKnotIndex()

static int BSplCLib::LastUKnotIndex ( const int Degree, const NCollection_Array1< int > & Mults )

static

Computes the index of the knots value which gives the end point of the curve.

LocateParameter() [1/3]

static void BSplCLib::LocateParameter ( const int Degree, const NCollection_Array1< double > & Knots, const double U, const bool IsPeriodic, const int FromK1, const int ToK2, int & KnotIndex, double & NewU )

static

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"

LocateParameter() [2/3]

static void BSplCLib::LocateParameter ( const int Degree, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const double U, const bool IsPeriodic, const int FromK1, const int ToK2, int & KnotIndex, double & NewU )

static

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 "with repetitions"

LocateParameter() [3/3]

static void BSplCLib::LocateParameter ( const int Degree, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > * Mults, const double U, const bool Periodic, int & Index, double & NewU )

static

MaxDegree()

static constexpr int BSplCLib::MaxDegree ( )

inlinestaticconstexpr

returns the degree maxima for a BSplineCurve.

MaxKnotMult()

static int BSplCLib::MaxKnotMult ( const NCollection_Array1< int > & Mults, const int K1, const int K2 )

static

Finds the greatest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.

MaxUnitWeightsSize()

static constexpr int BSplCLib::MaxUnitWeightsSize ( )

inlinestaticconstexpr

Returns the maximum number of elements supported by the pre-allocated unit weights array (2049). For sizes larger than this, UnitWeights() will allocate a new array.

MergeBSplineKnots()

static void BSplCLib::MergeBSplineKnots ( const double Tolerance, const double StartValue, const double EndValue, const int Degree1, const NCollection_Array1< double > & Knots1, const NCollection_Array1< int > & Mults1, const int Degree2, const NCollection_Array1< double > & Knots2, const NCollection_Array1< int > & Mults2, int & NumPoles, occ::handle< NCollection_HArray1< double > > & NewKnots, occ::handle< NCollection_HArray1< int > > & NewMults )

static

Merges two knot vector by setting the starting and ending values to StartValue and EndValue.

MinKnotMult()

static int BSplCLib::MinKnotMult ( const NCollection_Array1< int > & Mults, const int K1, const int K2 )

static

Finds the lowest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.

MovePoint() [1/2]

static void BSplCLib::MovePoint ( const double U, const gp_Vec & Displ, const int Index1, const int Index2, const int Degree, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & FlatKnots, int & FirstIndex, int & LastIndex, NCollection_Array1< gp_Pnt > & NewPoles )

static

Find the new poles which allows an old point (with a given 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.

MovePoint() [2/2]

static void BSplCLib::MovePoint ( const double U, const gp_Vec2d & Displ, const int Index1, const int Index2, const int Degree, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & FlatKnots, int & FirstIndex, int & LastIndex, NCollection_Array1< gp_Pnt2d > & NewPoles )

static

Find the new poles which allows an old point (with a given 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.

MovePointAndTangent() [1/3]

static void BSplCLib::MovePointAndTangent ( const double U, const gp_Vec & Delta, const gp_Vec & DeltaDerivative, const double Tolerance, const int Degree, const int StartingCondition, const int EndingCondition, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & FlatKnots, NCollection_Array1< gp_Pnt > & NewPoles, int & ErrorStatus )

static

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.

MovePointAndTangent() [2/3]

static void BSplCLib::MovePointAndTangent ( const double U, const gp_Vec2d & Delta, const gp_Vec2d & DeltaDerivative, const double Tolerance, const int Degree, const int StartingCondition, const int EndingCondition, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & FlatKnots, NCollection_Array1< gp_Pnt2d > & NewPoles, int & ErrorStatus )

static

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.

MovePointAndTangent() [3/3]

static void BSplCLib::MovePointAndTangent ( const double U, const int ArrayDimension, double & Delta, double & DeltaDerivative, const double Tolerance, const int Degree, const int StartingCondition, const int EndingCondition, double & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & FlatKnots, double & NewPoles, int & ErrorStatus )

static

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.

MultForm()

static BSplCLib_MultDistribution BSplCLib::MultForm ( const NCollection_Array1< int > & Mults, const int FromK1, const int ToK2 )

static

Analyses the distribution of multiplicities between the knot FromK1 and the Knot ToK2.

NbPoles()

static int BSplCLib::NbPoles ( const int Degree, const bool Periodic, const NCollection_Array1< int > & Mults )

static

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.

NoMults()

static NCollection_Array1< int > * BSplCLib::NoMults ( )

static

Used as argument for a flatknots evaluation.

NoWeights()

static NCollection_Array1< double > * BSplCLib::NoWeights ( )

static

Used as argument for a non rational curve.

PoleIndex()

static int BSplCLib::PoleIndex ( const int Degree, const int Index, const bool Periodic, const NCollection_Array1< int > & Mults )

static

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().

PolesCoefficients() [1/4]

static void BSplCLib::PolesCoefficients ( const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, NCollection_Array1< gp_Pnt > & CachePoles, NCollection_Array1< double > * CacheWeights )

static

Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziercurves at parameter 0. Warning: To be used for Beziercurves ONLY!!!

PolesCoefficients() [2/4]

static void BSplCLib::PolesCoefficients ( const NCollection_Array1< gp_Pnt > & Poles, NCollection_Array1< gp_Pnt > & CachePoles )

static

PolesCoefficients() [3/4]

static void BSplCLib::PolesCoefficients ( const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, NCollection_Array1< gp_Pnt2d > & CachePoles, NCollection_Array1< double > * CacheWeights )

static

PolesCoefficients() [4/4]

static void BSplCLib::PolesCoefficients ( const NCollection_Array1< gp_Pnt2d > & Poles, NCollection_Array1< gp_Pnt2d > & CachePoles )

static

PrepareInsertKnots()

static bool BSplCLib::PrepareInsertKnots ( const int Degree, const bool Periodic, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & AddKnots, const NCollection_Array1< int > * AddMults, int & NbPoles, int & NbKnots, const double Epsilon, const bool Add = true )

static

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.

PrepareTrimming()

static void BSplCLib::PrepareTrimming ( const int Degree, const bool Periodic, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const double U1, const double U2, int & NbKnots, int & NbPoles )

static

Set in <NbKnots> and <NbPoles> the number of Knots and Poles of the curve resulting from the trimming of the BSplinecurve defined with <degree>, <knots>, <mults>

PrepareUnperiodize()

static void BSplCLib::PrepareUnperiodize ( const int Degree, const NCollection_Array1< int > & Mults, int & NbKnots, int & NbPoles )

static

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>.

RaiseMultiplicity() [1/2]

static void BSplCLib::RaiseMultiplicity ( const int KnotIndex, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights )

static

RaiseMultiplicity() [2/2]

static void BSplCLib::RaiseMultiplicity ( const int KnotIndex, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt2d > & NewPoles, NCollection_Array1< double > * NewWeights )

static

Raise the multiplicity of knot to <UMult>.

The new control points are returned. Knots and Mults are not updated.

RemoveKnot() [1/3]

static bool BSplCLib::RemoveKnot ( const int Index, const int Mult, const int Degree, const bool Periodic, const int Dimension, const NCollection_Array1< double > & Poles, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< double > & NewPoles, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Tolerance )

static

RemoveKnot() [2/3]

static bool BSplCLib::RemoveKnot ( const int Index, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Tolerance )

static

RemoveKnot() [3/3]

static bool BSplCLib::RemoveKnot ( const int Index, const int Mult, const int Degree, const bool Periodic, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, NCollection_Array1< gp_Pnt2d > & NewPoles, NCollection_Array1< double > * NewWeights, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, const double Tolerance )

static

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.

Reparametrize()

static void BSplCLib::Reparametrize ( const double U1, const double U2, NCollection_Array1< double > & Knots )

static

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.

Resolution() [1/3]

static void BSplCLib::Resolution ( const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const int NumPoles, const NCollection_Array1< double > & FlatKnots, const int Degree, const double Tolerance3D, double & UTolerance )

static

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

Resolution() [2/3]

static void BSplCLib::Resolution ( const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const int NumPoles, const NCollection_Array1< double > & FlatKnots, const int Degree, const double Tolerance3D, double & UTolerance )

static

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

Resolution() [3/3]

static void BSplCLib::Resolution ( double & PolesArray, const int ArrayDimension, const int NumPoles, const NCollection_Array1< double > * Weights, const NCollection_Array1< double > & FlatKnots, const int Degree, const double Tolerance3D, double & UTolerance )

static

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

Reverse() [1/5]

static void BSplCLib::Reverse ( NCollection_Array1< double > & Knots )

static

Reverses the array knots to become the knots sequence of the reversed curve.

Reverse() [2/5]

static void BSplCLib::Reverse ( NCollection_Array1< double > & Weights, const int Last )

static

Reverses the array of poles.

Reverse() [3/5]

static void BSplCLib::Reverse ( NCollection_Array1< gp_Pnt > & Poles, const int Last )

static

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)

Reverse() [4/5]

static void BSplCLib::Reverse ( NCollection_Array1< gp_Pnt2d > & Poles, const int Last )

static

Reverses the array of poles.

Reverse() [5/5]

static void BSplCLib::Reverse ( NCollection_Array1< int > & Mults )

static

Reverses the array of multiplicities.

SolveBandedSystem() [1/6]

static int BSplCLib::SolveBandedSystem ( const math_Matrix & Matrix, const int UpperBandWidth, const int LowerBandWidth, const bool HomogeneousFlag, NCollection_Array1< gp_Pnt > & Array, NCollection_Array1< double > & Weights )

static

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 Weights are treated homogeneously that is that those are interpolated as they are and result is returned without division by the interpolated weights.

SolveBandedSystem() [2/6]

static int BSplCLib::SolveBandedSystem ( const math_Matrix & Matrix, const int UpperBandWidth, const int LowerBandWidth, const bool HomogenousFlag, const int ArrayDimension, double & Array, double & Weights )

static

SolveBandedSystem() [3/6]

static int BSplCLib::SolveBandedSystem ( const math_Matrix & Matrix, const int UpperBandWidth, const int LowerBandWidth, const bool HomogenousFlag, NCollection_Array1< gp_Pnt2d > & Array, NCollection_Array1< double > & Weights )

static

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 Weights are treated homogeneously that is that those are interpolated as they are and result is returned without division by the interpolated weights.

SolveBandedSystem() [4/6]

static int BSplCLib::SolveBandedSystem ( const math_Matrix & Matrix, const int UpperBandWidth, const int LowerBandWidth, const int ArrayDimension, double & Array )

static

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.

SolveBandedSystem() [5/6]

static int BSplCLib::SolveBandedSystem ( const math_Matrix & Matrix, const int UpperBandWidth, const int LowerBandWidth, NCollection_Array1< gp_Pnt > & Array )

static

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.

SolveBandedSystem() [6/6]

static int BSplCLib::SolveBandedSystem ( const math_Matrix & Matrix, const int UpperBandWidth, const int LowerBandWidth, NCollection_Array1< gp_Pnt2d > & Array )

static

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.

TangExtendToConstraint()

static void BSplCLib::TangExtendToConstraint ( const NCollection_Array1< double > & FlatKnots, const double C1Coefficient, const int NumPoles, double & Poles, const int Dimension, const int Degree, const NCollection_Array1< double > & ConstraintPoint, const int Continuity, const bool After, int & NbPolesResult, int & NbKnotsRsult, double & KnotsResult, double & PolesResult )

static

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 dimensioned properly.

Trimming() [1/3]

static void BSplCLib::Trimming ( const int Degree, const bool Periodic, const int Dimension, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & Poles, const double U1, const double U2, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, NCollection_Array1< double > & NewPoles )

static

Trimming() [2/3]

static void BSplCLib::Trimming ( const int Degree, const bool Periodic, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, const double U1, const double U2, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights )

static

Trimming() [3/3]

static void BSplCLib::Trimming ( const int Degree, const bool Periodic, const NCollection_Array1< double > & Knots, const NCollection_Array1< int > & Mults, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, const double U1, const double U2, NCollection_Array1< double > & NewKnots, NCollection_Array1< int > & NewMults, NCollection_Array1< gp_Pnt2d > & NewPoles, NCollection_Array1< double > * NewWeights )

static

UnitWeights()

static NCollection_Array1< double > BSplCLib::UnitWeights ( const int theNbElems )

static

Returns an NCollection_Array1<double> filled with 1.0 values. If theNbElems <= MaxUnitWeightsSize(), references a pre-allocated global array (zero allocation). Otherwise, allocates a new array and fills with 1.0.

Warning

The returned array may reference global static memory – do NOT modify elements.

Parameters

[in]

theNbElems

the number of elements in the returned array

Returns

array of unit weights with bounds [1, theNbElems]

UnitWeightsData()

static const double * BSplCLib::UnitWeightsData ( )

static

Returns a pointer to the pre-allocated unit weights static array. The array contains MaxUnitWeightsSize() elements, all equal to 1.0.

Warning

Do NOT modify elements through this pointer.

Returns

pointer to the first element of the static unit weights array

Unperiodize() [1/3]

static void BSplCLib::Unperiodize ( const int Degree, const int Dimension, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & Knots, const NCollection_Array1< double > & Poles, NCollection_Array1< int > & NewMults, NCollection_Array1< double > & NewKnots, NCollection_Array1< double > & NewPoles )

static

Unperiodize() [2/3]

static void BSplCLib::Unperiodize ( const int Degree, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & Knots, const NCollection_Array1< gp_Pnt > & Poles, const NCollection_Array1< double > * Weights, NCollection_Array1< int > & NewMults, NCollection_Array1< double > & NewKnots, NCollection_Array1< gp_Pnt > & NewPoles, NCollection_Array1< double > * NewWeights )

static

Unperiodize() [3/3]

static void BSplCLib::Unperiodize ( const int Degree, const NCollection_Array1< int > & Mults, const NCollection_Array1< double > & Knots, const NCollection_Array1< gp_Pnt2d > & Poles, const NCollection_Array1< double > * Weights, NCollection_Array1< int > & NewMults, NCollection_Array1< double > & NewKnots, NCollection_Array1< gp_Pnt2d > & NewPoles, NCollection_Array1< double > * NewWeights )

static

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The documentation for this class was generated from the following file:

• BSplCLib.hxx