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| static void | Hunt (const TColStd_Array1OfReal &theArray, const Standard_Real theX, Standard_Integer &theXPos) |
| | This routine searches the position of the real value theX in the monotonically increasing set of real values theArray using bisection algorithm. More...
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| static Standard_Integer | FirstUKnotIndex (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults) |
| | Computes the index of the knots value which gives the start point of the curve. More...
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| static Standard_Integer | LastUKnotIndex (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults) |
| | Computes the index of the knots value which gives the end point of the curve. More...
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| static Standard_Integer | FlatIndex (const Standard_Integer Degree, const Standard_Integer Index, const TColStd_Array1OfInteger &Mults, const Standard_Boolean Periodic) |
| | Computes the index of the flats knots sequence corresponding to <Index> in the knots sequence which multiplicities are <Mults>. More...
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| static void | LocateParameter (const Standard_Integer Degree, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real U, const Standard_Boolean IsPeriodic, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Integer &KnotIndex, Standard_Real &NewU) |
| | Locates the parametric value U in the knots sequence between the knot K1 and the knot K2. The value return in Index verifies. More...
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| static void | LocateParameter (const Standard_Integer Degree, const TColStd_Array1OfReal &Knots, const Standard_Real U, const Standard_Boolean IsPeriodic, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Integer &KnotIndex, Standard_Real &NewU) |
| | Locates the parametric value U in the knots sequence between the knot K1 and the knot K2. The value return in Index verifies. More...
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| static void | LocateParameter (const Standard_Integer Degree, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, const Standard_Real U, const Standard_Boolean Periodic, Standard_Integer &Index, Standard_Real &NewU) |
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| static Standard_Integer | MaxKnotMult (const TColStd_Array1OfInteger &Mults, const Standard_Integer K1, const Standard_Integer K2) |
| | Finds the greatest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value. More...
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| static Standard_Integer | MinKnotMult (const TColStd_Array1OfInteger &Mults, const Standard_Integer K1, const Standard_Integer K2) |
| | Finds the lowest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value. More...
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| static Standard_Integer | NbPoles (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfInteger &Mults) |
| | Returns the number of poles of the curve. Returns 0 if one of the multiplicities is incorrect. More...
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| static Standard_Integer | KnotSequenceLength (const TColStd_Array1OfInteger &Mults, const Standard_Integer Degree, const Standard_Boolean Periodic) |
| | Returns the length of the sequence of knots with repetition. More...
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| static void | KnotSequence (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColStd_Array1OfReal &KnotSeq, const Standard_Boolean Periodic=Standard_False) |
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| static void | KnotSequence (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Integer Degree, const Standard_Boolean Periodic, TColStd_Array1OfReal &KnotSeq) |
| | Computes the sequence of knots KnotSeq with repetition of the knots of multiplicity greater than 1. More...
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| static Standard_Integer | KnotsLength (const TColStd_Array1OfReal &KnotSeq, const Standard_Boolean Periodic=Standard_False) |
| | Returns the length of the sequence of knots (and Mults) without repetition. More...
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| |
| static void | Knots (const TColStd_Array1OfReal &KnotSeq, TColStd_Array1OfReal &Knots, TColStd_Array1OfInteger &Mults, const Standard_Boolean Periodic=Standard_False) |
| | Computes the sequence of knots Knots without repetition of the knots of multiplicity greater than 1. More...
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| static BSplCLib_KnotDistribution | KnotForm (const TColStd_Array1OfReal &Knots, const Standard_Integer FromK1, const Standard_Integer 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>. More...
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| static BSplCLib_MultDistribution | MultForm (const TColStd_Array1OfInteger &Mults, const Standard_Integer FromK1, const Standard_Integer ToK2) |
| | Analyses the distribution of multiplicities between the knot FromK1 and the Knot ToK2. More...
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| static void | KnotAnalysis (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &CKnots, const TColStd_Array1OfInteger &CMults, GeomAbs_BSplKnotDistribution &KnotForm, Standard_Integer &MaxKnotMult) |
| | Analyzes the array of knots. Returns the form and the maximum knot multiplicity. More...
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| static void | Reparametrize (const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &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. More...
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| static void | Reverse (TColStd_Array1OfReal &Knots) |
| | Reverses the array knots to become the knots sequence of the reversed curve. More...
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| static void | Reverse (TColStd_Array1OfInteger &Mults) |
| | Reverses the array of multiplicities. More...
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| static void | Reverse (TColgp_Array1OfPnt &Poles, const Standard_Integer 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. More...
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| static void | Reverse (TColgp_Array1OfPnt2d &Poles, const Standard_Integer Last) |
| | Reverses the array of poles. More...
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| static void | Reverse (TColStd_Array1OfReal &Weights, const Standard_Integer Last) |
| | Reverses the array of poles. More...
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| static Standard_Boolean | IsRational (const TColStd_Array1OfReal &Weights, const Standard_Integer I1, const Standard_Integer I2, const Standard_Real 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. More...
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| static Standard_Integer | MaxDegree () |
| | returns the degree maxima for a BSplineCurve. More...
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| static void | Eval (const Standard_Real U, const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles) |
| | Perform the Boor algorithm to evaluate a point at parameter , with <Degree> and <Dimension>. More...
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| static void | BoorScheme (const Standard_Real U, const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles, const Standard_Integer Depth, const Standard_Integer Length) |
| | 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. More...
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| static Standard_Boolean | AntiBoorScheme (const Standard_Real U, const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles, const Standard_Integer Depth, const Standard_Integer Length, const Standard_Real Tolerance) |
| | Compute the content of Pole before the BoorScheme. This method is used to remove poles. More...
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| static void | Derivative (const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, const Standard_Integer Length, const Standard_Integer Order, Standard_Real &Poles) |
| | Computes the poles of the BSpline giving the derivatives of order <Order>. More...
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| |
| static void | Bohm (const Standard_Real U, const Standard_Integer Degree, const Standard_Integer N, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles) |
| | Performs the Bohm Algorithm at parameter . This algorithm computes the value and all the derivatives up to order N (N <= Degree). More...
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| static TColStd_Array1OfReal * | NoWeights () |
| | Used as argument for a non rational curve. More...
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| static TColStd_Array1OfInteger * | NoMults () |
| | Used as argument for a flatknots evaluation. More...
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| |
| static void | BuildKnots (const Standard_Integer Degree, const Standard_Integer Index, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, Standard_Real &LK) |
| | Stores in LK the useful knots for the BoorSchem on the span Knots(Index) - Knots(Index+1) More...
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| static Standard_Integer | PoleIndex (const Standard_Integer Degree, const Standard_Integer Index, const Standard_Boolean Periodic, const TColStd_Array1OfInteger &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(). More...
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| |
| static void | BuildEval (const Standard_Integer Degree, const Standard_Integer Index, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal *Weights, Standard_Real &LP) |
| |
| static void | BuildEval (const Standard_Integer Degree, const Standard_Integer Index, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, Standard_Real &LP) |
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| static void | BuildEval (const Standard_Integer Degree, const Standard_Integer Index, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, Standard_Real &LP) |
| | Copy in <LP> the poles and weights for the Eval scheme. starting from Poles(Poles.Lower()+Index) More...
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| static void | BuildBoor (const Standard_Integer Index, const Standard_Integer Length, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, Standard_Real &LP) |
| | Copy in <LP> poles for <Dimension> Boor scheme. Starting from <Index> * <Dimension>, copy <Length+1> poles. More...
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| static Standard_Integer | BoorIndex (const Standard_Integer Index, const Standard_Integer Length, const Standard_Integer Depth) |
| | Returns the index in the Boor result array of the poles <Index>. If the Boor algorithm was perform with <Length> and <Depth>. More...
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| |
| static void | GetPole (const Standard_Integer Index, const Standard_Integer Length, const Standard_Integer Depth, const Standard_Integer Dimension, Standard_Real &LocPoles, Standard_Integer &Position, TColStd_Array1OfReal &Pole) |
| | Copy the pole at position <Index> in the Boor scheme of dimension <Dimension> to <Position> in the array <Pole>. <Position> is updated. More...
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| static Standard_Boolean | PrepareInsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger *AddMults, Standard_Integer &NbPoles, Standard_Integer &NbKnots, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True) |
| | 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>. More...
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| static void | InsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger *AddMults, TColStd_Array1OfReal &NewPoles, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True) |
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| static void | InsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger *AddMults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True) |
| |
| static void | InsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger *AddMults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True) |
| | Insert a sequence of knots <AddKnots> with multiplicities <AddMults>. <AddKnots> must be a non decreasing sequence and verifies : More...
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| |
| static void | InsertKnot (const Standard_Integer UIndex, const Standard_Real U, const Standard_Integer UMult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights) |
| |
| static void | InsertKnot (const Standard_Integer UIndex, const Standard_Real U, const Standard_Integer UMult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal *NewWeights) |
| | Insert a new knot U of multiplicity UMult in the knot sequence. More...
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| |
| static void | RaiseMultiplicity (const Standard_Integer KnotIndex, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights) |
| |
| static void | RaiseMultiplicity (const Standard_Integer KnotIndex, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal *NewWeights) |
| | Raise the multiplicity of knot to <UMult>. More...
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| |
| static Standard_Boolean | RemoveKnot (const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColStd_Array1OfReal &NewPoles, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance) |
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| static Standard_Boolean | RemoveKnot (const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance) |
| |
| static Standard_Boolean | RemoveKnot (const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance) |
| | Decrement the multiplicity of <Knots(Index)> to <Mult>. If <Mult> is null the knot is removed. More...
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| |
| static Standard_Integer | IncreaseDegreeCountKnots (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColStd_Array1OfInteger &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. More...
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| |
| static void | IncreaseDegree (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColStd_Array1OfReal &NewPoles, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults) |
| |
| static void | IncreaseDegree (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults) |
| |
| static void | IncreaseDegree (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal *NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults) |
| |
| static void | IncreaseDegree (const Standard_Integer NewDegree, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights) |
| |
| static void | IncreaseDegree (const Standard_Integer theNewDegree, const TColgp_Array1OfPnt2d &thePoles, const TColStd_Array1OfReal *theWeights, TColgp_Array1OfPnt2d &theNewPoles, TColStd_Array1OfReal *theNewWeights) |
| | Increase the degree of a bspline (or bezier) curve of dimension theDimension form theDegree to theNewDegree. More...
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| |
| static void | PrepareUnperiodize (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, Standard_Integer &NbKnots, Standard_Integer &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>. More...
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| |
| static void | Unperiodize (const Standard_Integer Degree, const Standard_Integer Dimension, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfReal &Poles, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfReal &NewPoles) |
| |
| static void | Unperiodize (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights) |
| |
| static void | Unperiodize (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal *NewWeights) |
| |
| static void | PrepareTrimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real U1, const Standard_Real U2, Standard_Integer &NbKnots, Standard_Integer &NbPoles) |
| | 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> More...
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| |
| static void | Trimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Poles, const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewPoles) |
| |
| static void | Trimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal *NewWeights) |
| |
| static void | Trimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal *NewWeights) |
| |
| static void | D0 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, Standard_Real &P) |
| |
| static void | D0 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt &P) |
| |
| static void | D0 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt2d &P) |
| |
| static void | D0 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &P) |
| |
| static void | D0 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &P) |
| |
| static void | D1 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, Standard_Real &P, Standard_Real &V) |
| |
| static void | D1 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt &P, gp_Vec &V) |
| |
| static void | D1 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt2d &P, gp_Vec2d &V) |
| |
| static void | D1 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &P, gp_Vec &V) |
| |
| static void | D1 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &P, gp_Vec2d &V) |
| |
| static void | D2 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, Standard_Real &P, Standard_Real &V1, Standard_Real &V2) |
| |
| static void | D2 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) |
| |
| static void | D2 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) |
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| static void | D2 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) |
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| static void | D2 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) |
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| static void | D3 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, Standard_Real &P, Standard_Real &V1, Standard_Real &V2, Standard_Real &V3) |
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| static void | D3 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) |
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| static void | D3 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) |
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| static void | D3 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) |
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| static void | D3 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) |
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| static void | DN (const Standard_Real U, const Standard_Integer N, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, Standard_Real &VN) |
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| static void | DN (const Standard_Real U, const Standard_Integer N, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Vec &VN) |
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| static void | DN (const Standard_Real U, const Standard_Integer N, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger *Mults, gp_Vec2d &V) |
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| static void | DN (const Standard_Real U, const Standard_Integer N, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &P, gp_Vec &VN) |
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| static void | DN (const Standard_Real U, const Standard_Integer N, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &P, gp_Vec2d &VN) |
| | The above functions compute values and derivatives in the following situations : More...
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| static Standard_Integer | EvalBsplineBasis (const Standard_Integer DerivativeOrder, const Standard_Integer Order, const TColStd_Array1OfReal &FlatKnots, const Standard_Real Parameter, Standard_Integer &FirstNonZeroBsplineIndex, math_Matrix &BsplineBasis, const Standard_Boolean isPeriodic=Standard_False) |
| | This 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. More...
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| static Standard_Integer | BuildBSpMatrix (const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &OrderArray, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, math_Matrix &Matrix, Standard_Integer &UpperBandWidth, Standard_Integer &LowerBandWidth) |
| | This Builds a fully blown Matrix of (ni) Bi (tj) More...
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| static Standard_Integer | FactorBandedMatrix (math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, Standard_Integer &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 More...
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| static Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Integer ArrayDimension, Standard_Real &Array) |
| | This solves the system Matrix.X = B with when Matrix is factored in LU form The Array 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. More...
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| static Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, TColgp_Array1OfPnt2d &Array) |
| | This solves the system Matrix.X = B with when Matrix is factored in LU form The Array has the length of the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension. More...
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| static Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, TColgp_Array1OfPnt &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. More...
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| static Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Boolean HomogenousFlag, const Standard_Integer ArrayDimension, Standard_Real &Array, Standard_Real &Weights) |
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| static Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Boolean HomogenousFlag, TColgp_Array1OfPnt2d &Array, TColStd_Array1OfReal &Weights) |
| | This solves the system Matrix.X = B with when Matrix is factored in LU form The Array is an seen as an Array[1..N][1..ArrayDimension] with N = the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension. If HomogeneousFlag == 0 the Poles are multiplied by the Weights upon Entry and once interpolation is carried over the result of the poles are divided by the result of the interpolation of the weights. Otherwise if HomogenousFlag == 1 the Poles and Weigths are treated homogeneously that is that those are interpolated as they are and result is returned without division by the interpolated weigths. More...
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| static Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Boolean HomogeneousFlag, TColgp_Array1OfPnt &Array, TColStd_Array1OfReal &Weights) |
| | This solves the system Matrix.X = B with when Matrix is factored in LU form The Array is an seen as an Array[1..N][1..ArrayDimension] with N = the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension If HomogeneousFlag == 0 the Poles are multiplied by the Weights upon Entry and once interpolation is carried over the result of the poles are divided by the result of the interpolation of the weights. Otherwise if HomogenousFlag == 1 the Poles and Weigths are treated homogeneously that is that those are interpolated as they are and result is returned without division by the interpolated weigths. More...
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| static void | MergeBSplineKnots (const Standard_Real Tolerance, const Standard_Real StartValue, const Standard_Real EndValue, const Standard_Integer Degree1, const TColStd_Array1OfReal &Knots1, const TColStd_Array1OfInteger &Mults1, const Standard_Integer Degree2, const TColStd_Array1OfReal &Knots2, const TColStd_Array1OfInteger &Mults2, Standard_Integer &NumPoles, Handle< TColStd_HArray1OfReal > &NewKnots, Handle< TColStd_HArray1OfInteger > &NewMults) |
| | Merges two knot vector by setting the starting and ending values to StartValue and EndValue. More...
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| static void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const Standard_Integer PolesDimension, Standard_Real &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, Standard_Real &NewPoles, Standard_Integer &theStatus) |
| | This function will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following: More...
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| static void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColStd_Array1OfReal &NewPoles, Standard_Integer &theStatus) |
| | This 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: More...
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| static void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt &NewPoles, Standard_Integer &theStatus) |
| | this will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following : 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots More...
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| static void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt2d &NewPoles, Standard_Integer &theStatus) |
| | this will 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 More...
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| static void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const Standard_Integer PolesDimension, Standard_Real &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, Standard_Real &NewPoles, Standard_Integer &theStatus) |
| | this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller's responsibility to insure that conditions More...
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| static void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColStd_Array1OfReal &NewPoles, Standard_Integer &theStatus) |
| | this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller's responsibility to insure that conditions More...
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| static void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt2d &NewPoles, Standard_Integer &theStatus) |
| | this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller's responsibility to insure that conditions More...
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| static void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt &NewPoles, Standard_Integer &theStatus) |
| | 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 More...
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| static void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Integer DerivativeRequest, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Real &Result) |
| | Perform the De Boor algorithm to evaluate a point at parameter , with <Degree> and <Dimension>. More...
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| static void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Integer DerivativeRequest, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Real &Weights, Standard_Real &PolesResult, Standard_Real &WeightsResult) |
| | Perform the 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. More...
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| static void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Boolean HomogeneousFlag, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, Standard_Real &Weight) |
| | Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point. More...
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| static void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Boolean HomogeneousFlag, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, Standard_Real &Weight) |
| | Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point. More...
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| static void | TangExtendToConstraint (const TColStd_Array1OfReal &FlatKnots, const Standard_Real C1Coefficient, const Standard_Integer NumPoles, Standard_Real &Poles, const Standard_Integer Dimension, const Standard_Integer Degree, const TColStd_Array1OfReal &ConstraintPoint, const Standard_Integer Continuity, const Standard_Boolean After, Standard_Integer &NbPolesResult, Standard_Integer &NbKnotsRsult, Standard_Real &KnotsResult, Standard_Real &PolesResult) |
| | 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. More...
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| static void | CacheD0 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point) |
| | Perform the evaluation of the 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. More...
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| static void | CacheD0 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point) |
| | 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. More...
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| static void | CoefsD0 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point) |
| | Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | CoefsD0 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point) |
| | Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | CacheD1 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point, gp_Vec &Vec) |
| | Perform the evaluation of the 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. More...
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| static void | CacheD1 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec) |
| | 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. More...
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| static void | CoefsD1 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point, gp_Vec &Vec) |
| | Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | CoefsD1 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec) |
| | Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | CacheD2 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2) |
| | Perform the evaluation of the 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. More...
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| static void | CacheD2 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2) |
| | 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. More...
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| static void | CoefsD2 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2) |
| | Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | CoefsD2 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2) |
| | Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | CacheD3 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2, gp_Vec &Vec3) |
| | Perform the evaluation of the 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. More...
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| static void | CacheD3 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2, gp_Vec2d &Vec3) |
| | 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. More...
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| static void | CoefsD3 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2, gp_Vec &Vec3) |
| | Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | CoefsD3 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2, gp_Vec2d &Vec3) |
| | Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! More...
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| static void | BuildCache (const Standard_Real U, const Standard_Real InverseOfSpanDomain, const Standard_Boolean PeriodicFlag, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, TColgp_Array1OfPnt &CachePoles, TColStd_Array1OfReal *CacheWeights) |
| | Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expension for the numerator and stores it in CachePoles. More...
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| static void | BuildCache (const Standard_Real U, const Standard_Real InverseOfSpanDomain, const Standard_Boolean PeriodicFlag, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, TColgp_Array1OfPnt2d &CachePoles, TColStd_Array1OfReal *CacheWeights) |
| | Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expension for the numerator and stores it in CachePoles. More...
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| static void | BuildCache (const Standard_Real theParameter, const Standard_Real theSpanDomain, const Standard_Boolean thePeriodicFlag, const Standard_Integer theDegree, const Standard_Integer theSpanIndex, const TColStd_Array1OfReal &theFlatKnots, const TColgp_Array1OfPnt &thePoles, const TColStd_Array1OfReal *theWeights, TColStd_Array2OfReal &theCacheArray) |
| | Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplCLib_Cache. More...
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| static void | BuildCache (const Standard_Real theParameter, const Standard_Real theSpanDomain, const Standard_Boolean thePeriodicFlag, const Standard_Integer theDegree, const Standard_Integer theSpanIndex, const TColStd_Array1OfReal &theFlatKnots, const TColgp_Array1OfPnt2d &thePoles, const TColStd_Array1OfReal *theWeights, TColStd_Array2OfReal &theCacheArray) |
| | Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. Structure of result optimized for BSplCLib_Cache. More...
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| static void | PolesCoefficients (const TColgp_Array1OfPnt2d &Poles, TColgp_Array1OfPnt2d &CachePoles) |
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| static void | PolesCoefficients (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, TColgp_Array1OfPnt2d &CachePoles, TColStd_Array1OfReal *CacheWeights) |
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| static void | PolesCoefficients (const TColgp_Array1OfPnt &Poles, TColgp_Array1OfPnt &CachePoles) |
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| static void | PolesCoefficients (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, TColgp_Array1OfPnt &CachePoles, TColStd_Array1OfReal *CacheWeights) |
| | Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziercurves at parameter 0. Warning: To be used for Beziercurves ONLY!!! More...
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| static const Standard_Real & | FlatBezierKnots (const Standard_Integer Degree) |
| | Returns pointer to statically allocated array representing flat knots for bezier curve of the specified degree. Raises OutOfRange if Degree > MaxDegree() More...
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| static void | BuildSchoenbergPoints (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, TColStd_Array1OfReal &Parameters) |
| | builds the Schoenberg points from the flat knot used to interpolate a BSpline since the BSpline matrix is invertible. More...
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| static void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt &Poles, Standard_Integer &InversionProblem) |
| | Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) contains the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation 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. More...
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| static void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt2d &Poles, Standard_Integer &InversionProblem) |
| | Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) contains the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem w ll report 0 if there was no problem else it will give the index of the faulty pivot. More...
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| static void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal &Weights, Standard_Integer &InversionProblem) |
| | Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) contains the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot. More...
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| static void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal &Weights, Standard_Integer &InversionProblem) |
| | Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) contains the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem w ll report 0 if there was no problem else it will give the i. More...
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| static void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Integer &InversionProblem) |
| | 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. More...
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| static void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Real &Weights, Standard_Integer &InversionProblem) |
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| static void | MovePoint (const Standard_Real U, const gp_Vec2d &Displ, const Standard_Integer Index1, const Standard_Integer Index2, const Standard_Integer Degree, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &FlatKnots, Standard_Integer &FirstIndex, Standard_Integer &LastIndex, TColgp_Array1OfPnt2d &NewPoles) |
| | Find the new poles which allows an old point (with a given u as parameter) to reach a new position Index1 and Index2 indicate the range of poles we can move (1, NbPoles-1) or (2, NbPoles) -> no constraint for one side don't enter (1,NbPoles) -> error: rigid move (2, NbPoles-1) -> the ends are enforced (3, NbPoles-2) -> the ends and the tangency are enforced if Problem in BSplineBasis calculation, no change for the curve and FirstIndex, LastIndex = 0. More...
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| static void | MovePoint (const Standard_Real U, const gp_Vec &Displ, const Standard_Integer Index1, const Standard_Integer Index2, const Standard_Integer Degree, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &FlatKnots, Standard_Integer &FirstIndex, Standard_Integer &LastIndex, TColgp_Array1OfPnt &NewPoles) |
| | Find the new poles which allows an old point (with a given u as parameter) to reach a new position Index1 and Index2 indicate the range of poles we can move (1, NbPoles-1) or (2, NbPoles) -> no constraint for one side don't enter (1,NbPoles) -> error: rigid move (2, NbPoles-1) -> the ends are enforced (3, NbPoles-2) -> the ends and the tangency are enforced if Problem in BSplineBasis calculation, no change for the curve and FirstIndex, LastIndex = 0. More...
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| static void | MovePointAndTangent (const Standard_Real U, const Standard_Integer ArrayDimension, Standard_Real &Delta, Standard_Real &DeltaDerivative, const Standard_Real Tolerance, const Standard_Integer Degree, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Real &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &FlatKnots, Standard_Real &NewPoles, Standard_Integer &ErrorStatus) |
| | This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the curve cannot move but tangent starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = ... Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if not NULL NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots. More...
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| static void | MovePointAndTangent (const Standard_Real U, const gp_Vec &Delta, const gp_Vec &DeltaDerivative, const Standard_Real Tolerance, const Standard_Integer Degree, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &FlatKnots, TColgp_Array1OfPnt &NewPoles, Standard_Integer &ErrorStatus) |
| | This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the curve cannot move but tangent starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = ... Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if not NULL NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots. More...
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| static void | MovePointAndTangent (const Standard_Real U, const gp_Vec2d &Delta, const gp_Vec2d &DeltaDerivative, const Standard_Real Tolerance, const Standard_Integer Degree, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &FlatKnots, TColgp_Array1OfPnt2d &NewPoles, Standard_Integer &ErrorStatus) |
| | 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. More...
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| static void | Resolution (Standard_Real &PolesArray, const Standard_Integer ArrayDimension, const Standard_Integer NumPoles, const TColStd_Array1OfReal *Weights, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, const Standard_Real Tolerance3D, Standard_Real &UTolerance) |
| | given a tolerance in 3D space returns a tolerance in U parameter space such that all u1 and u0 in the domain of the curve f(u) | u1 - u0 | < UTolerance and we have |f (u1) - f (u0)| < Tolerance3D More...
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| static void | Resolution (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal *Weights, const Standard_Integer NumPoles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, const Standard_Real Tolerance3D, Standard_Real &UTolerance) |
| | given a tolerance in 3D space returns a tolerance in U parameter space such that all u1 and u0 in the domain of the curve f(u) | u1 - u0 | < UTolerance and we have |f (u1) - f (u0)| < Tolerance3D More...
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| static void | Resolution (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal *Weights, const Standard_Integer NumPoles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, const Standard_Real Tolerance3D, Standard_Real &UTolerance) |
| | 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 More...
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