OCC.BSplCLib module

BSplCLib B-spline curve Library.The BSplCLib package is a basic library for BSplines. Itprovides three categories of functions.* Management methods to process knots and multiplicities.* Multi-Dimensions spline methods. BSpline methods wherepoles have an arbitrary number of dimensions. They dividesin two groups :- Global methods modifying the whole set of poles. Thepoles are described by an array of Reals and aDimension. Example : Inserting knots.- Local methods computing points and derivatives. Thepoles are described by a pointer on a local array ofReals and a Dimension. The local array is modified.* 2D and 3D spline curves methods.Methods for 2d and 3d BSplines curves rational or notrational.Those methods have the following structure :- They extract the pole informations in a working array.- They process the working array with themulti-dimension methods. (for example a 3d rationalcurve is processed as a 4 dimension curve).- They get back the result in the original dimension.Note that the bspline surface methods found in thepackage BSplSLib uses the same structure and rely onBSplCLib.In the following list of methods the 2d and 3d curvemethods will be described with the correspondingmulti-dimension method.The 3d or 2d B-spline curve is defined with :. its control points : TColgp_Array1OfPnt(2d) Poles. its weights : TColStd_Array1OfReal Weights. its knots : TColStd_Array1OfReal Knots. its multiplicities : TColStd_Array1OfInteger Mults. its degree : Standard_Integer Degree. its periodicity : Standard_Boolean PeriodicWarnings :The bounds of Poles and Weights should be the same.The bounds of Knots and Mults should be the same.Weights can be a null reference (BSplCLib::NoWeights())the curve is non rational.Mults can be a null reference (BSplCLib::NoMults())the knots are ‘flat’ knots.KeyWords :B-spline curve, Functions, LibraryReferences :. A survey of curves and surfaces methods in CADG WolfgangBOHM CAGD 1 (1984). On de Boor-like algorithms and blossoming Wolfgang BOEHMcagd 5 (1988). Blossoming and knot insertion algorithms for B-spline curvesRonald N. GOLDMAN. Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA. Curves and Surfaces for Computer Aided Geometric Design,a practical guide Gerald Farin

class SwigPyIterator(*args, **kwargs)

Bases: object

advance()
copy()
decr()
distance()
equal()
incr()
next()
previous()
thisown

The membership flag

value()
class bsplclib

Bases: object

static AntiBoorScheme()
  • 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.
Parameters:
  • U (float) –
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
  • Depth (int) –
  • Length (int) –
  • Tolerance (float) –
Return type:

bool
static Bohm()
  • Performs the Bohm Algorithm at parameter <U>. This algorithm computes the value and all the derivatives up to order N (N <= Degree). //! <Poles> is the original array of poles. //! The result in <Poles> is the value and the derivatives. Poles[0] is the value, Poles[Degree] is the last derivative.
Parameters:
  • U (float) –
  • Degree (int) –
  • N (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
Return type:

void
static BoorIndex()
  • Returns the index in the Boor result array of the poles <Index>. If the Boor algorithm was perform with <Length> and <Depth>.
Parameters:
  • Index (int) –
  • Length (int) –
  • Depth (int) –
Return type:

int
static BoorScheme()
  • Performs the Boor Algorithm at parameter <U> with the given <Degree> and the array of <Knots> on the poles <Poles> of dimension <Dimension>. The schema is computed until level <Depth> on a basis of <Length+1> poles. //! * Knots is an array of reals of length : //! <Length> + <Degree> //! * Poles is an array of reals of length : //! (2 * <Length> + 1) * <Dimension> //! The poles values must be set in the array at the positions. //! 0..Dimension, //! 2 * Dimension .. 3 * Dimension //! 4 * Dimension .. 5 * Dimension //! … //! The results are found in the array poles depending on the Depth. (See the method GetPole).
Parameters:
  • U (float) –
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
  • Depth (int) –
  • Length (int) –
Return type:

void
static BuildBSpMatrix()
  • 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
Parameters:
  • Parameters (TColStd_Array1OfReal &) –
  • OrderArray (TColStd_Array1OfInteger &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int &) –
  • LowerBandWidth (int &) –
Return type:

int
static BuildBoor()
  • Copy in <LP> poles for <Dimension> Boor scheme. Starting from <Index> * <Dimension>, copy <Length+1> poles.
Parameters:
  • Index (int) –
  • Length (int) –
  • Dimension (int) –
  • Poles (TColStd_Array1OfReal &) –
  • LP (float &) –
Return type:

void
static BuildCache()
  • 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
Parameters:
  • U (float) –
  • InverseOfSpanDomain (float) –
  • PeriodicFlag (bool) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • CachePoles (TColgp_Array1OfPnt) –
  • CacheWeights (TColStd_Array1OfReal &) –
Return type:

void
  • 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
Parameters:
Return type:

void
static BuildEval()
Parameters:
  • Degree (int) –
  • Index (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • LP (float &) –
  • Degree –
  • Index –
  • Poles –
  • Weights –
  • LP –
Return type:

void
Return type:

void
  • Copy in <LP> the poles and weights for the Eval scheme. starting from Poles(Poles.Lower()+Index)
Parameters:
Return type:

void
static BuildKnots()
  • Stores in LK the usefull knots for the BoorSchem on the span Knots(Index) - Knots(Index+1)
Parameters:
  • Degree (int) –
  • Index (int) –
  • Periodic (bool) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • LK (float &) –
Return type:

void
static BuildSchoenbergPoints()
  • builds the Schoenberg points from the flat knot used to interpolate a BSpline since the BSpline matrix is invertible.
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
Return type:

void
static CacheD0()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
static CacheD1()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
static CacheD2()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
static CacheD3()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
static CoefsD0()
  • Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
static CoefsD1()
  • Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
static CoefsD2()
  • Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
static CoefsD3()
  • Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
static D0()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • U –
  • Poles –
  • Weights –
  • P –
  • U –
  • Poles –
  • Weights –
  • P –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
static D1()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • V (gp_Vec2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V –
  • U –
  • Poles –
  • Weights –
  • P –
  • V –
  • U –
  • Poles –
  • Weights –
  • P –
  • V –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
static D2()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • V1 (gp_Vec2d) –
  • V2 (gp_Vec2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
static D3()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • V1 (gp_Vec2d) –
  • V2 (gp_Vec2d) –
  • V3 (gp_Vec2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • V3 –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • V3 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
  • V3 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
  • V3 –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
static Derivative()
  • 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).
Parameters:
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Length (int) –
  • Order (int) –
  • Poles (float &) –
Return type:

void
static Eval()
  • Perform the Boor algorithm to evaluate a point at parameter <U>, with <Degree> and <Dimension>. //! Poles is an array of Reals of size //! <Dimension> * <Degree>+1 //! Containing the poles. At the end <Poles> contains the current point.
Parameters:
  • U (float) –
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
Return type:

void
  • Perform the De Boor algorithm to evaluate a point at parameter <U>, with <Degree> and <Dimension>. //! Poles is an array of Reals of size //! <Dimension> * <Degree>+1 //! Containing the poles. At the end <Poles> contains the current point. Poles Contain all the poles of the BsplineCurve, Knots also Contains all the knots of the BsplineCurve. ExtrapMode has two slots [0] = Degree used to extrapolate before the first knot [1] = Degre used to extrapolate after the last knot has to be between 1 and Degree
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • DerivativeRequest (int) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • ArrayDimension (int) –
  • Poles (float &) –
  • Result (float &) –
Return type:

void
  • Perform the De Boor algorithm to evaluate a point at parameter <U>, with <Degree> and <Dimension>. Evaluates by multiplying the Poles by the Weights and gives the homogeneous result in PolesResult that is the results of the evaluation of the numerator once it has been multiplied by the weights and in WeightsResult one has the result of the evaluation of the denominator //! Warning: <PolesResult> and <WeightsResult> must be dimensionned properly.
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • DerivativeRequest (int) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • ArrayDimension (int) –
  • Poles (float &) –
  • Weights (float &) –
  • PolesResult (float &) –
  • WeightsResult (float &) –
Return type:

void
  • Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • HomogeneousFlag (bool) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • Point (gp_Pnt) –
  • Weight (float &) –
Return type:

void
  • Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • HomogeneousFlag (bool) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Point (gp_Pnt2d) –
  • Weight (float &) –
Return type:

void
static EvalBsplineBasis()
  • 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
Parameters:
  • Side (int) –
  • DerivativeOrder (int) –
  • Order (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameter (float) –
  • FirstNonZeroBsplineIndex (int &) –
  • BsplineBasis (math_Matrix &) –
  • isPeriodic (bool) – default value is Standard_False
Return type:

int
static FactorBandedMatrix()
  • 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
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • PivotIndexProblem (int &) –
Return type:

int
static FirstUKnotIndex()
  • Computes the index of the knots value which gives the start point of the curve.
Parameters:
  • Degree (int) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
static FlatBezierKnots()
  • Returns pointer to statically allocated array representing flat knots for bezier curve of the specified degree. Raises OutOfRange if Degree > MaxDegree()
Parameters:Degree (int) –
Return type:float
static FlatIndex()
  • Computes the index of the flats knots sequence corresponding to <Index> in the knots sequence which multiplicities are <Mults>.
Parameters:
  • Degree (int) –
  • Index (int) –
  • Mults (TColStd_Array1OfInteger &) –
  • Periodic (bool) –
Return type:

int
static FunctionMultiply()
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • PolesDimension (int) –
  • Poles (float &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (float &) –
  • Status (int &) –
Return type:

void
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColStd_Array1OfReal &) –
  • Status (int &) –
Return type:

void
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Status (int &) –
Return type:

void
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt) –
  • Status (int &) –
Return type:

void
static FunctionReparameterise()
  • This function will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following: //! 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots //! 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) //! Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method //! Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • PolesDimension (int) –
  • Poles (float &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (float &) –
  • Status (int &) –
Return type:

void
  • This function will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following: //! 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots //! 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) //! Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method //! Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColStd_Array1OfReal &) –
  • Status (int &) –
Return type:

void
  • this will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following : 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt) –
  • Status (int &) –
Return type:

void
  • this will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following : 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Status (int &) –
Return type:

void
static GetPole()
  • Copy the pole at position <Index> in the Boor scheme of dimension <Dimension> to <Position> in the array <Pole>. <Position> is updated.
Parameters:
  • Index (int) –
  • Length (int) –
  • Depth (int) –
  • Dimension (int) –
  • LocPoles (float &) –
  • Position (int &) –
  • Pole (TColStd_Array1OfReal &) –
Return type:

void
static Hunt()
  • This routine searches the position of the real value X in the ordered set of real values XX. //! The elements in the table XX are either monotonically increasing or monotonically decreasing. //! The input value Iloc is used to initialize the algorithm : if Iloc is outside of the bounds [XX.Lower(), – XX.Upper()] the bisection algorithm is used else the routine searches from a previous known position by increasing steps then converges by bisection. //! This routine is used to locate a knot value in a set of knots.
Parameters:
  • XX (TColStd_Array1OfReal &) –
  • X (float) –
  • Iloc (int &) –
Return type:

void
static IncreaseDegree()
Parameters:
  • Degree (int) –
  • NewDegree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Degree –
  • NewDegree –
  • Periodic –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • Knots –
  • Mults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots –
  • NewMults –
  • Degree –
  • NewDegree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • NewPoles –
  • NewWeights –
  • NewKnots –
  • NewMults –
  • NewDegree –
  • Poles –
  • Weights –
  • NewPoles –
  • NewWeights –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
  • Increase the degree of a bspline (or bezier) curve of dimension <Dimension> form <Degree> to <NewDegree>. //! The number of poles in the new curve is : //! Poles.Length() + (NewDegree - Degree) * Number of spans //! Where the number of spans is : //! LastUKnotIndex(Mults) - FirstUKnotIndex(Mults) + 1 //! for a non-periodic curve //! And Knots.Length() - 1 for a periodic curve. //! The multiplicities of all knots are increased by the degree elevation. //! The new knots are usually the same knots with the exception of a non-periodic curve with the first and last multiplicity not equal to Degree+1 where knots are removed form the start and the bottom untils the sum of the multiplicities is equal to NewDegree+1 at the knots corresponding to the first and last parameters of the curve. //! Example : Suppose a curve of degree 3 starting with following knots and multiplicities : //! knot : 0. 1. 2. mult : 1 2 1 //! The FirstUKnot is 2. because the sum of multiplicities is Degree+1 : 1 + 2 + 1 = 4 = 3 + 1 //! i.e. the first parameter of the curve is 2. and will still be 2. after degree elevation. Let raises this curve to degree 4. The multiplicities are increased by 2. //! They become 2 3 2. But we need a sum of multiplicities of 5 at knot 2. So the first knot is removed and the new knots are : //! knot : 1. 2. mult : 3 2 //! The multipicity of the first knot may also be reduced if the sum is still to big. //! In the most common situations (periodic curve or curve with first and last multiplicities equals to Degree+1) the knots are knot changes. //! The method IncreaseDegreeCountKnots can be used to compute the new number of knots.
Parameters:
Return type:

void
static IncreaseDegreeCountKnots()
  • 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.
Parameters:
  • Degree (int) –
  • NewDegree (int) –
  • Periodic (bool) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
static InsertKnot()
Parameters:
  • UIndex (int) –
  • U (float) –
  • UMult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
  • 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.
Parameters:
  • UIndex (int) –
  • U (float) –
  • UMult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
static InsertKnots()
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • AddKnots (TColStd_Array1OfReal &) –
  • AddMults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Epsilon (float) –
  • Add (bool) – default value is Standard_True
  • Degree –
  • Periodic –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • Knots –
  • Mults –
  • AddKnots –
  • AddMults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots –
  • NewMults –
  • Epsilon –
  • Add – default value is Standard_True
Return type:

void
Return type:

void
  • 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.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • AddKnots (TColStd_Array1OfReal &) –
  • AddMults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Epsilon (float) –
  • Add (bool) – default value is Standard_True
Return type:

void
static Interpolate()
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation or interpolation at Scheonberg points the method will work The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem w ll report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem w ll report 0 if there was no problem else it will give the i
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray The length of FlatKnots is Degree + L + 1 The PolesArray is an seen as an Array[1..N][1..ArrayDimension] with N = tge length of the parameters array Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation or interpolation at Scheonberg points the method will work The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • ArrayDimension (int) –
  • Poles (float &) –
  • InversionProblem (int &) –
  • Degree –
  • FlatKnots –
  • Parameters –
  • ContactOrderArray –
  • ArrayDimension –
  • Poles –
  • Weights (float &) –
  • InversionProblem –
Return type:

void
Return type:

void
static IsRational()
  • 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.
Parameters:
  • Weights (TColStd_Array1OfReal &) –
  • I1 (int) –
  • I2 (int) –
  • Epsilon (float) – default value is 0.0
Return type:

bool
static KnotAnalysis()
  • Analyzes the array of knots. Returns the form and the maximum knot multiplicity.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • CKnots (TColStd_Array1OfReal &) –
  • CMults (TColStd_Array1OfInteger &) –
  • KnotForm (GeomAbs_BSplKnotDistribution &) –
  • MaxKnotMult (int &) –
Return type:

void
static KnotForm()
  • 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>.
Parameters:
  • Knots (TColStd_Array1OfReal &) –
  • FromK1 (int) –
  • ToK2 (int) –
Return type:

BSplCLib_KnotDistribution
static KnotSequence()
Parameters:
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • KnotSeq (TColStd_Array1OfReal &) –
  • Periodic (bool) – default value is Standard_False
Return type:

void
  • 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)
Parameters:
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • Degree (int) –
  • Periodic (bool) –
  • KnotSeq (TColStd_Array1OfReal &) –
Return type:

void
static KnotSequenceLength()
  • 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
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • Degree (int) –
  • Periodic (bool) –
Return type:

int
static Knots()
  • 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)
Parameters:
  • KnotSeq (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • Periodic (bool) – default value is Standard_False
Return type:

void
static KnotsLength()
  • Returns the length of the sequence of knots (and Mults) without repetition.
Parameters:
  • KnotSeq (TColStd_Array1OfReal &) –
  • Periodic (bool) – default value is Standard_False
Return type:

int
static LastUKnotIndex()
  • Computes the index of the knots value which gives the end point of the curve.
Parameters:
  • Degree (int) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
static LocateParameter()
  • Locates the parametric value U in the knots sequence between the knot K1 and the knot K2. The value return in Index verifies. //! Knots(Index) <= U < Knots(Index + 1) if U <= Knots (K1) then Index = K1 if U >= Knots (K2) then Index = K2 - 1 //! If Periodic is True U may be modified to fit in the range Knots(K1), Knots(K2). In any case the correct value is returned in NewU. //! Warnings :Index is used as input data to initialize the searching function. Warning: Knots have to be ‘withe repetitions’
Parameters:
  • Degree (int) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • U (float) –
  • IsPeriodic (bool) –
  • FromK1 (int) –
  • ToK2 (int) –
  • KnotIndex (int &) –
  • NewU (float &) –
Return type:

void
  • 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’
Parameters:
  • Degree (int) –
  • Knots (TColStd_Array1OfReal &) –
  • U (float) –
  • IsPeriodic (bool) –
  • FromK1 (int) –
  • ToK2 (int) –
  • KnotIndex (int &) –
  • NewU (float &) –
  • Degree –
  • Knots –
  • Mults (TColStd_Array1OfInteger &) –
  • U –
  • Periodic (bool) –
  • Index (int &) –
  • NewU –
Return type:

void
Return type:

void
static MaxDegree()
  • returns the degree maxima for a BSplineCurve.
Return type:int
static MaxKnotMult()
  • Finds the greatest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • K1 (int) –
  • K2 (int) –
Return type:

int
static MergeBSplineKnots()
  • Merges two knot vector by setting the starting and ending values to StartValue and EndValue
Parameters:
  • Tolerance (float) –
  • StartValue (float) –
  • EndValue (float) –
  • Degree1 (int) –
  • Knots1 (TColStd_Array1OfReal &) –
  • Mults1 (TColStd_Array1OfInteger &) –
  • Degree2 (int) –
  • Knots2 (TColStd_Array1OfReal &) –
  • Mults2 (TColStd_Array1OfInteger &) –
  • NumPoles (int &) –
  • NewKnots (Handle_TColStd_HArray1OfReal &) –
  • NewMults (Handle_TColStd_HArray1OfInteger &) –
Return type:

void
static MinKnotMult()
  • Finds the lowest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • K1 (int) –
  • K2 (int) –
Return type:

int
static MovePoint()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
static MovePointAndTangent()
  • This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the cuve cannot move but tangen starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = … Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if Rational = Standard_True NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.
Parameters:
  • U (float) –
  • ArrayDimension (int) –
  • Delta (float &) –
  • DeltaDerivative (float &) –
  • Tolerance (float) –
  • Degree (int) –
  • Rational (bool) –
  • StartingCondition (int) –
  • EndingCondition (int) –
  • Poles (float &) –
  • Weights (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewPoles (float &) –
  • ErrorStatus (int &) –
Return type:

void
  • This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the cuve cannot move but tangen starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = … Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if Rational = Standard_True NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.
Parameters:
Return type:

void
  • This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the cuve cannot move but tangen starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = … Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if Rational = Standard_True NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.
Parameters:
Return type:

void
static MultForm()
  • Analyses the distribution of multiplicities between the knot FromK1 and the Knot ToK2.
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • FromK1 (int) –
  • ToK2 (int) –
Return type:

BSplCLib_MultDistribution
static NbPoles()
  • 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.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
static NoMults()
  • Used as argument for a flatknots evaluation.
Return type:TColStd_Array1OfInteger
static NoWeights()
  • Used as argument for a non rational curve.
Return type:TColStd_Array1OfReal
static PoleIndex()
  • 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().
Parameters:
  • Degree (int) –
  • Index (int) –
  • Periodic (bool) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
static PolesCoefficients()
Parameters:
  • Poles (TColgp_Array1OfPnt) –
  • CachePoles (TColgp_Array1OfPnt) –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • CachePoles –
  • CacheWeights (TColStd_Array1OfReal &) –
  • Poles –
  • CachePoles –
Return type:

void
Return type:

void
Return type:

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

void
static PrepareInsertKnots()
  • 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.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • AddKnots (TColStd_Array1OfReal &) –
  • AddMults (TColStd_Array1OfInteger &) –
  • NbPoles (int &) –
  • NbKnots (int &) –
  • Epsilon (float) –
  • Add (bool) – default value is Standard_True
Return type:

bool
static PrepareTrimming()
  • Set in <NbKnots> and <NbPoles> the number of Knots and Poles of the curve resulting of the trimming of the BSplinecurve definded with <degree>, <knots>, <mults>
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • U1 (float) –
  • U2 (float) –
  • NbKnots (int &) –
  • NbPoles (int &) –
Return type:

void
static PrepareUnperiodize()
  • 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>.
Parameters:
  • Degree (int) –
  • Mults (TColStd_Array1OfInteger &) –
  • NbKnots (int &) –
  • NbPoles (int &) –
Return type:

void
static RaiseMultiplicity()
Parameters:
  • KnotIndex (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
  • Raise the multiplicity of knot to <UMult>. //! The new control points are returned. Knots and Mults are not updated.
Parameters:
  • KnotIndex (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
static RemoveKnot()
Parameters:
  • Index (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Tolerance (float) –
  • Index –
  • Mult –
  • Degree –
  • Periodic –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • Knots –
  • Mults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots –
  • NewMults –
  • Tolerance –
Return type:

bool
Return type:

bool
  • 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.
Parameters:
  • Index (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Tolerance (float) –
Return type:

bool
static Reparametrize()
  • 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.
Parameters:
  • U1 (float) –
  • U2 (float) –
  • Knots (TColStd_Array1OfReal &) –
Return type:

void
static Resolution()
  • 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
Parameters:
  • PolesArray (float &) –
  • ArrayDimension (int) –
  • NumPoles (int) –
  • Weights (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Tolerance3D (float) –
  • UTolerance (float &) –
Return type:

void
  • 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
Parameters:
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • NumPoles (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Tolerance3D (float) –
  • UTolerance (float &) –
Return type:

void
  • 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
Parameters:
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • NumPoles (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Tolerance3D (float) –
  • UTolerance (float &) –
Return type:

void
static Reverse()
  • Reverses the array knots to become the knots sequence of the reversed curve.
Parameters:Knots (TColStd_Array1OfReal &) –
Return type:void
  • Reverses the array of multiplicities.
Parameters:Mults (TColStd_Array1OfInteger &) –
Return type:void
  • 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)
Parameters:
Return type:

void
  • Reverses the array of poles.
Parameters:
Return type:

void
  • Reverses the array of poles.
Parameters:
  • Weights (TColStd_Array1OfReal &) –
  • Last (int) –
Return type:

void
static SolveBandedSystem()
  • 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
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • ArrayDimension (int) –
  • Array (float &) –
Return type:

int
  • 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
Parameters:
Return type:

int
  • 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
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • Array (float &) –
  • Matrix –
  • UpperBandWidth –
  • LowerBandWidth –
  • HomogenousFlag (bool) –
  • ArrayDimension (int) –
  • Array –
  • Weights (float &) –
Return type:

int
Return type:

int
  • This solves the system Matrix.X = B with when Matrix is factored in LU form The Array is an seen as an Array[1..N][1..ArrayDimension] with N = the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension. If HomogeneousFlag == 0 the Poles are multiplied by the Weights uppon Entry and once interpolation is carried over the result of the poles are divided by the result of the interpolation of the weights. Otherwise if HomogenousFlag == 1 the Poles and Weigths are treated homogenously that is that those are interpolated as they are and result is returned without division by the interpolated weigths.
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • HomogenousFlag (bool) –
  • Array (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
Return type:

int
  • This solves the system Matrix.X = B with when Matrix is factored in LU form The Array is an seen as an Array[1..N][1..ArrayDimension] with N = the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension If HomogeneousFlag == 0 the Poles are multiplied by the Weights uppon Entry and once interpolation is carried over the result of the poles are divided by the result of the interpolation of the weights. Otherwise if HomogenousFlag == 1 the Poles and Weigths are treated homogenously that is that those are interpolated as they are and result is returned without division by the interpolated weigths.
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • HomogeneousFlag (bool) –
  • Array (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
Return type:

int
static TangExtendToConstraint()
  • Extend a BSpline nD using the tangency map <C1Coefficient> is the coefficient of reparametrisation <Continuity> must be equal to 1, 2 or 3. <Degree> must be greater or equal than <Continuity> + 1. //! Warning: <KnotsResult> and <PolesResult> must be dimensionned properly.
Parameters:
  • FlatKnots (TColStd_Array1OfReal &) –
  • C1Coefficient (float) –
  • NumPoles (int) –
  • Poles (float &) –
  • Dimension (int) –
  • Degree (int) –
  • ConstraintPoint (TColStd_Array1OfReal &) –
  • Continuity (int) –
  • After (bool) –
  • NbPolesResult (int &) –
  • NbKnotsRsult (int &) –
  • KnotsResult (float &) –
  • PolesResult (float &) –
Return type:

void
static Trimming()
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • U1 (float) –
  • U2 (float) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Degree –
  • Periodic –
  • Knots –
  • Mults –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • U1 –
  • U2 –
  • NewKnots –
  • NewMults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • Degree –
  • Periodic –
  • Knots –
  • Mults –
  • Poles –
  • Weights –
  • U1 –
  • U2 –
  • NewKnots –
  • NewMults –
  • NewPoles –
  • NewWeights –
Return type:

void
Return type:

void
Return type:

void
static Unperiodize()
Parameters:
  • Degree (int) –
  • Dimension (int) –
  • Mults (TColStd_Array1OfInteger &) –
  • Knots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • NewMults (TColStd_Array1OfInteger &) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Degree –
  • Mults –
  • Knots –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • NewMults –
  • NewKnots –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • Degree –
  • Mults –
  • Knots –
  • Poles –
  • Weights –
  • NewMults –
  • NewKnots –
  • NewPoles –
  • NewWeights –
Return type:

void
Return type:

void
Return type:

void
thisown

The membership flag

bsplclib_AntiBoorScheme()
  • 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.
Parameters:
  • U (float) –
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
  • Depth (int) –
  • Length (int) –
  • Tolerance (float) –
Return type:

bool
bsplclib_Bohm()
  • Performs the Bohm Algorithm at parameter <U>. This algorithm computes the value and all the derivatives up to order N (N <= Degree). //! <Poles> is the original array of poles. //! The result in <Poles> is the value and the derivatives. Poles[0] is the value, Poles[Degree] is the last derivative.
Parameters:
  • U (float) –
  • Degree (int) –
  • N (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
Return type:

void
bsplclib_BoorIndex()
  • Returns the index in the Boor result array of the poles <Index>. If the Boor algorithm was perform with <Length> and <Depth>.
Parameters:
  • Index (int) –
  • Length (int) –
  • Depth (int) –
Return type:

int
bsplclib_BoorScheme()
  • Performs the Boor Algorithm at parameter <U> with the given <Degree> and the array of <Knots> on the poles <Poles> of dimension <Dimension>. The schema is computed until level <Depth> on a basis of <Length+1> poles. //! * Knots is an array of reals of length : //! <Length> + <Degree> //! * Poles is an array of reals of length : //! (2 * <Length> + 1) * <Dimension> //! The poles values must be set in the array at the positions. //! 0..Dimension, //! 2 * Dimension .. 3 * Dimension //! 4 * Dimension .. 5 * Dimension //! … //! The results are found in the array poles depending on the Depth. (See the method GetPole).
Parameters:
  • U (float) –
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
  • Depth (int) –
  • Length (int) –
Return type:

void
bsplclib_BuildBSpMatrix()
  • 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
Parameters:
  • Parameters (TColStd_Array1OfReal &) –
  • OrderArray (TColStd_Array1OfInteger &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int &) –
  • LowerBandWidth (int &) –
Return type:

int
bsplclib_BuildBoor()
  • Copy in <LP> poles for <Dimension> Boor scheme. Starting from <Index> * <Dimension>, copy <Length+1> poles.
Parameters:
  • Index (int) –
  • Length (int) –
  • Dimension (int) –
  • Poles (TColStd_Array1OfReal &) –
  • LP (float &) –
Return type:

void
bsplclib_BuildCache()
  • 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
Parameters:
  • U (float) –
  • InverseOfSpanDomain (float) –
  • PeriodicFlag (bool) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • CachePoles (TColgp_Array1OfPnt) –
  • CacheWeights (TColStd_Array1OfReal &) –
Return type:

void
  • 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
Parameters:
Return type:

void
bsplclib_BuildEval()
Parameters:
  • Degree (int) –
  • Index (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • LP (float &) –
  • Degree –
  • Index –
  • Poles –
  • Weights –
  • LP –
Return type:

void
Return type:

void
  • Copy in <LP> the poles and weights for the Eval scheme. starting from Poles(Poles.Lower()+Index)
Parameters:
Return type:

void
bsplclib_BuildKnots()
  • Stores in LK the usefull knots for the BoorSchem on the span Knots(Index) - Knots(Index+1)
Parameters:
  • Degree (int) –
  • Index (int) –
  • Periodic (bool) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • LK (float &) –
Return type:

void
bsplclib_BuildSchoenbergPoints()
  • builds the Schoenberg points from the flat knot used to interpolate a BSpline since the BSpline matrix is invertible.
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
Return type:

void
bsplclib_CacheD0()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
bsplclib_CacheD1()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
bsplclib_CacheD2()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
bsplclib_CacheD3()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
bsplclib_CoefsD0()
  • Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
bsplclib_CoefsD1()
  • Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
bsplclib_CoefsD2()
  • Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
bsplclib_CoefsD3()
  • Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!
Parameters:
Return type:

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

void
bsplclib_D0()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • U –
  • Poles –
  • Weights –
  • P –
  • U –
  • Poles –
  • Weights –
  • P –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
bsplclib_D1()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • V (gp_Vec2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V –
  • U –
  • Poles –
  • Weights –
  • P –
  • V –
  • U –
  • Poles –
  • Weights –
  • P –
  • V –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
bsplclib_D2()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • V1 (gp_Vec2d) –
  • V2 (gp_Vec2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
bsplclib_D3()
Parameters:
  • U (float) –
  • Index (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • P (gp_Pnt2d) –
  • V1 (gp_Vec2d) –
  • V2 (gp_Vec2d) –
  • V3 (gp_Vec2d) –
  • U –
  • Index –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • V3 –
  • U –
  • UIndex (int) –
  • Degree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • P –
  • V1 –
  • V2 –
  • V3 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
  • V3 –
  • U –
  • Poles –
  • Weights –
  • P –
  • V1 –
  • V2 –
  • V3 –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
Return type:

void
bsplclib_Derivative()
  • 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).
Parameters:
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Length (int) –
  • Order (int) –
  • Poles (float &) –
Return type:

void
bsplclib_Eval()
  • Perform the Boor algorithm to evaluate a point at parameter <U>, with <Degree> and <Dimension>. //! Poles is an array of Reals of size //! <Dimension> * <Degree>+1 //! Containing the poles. At the end <Poles> contains the current point.
Parameters:
  • U (float) –
  • Degree (int) –
  • Knots (float &) –
  • Dimension (int) –
  • Poles (float &) –
Return type:

void
  • Perform the De Boor algorithm to evaluate a point at parameter <U>, with <Degree> and <Dimension>. //! Poles is an array of Reals of size //! <Dimension> * <Degree>+1 //! Containing the poles. At the end <Poles> contains the current point. Poles Contain all the poles of the BsplineCurve, Knots also Contains all the knots of the BsplineCurve. ExtrapMode has two slots [0] = Degree used to extrapolate before the first knot [1] = Degre used to extrapolate after the last knot has to be between 1 and Degree
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • DerivativeRequest (int) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • ArrayDimension (int) –
  • Poles (float &) –
  • Result (float &) –
Return type:

void
  • Perform the De Boor algorithm to evaluate a point at parameter <U>, with <Degree> and <Dimension>. Evaluates by multiplying the Poles by the Weights and gives the homogeneous result in PolesResult that is the results of the evaluation of the numerator once it has been multiplied by the weights and in WeightsResult one has the result of the evaluation of the denominator //! Warning: <PolesResult> and <WeightsResult> must be dimensionned properly.
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • DerivativeRequest (int) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • ArrayDimension (int) –
  • Poles (float &) –
  • Weights (float &) –
  • PolesResult (float &) –
  • WeightsResult (float &) –
Return type:

void
  • Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • HomogeneousFlag (bool) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • Point (gp_Pnt) –
  • Weight (float &) –
Return type:

void
  • Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point
Parameters:
  • U (float) –
  • PeriodicFlag (bool) –
  • HomogeneousFlag (bool) –
  • ExtrapMode (int &) –
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Point (gp_Pnt2d) –
  • Weight (float &) –
Return type:

void
bsplclib_EvalBsplineBasis()
  • 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
Parameters:
  • Side (int) –
  • DerivativeOrder (int) –
  • Order (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameter (float) –
  • FirstNonZeroBsplineIndex (int &) –
  • BsplineBasis (math_Matrix &) –
  • isPeriodic (bool) – default value is Standard_False
Return type:

int
bsplclib_FactorBandedMatrix()
  • 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
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • PivotIndexProblem (int &) –
Return type:

int
bsplclib_FirstUKnotIndex()
  • Computes the index of the knots value which gives the start point of the curve.
Parameters:
  • Degree (int) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
bsplclib_FlatBezierKnots()
  • Returns pointer to statically allocated array representing flat knots for bezier curve of the specified degree. Raises OutOfRange if Degree > MaxDegree()
Parameters:Degree (int) –
Return type:float
bsplclib_FlatIndex()
  • Computes the index of the flats knots sequence corresponding to <Index> in the knots sequence which multiplicities are <Mults>.
Parameters:
  • Degree (int) –
  • Index (int) –
  • Mults (TColStd_Array1OfInteger &) –
  • Periodic (bool) –
Return type:

int
bsplclib_FunctionMultiply()
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • PolesDimension (int) –
  • Poles (float &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (float &) –
  • Status (int &) –
Return type:

void
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColStd_Array1OfReal &) –
  • Status (int &) –
Return type:

void
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Status (int &) –
Return type:

void
  • this will multiply a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] by a function a(t) which is assumed to satisfy the following : 1. a(t) * F(t) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. the range of a(t) is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt) –
  • Status (int &) –
Return type:

void
bsplclib_FunctionReparameterise()
  • This function will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following: //! 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots //! 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) //! Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method //! Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • PolesDimension (int) –
  • Poles (float &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (float &) –
  • Status (int &) –
Return type:

void
  • This function will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following: //! 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots //! 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) //! Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method //! Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColStd_Array1OfReal &) –
  • Status (int &) –
Return type:

void
  • this will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following : 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt) –
  • Status (int &) –
Return type:

void
  • this will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following : 1. F(a(t)) is a polynomial BSpline that can be expressed exactly as a BSpline of degree NewDegree on the knots FlatKnots 2. a(t) defines a differentiable isomorphism between the range of FlatKnots to the range of BSplineFlatKnots which is the same as the range of F(t) Warning: it is the caller’s responsability to insure that conditions 1. and 2. above are satisfied : no check whatsoever is made in this method Status will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))
Parameters:
  • Function (BSplCLib_EvaluatorFunction &) –
  • BSplineDegree (int) –
  • BSplineFlatKnots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewDegree (int) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Status (int &) –
Return type:

void
bsplclib_GetPole()
  • Copy the pole at position <Index> in the Boor scheme of dimension <Dimension> to <Position> in the array <Pole>. <Position> is updated.
Parameters:
  • Index (int) –
  • Length (int) –
  • Depth (int) –
  • Dimension (int) –
  • LocPoles (float &) –
  • Position (int &) –
  • Pole (TColStd_Array1OfReal &) –
Return type:

void
bsplclib_Hunt()
  • This routine searches the position of the real value X in the ordered set of real values XX. //! The elements in the table XX are either monotonically increasing or monotonically decreasing. //! The input value Iloc is used to initialize the algorithm : if Iloc is outside of the bounds [XX.Lower(), – XX.Upper()] the bisection algorithm is used else the routine searches from a previous known position by increasing steps then converges by bisection. //! This routine is used to locate a knot value in a set of knots.
Parameters:
  • XX (TColStd_Array1OfReal &) –
  • X (float) –
  • Iloc (int &) –
Return type:

void
bsplclib_IncreaseDegree()
Parameters:
  • Degree (int) –
  • NewDegree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Degree –
  • NewDegree –
  • Periodic –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • Knots –
  • Mults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots –
  • NewMults –
  • Degree –
  • NewDegree –
  • Periodic –
  • Poles –
  • Weights –
  • Knots –
  • Mults –
  • NewPoles –
  • NewWeights –
  • NewKnots –
  • NewMults –
  • NewDegree –
  • Poles –
  • Weights –
  • NewPoles –
  • NewWeights –
Return type:

void
Return type:

void
Return type:

void
Return type:

void
  • Increase the degree of a bspline (or bezier) curve of dimension <Dimension> form <Degree> to <NewDegree>. //! The number of poles in the new curve is : //! Poles.Length() + (NewDegree - Degree) * Number of spans //! Where the number of spans is : //! LastUKnotIndex(Mults) - FirstUKnotIndex(Mults) + 1 //! for a non-periodic curve //! And Knots.Length() - 1 for a periodic curve. //! The multiplicities of all knots are increased by the degree elevation. //! The new knots are usually the same knots with the exception of a non-periodic curve with the first and last multiplicity not equal to Degree+1 where knots are removed form the start and the bottom untils the sum of the multiplicities is equal to NewDegree+1 at the knots corresponding to the first and last parameters of the curve. //! Example : Suppose a curve of degree 3 starting with following knots and multiplicities : //! knot : 0. 1. 2. mult : 1 2 1 //! The FirstUKnot is 2. because the sum of multiplicities is Degree+1 : 1 + 2 + 1 = 4 = 3 + 1 //! i.e. the first parameter of the curve is 2. and will still be 2. after degree elevation. Let raises this curve to degree 4. The multiplicities are increased by 2. //! They become 2 3 2. But we need a sum of multiplicities of 5 at knot 2. So the first knot is removed and the new knots are : //! knot : 1. 2. mult : 3 2 //! The multipicity of the first knot may also be reduced if the sum is still to big. //! In the most common situations (periodic curve or curve with first and last multiplicities equals to Degree+1) the knots are knot changes. //! The method IncreaseDegreeCountKnots can be used to compute the new number of knots.
Parameters:
Return type:

void
bsplclib_IncreaseDegreeCountKnots()
  • 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.
Parameters:
  • Degree (int) –
  • NewDegree (int) –
  • Periodic (bool) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
bsplclib_InsertKnot()
Parameters:
  • UIndex (int) –
  • U (float) –
  • UMult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
  • 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.
Parameters:
  • UIndex (int) –
  • U (float) –
  • UMult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
bsplclib_InsertKnots()
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • AddKnots (TColStd_Array1OfReal &) –
  • AddMults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Epsilon (float) –
  • Add (bool) – default value is Standard_True
  • Degree –
  • Periodic –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • Knots –
  • Mults –
  • AddKnots –
  • AddMults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots –
  • NewMults –
  • Epsilon –
  • Add – default value is Standard_True
Return type:

void
Return type:

void
  • 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.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • AddKnots (TColStd_Array1OfReal &) –
  • AddMults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Epsilon (float) –
  • Add (bool) – default value is Standard_True
Return type:

void
bsplclib_Interpolate()
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation or interpolation at Scheonberg points the method will work The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem w ll report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray, Poles, The length of FlatKnots is Degree + L + 1 Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation at knots or interpolation at Scheonberg points the method will work. The InversionProblem w ll report 0 if there was no problem else it will give the i
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • InversionProblem (int &) –
Return type:

void
  • Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that is : if ContactOrderArray(i) has value d it means that Poles(i) containes the dth derivative of the function to be interpolated. The length L of the following arrays must be the same : Parameters, ContactOrderArray The length of FlatKnots is Degree + L + 1 The PolesArray is an seen as an Array[1..N][1..ArrayDimension] with N = tge length of the parameters array Warning: the method used to do that interpolation is gauss elimination WITHOUT pivoting. Thus if the diagonal is not dominant there is no guarantee that the algorithm will work. Nevertheless for Cubic interpolation or interpolation at Scheonberg points the method will work The InversionProblem will report 0 if there was no problem else it will give the index of the faulty pivot
Parameters:
  • Degree (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Parameters (TColStd_Array1OfReal &) –
  • ContactOrderArray (TColStd_Array1OfInteger &) –
  • ArrayDimension (int) –
  • Poles (float &) –
  • InversionProblem (int &) –
  • Degree –
  • FlatKnots –
  • Parameters –
  • ContactOrderArray –
  • ArrayDimension –
  • Poles –
  • Weights (float &) –
  • InversionProblem –
Return type:

void
Return type:

void
bsplclib_IsRational()
  • 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.
Parameters:
  • Weights (TColStd_Array1OfReal &) –
  • I1 (int) –
  • I2 (int) –
  • Epsilon (float) – default value is 0.0
Return type:

bool
bsplclib_KnotAnalysis()
  • Analyzes the array of knots. Returns the form and the maximum knot multiplicity.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • CKnots (TColStd_Array1OfReal &) –
  • CMults (TColStd_Array1OfInteger &) –
  • KnotForm (GeomAbs_BSplKnotDistribution &) –
  • MaxKnotMult (int &) –
Return type:

void
bsplclib_KnotForm()
  • 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>.
Parameters:
  • Knots (TColStd_Array1OfReal &) –
  • FromK1 (int) –
  • ToK2 (int) –
Return type:

BSplCLib_KnotDistribution
bsplclib_KnotSequence()
Parameters:
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • KnotSeq (TColStd_Array1OfReal &) –
  • Periodic (bool) – default value is Standard_False
Return type:

void
  • 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)
Parameters:
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • Degree (int) –
  • Periodic (bool) –
  • KnotSeq (TColStd_Array1OfReal &) –
Return type:

void
bsplclib_KnotSequenceLength()
  • 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
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • Degree (int) –
  • Periodic (bool) –
Return type:

int
bsplclib_Knots()
  • 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)
Parameters:
  • KnotSeq (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • Periodic (bool) – default value is Standard_False
Return type:

void
bsplclib_KnotsLength()
  • Returns the length of the sequence of knots (and Mults) without repetition.
Parameters:
  • KnotSeq (TColStd_Array1OfReal &) –
  • Periodic (bool) – default value is Standard_False
Return type:

int
bsplclib_LastUKnotIndex()
  • Computes the index of the knots value which gives the end point of the curve.
Parameters:
  • Degree (int) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
bsplclib_LocateParameter()
  • Locates the parametric value U in the knots sequence between the knot K1 and the knot K2. The value return in Index verifies. //! Knots(Index) <= U < Knots(Index + 1) if U <= Knots (K1) then Index = K1 if U >= Knots (K2) then Index = K2 - 1 //! If Periodic is True U may be modified to fit in the range Knots(K1), Knots(K2). In any case the correct value is returned in NewU. //! Warnings :Index is used as input data to initialize the searching function. Warning: Knots have to be ‘withe repetitions’
Parameters:
  • Degree (int) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • U (float) –
  • IsPeriodic (bool) –
  • FromK1 (int) –
  • ToK2 (int) –
  • KnotIndex (int &) –
  • NewU (float &) –
Return type:

void
  • 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’
Parameters:
  • Degree (int) –
  • Knots (TColStd_Array1OfReal &) –
  • U (float) –
  • IsPeriodic (bool) –
  • FromK1 (int) –
  • ToK2 (int) –
  • KnotIndex (int &) –
  • NewU (float &) –
  • Degree –
  • Knots –
  • Mults (TColStd_Array1OfInteger &) –
  • U –
  • Periodic (bool) –
  • Index (int &) –
  • NewU –
Return type:

void
Return type:

void
bsplclib_MaxDegree()
  • returns the degree maxima for a BSplineCurve.
Return type:int
bsplclib_MaxKnotMult()
  • Finds the greatest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • K1 (int) –
  • K2 (int) –
Return type:

int
bsplclib_MergeBSplineKnots()
  • Merges two knot vector by setting the starting and ending values to StartValue and EndValue
Parameters:
  • Tolerance (float) –
  • StartValue (float) –
  • EndValue (float) –
  • Degree1 (int) –
  • Knots1 (TColStd_Array1OfReal &) –
  • Mults1 (TColStd_Array1OfInteger &) –
  • Degree2 (int) –
  • Knots2 (TColStd_Array1OfReal &) –
  • Mults2 (TColStd_Array1OfInteger &) –
  • NumPoles (int &) –
  • NewKnots (Handle_TColStd_HArray1OfReal &) –
  • NewMults (Handle_TColStd_HArray1OfInteger &) –
Return type:

void
bsplclib_MinKnotMult()
  • Finds the lowest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value.
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • K1 (int) –
  • K2 (int) –
Return type:

int
bsplclib_MovePoint()
  • 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
Parameters:
Return type:

void
  • 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
Parameters:
Return type:

void
bsplclib_MovePointAndTangent()
  • This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the cuve cannot move but tangen starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = … Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if Rational = Standard_True NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.
Parameters:
  • U (float) –
  • ArrayDimension (int) –
  • Delta (float &) –
  • DeltaDerivative (float &) –
  • Tolerance (float) –
  • Degree (int) –
  • Rational (bool) –
  • StartingCondition (int) –
  • EndingCondition (int) –
  • Poles (float &) –
  • Weights (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • NewPoles (float &) –
  • ErrorStatus (int &) –
Return type:

void
  • This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the cuve cannot move but tangen starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = … Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if Rational = Standard_True NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.
Parameters:
Return type:

void
  • This is the dimension free version of the utility U is the parameter must be within the first FlatKnots and the last FlatKnots Delta is the amount the curve has to be moved DeltaDerivative is the amount the derivative has to be moved. Delta and DeltaDerivative must be array of dimension ArrayDimension Degree is the degree of the BSpline and the FlatKnots are the knots of the BSpline Starting Condition if = -1 means the starting point of the curve can move = 0 means the starting point of the cuve cannot move but tangen starting point of the curve cannot move = 1 means the starting point and tangents cannot move = 2 means the starting point tangent and curvature cannot move = … Same holds for EndingCondition Poles are the poles of the curve Weights are the weights of the curve if Rational = Standard_True NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.
Parameters:
Return type:

void
bsplclib_MultForm()
  • Analyses the distribution of multiplicities between the knot FromK1 and the Knot ToK2.
Parameters:
  • Mults (TColStd_Array1OfInteger &) –
  • FromK1 (int) –
  • ToK2 (int) –
Return type:

BSplCLib_MultDistribution
bsplclib_NbPoles()
  • 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.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
bsplclib_NoMults()
  • Used as argument for a flatknots evaluation.
Return type:TColStd_Array1OfInteger
bsplclib_NoWeights()
  • Used as argument for a non rational curve.
Return type:TColStd_Array1OfReal
bsplclib_PoleIndex()
  • 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().
Parameters:
  • Degree (int) –
  • Index (int) –
  • Periodic (bool) –
  • Mults (TColStd_Array1OfInteger &) –
Return type:

int
bsplclib_PolesCoefficients()
Parameters:
  • Poles (TColgp_Array1OfPnt) –
  • CachePoles (TColgp_Array1OfPnt) –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • CachePoles –
  • CacheWeights (TColStd_Array1OfReal &) –
  • Poles –
  • CachePoles –
Return type:

void
Return type:

void
Return type:

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

void
bsplclib_PrepareInsertKnots()
  • 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.
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • AddKnots (TColStd_Array1OfReal &) –
  • AddMults (TColStd_Array1OfInteger &) –
  • NbPoles (int &) –
  • NbKnots (int &) –
  • Epsilon (float) –
  • Add (bool) – default value is Standard_True
Return type:

bool
bsplclib_PrepareTrimming()
  • Set in <NbKnots> and <NbPoles> the number of Knots and Poles of the curve resulting of the trimming of the BSplinecurve definded with <degree>, <knots>, <mults>
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • U1 (float) –
  • U2 (float) –
  • NbKnots (int &) –
  • NbPoles (int &) –
Return type:

void
bsplclib_PrepareUnperiodize()
  • 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>.
Parameters:
  • Degree (int) –
  • Mults (TColStd_Array1OfInteger &) –
  • NbKnots (int &) –
  • NbPoles (int &) –
Return type:

void
bsplclib_RaiseMultiplicity()
Parameters:
  • KnotIndex (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
  • Raise the multiplicity of knot to <UMult>. //! The new control points are returned. Knots and Mults are not updated.
Parameters:
  • KnotIndex (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
Return type:

void
bsplclib_RemoveKnot()
Parameters:
  • Index (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Poles (TColgp_Array1OfPnt) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Tolerance (float) –
  • Index –
  • Mult –
  • Degree –
  • Periodic –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • Knots –
  • Mults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots –
  • NewMults –
  • Tolerance –
Return type:

bool
Return type:

bool
  • 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.
Parameters:
  • Index (int) –
  • Mult (int) –
  • Degree (int) –
  • Periodic (bool) –
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • NewWeights (TColStd_Array1OfReal &) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • Tolerance (float) –
Return type:

bool
bsplclib_Reparametrize()
  • 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.
Parameters:
  • U1 (float) –
  • U2 (float) –
  • Knots (TColStd_Array1OfReal &) –
Return type:

void
bsplclib_Resolution()
  • 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
Parameters:
  • PolesArray (float &) –
  • ArrayDimension (int) –
  • NumPoles (int) –
  • Weights (TColStd_Array1OfReal &) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Tolerance3D (float) –
  • UTolerance (float &) –
Return type:

void
  • 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
Parameters:
  • Poles (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
  • NumPoles (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Tolerance3D (float) –
  • UTolerance (float &) –
Return type:

void
  • 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
Parameters:
  • Poles (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
  • NumPoles (int) –
  • FlatKnots (TColStd_Array1OfReal &) –
  • Degree (int) –
  • Tolerance3D (float) –
  • UTolerance (float &) –
Return type:

void
bsplclib_Reverse()
  • Reverses the array knots to become the knots sequence of the reversed curve.
Parameters:Knots (TColStd_Array1OfReal &) –
Return type:void
  • Reverses the array of multiplicities.
Parameters:Mults (TColStd_Array1OfInteger &) –
Return type:void
  • 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)
Parameters:
Return type:

void
  • Reverses the array of poles.
Parameters:
Return type:

void
  • Reverses the array of poles.
Parameters:
  • Weights (TColStd_Array1OfReal &) –
  • Last (int) –
Return type:

void
bsplclib_SolveBandedSystem()
  • 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
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • ArrayDimension (int) –
  • Array (float &) –
Return type:

int
  • 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
Parameters:
Return type:

int
  • 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
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • Array (float &) –
  • Matrix –
  • UpperBandWidth –
  • LowerBandWidth –
  • HomogenousFlag (bool) –
  • ArrayDimension (int) –
  • Array –
  • Weights (float &) –
Return type:

int
Return type:

int
  • This solves the system Matrix.X = B with when Matrix is factored in LU form The Array is an seen as an Array[1..N][1..ArrayDimension] with N = the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension. If HomogeneousFlag == 0 the Poles are multiplied by the Weights uppon Entry and once interpolation is carried over the result of the poles are divided by the result of the interpolation of the weights. Otherwise if HomogenousFlag == 1 the Poles and Weigths are treated homogenously that is that those are interpolated as they are and result is returned without division by the interpolated weigths.
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • HomogenousFlag (bool) –
  • Array (TColgp_Array1OfPnt2d) –
  • Weights (TColStd_Array1OfReal &) –
Return type:

int
  • This solves the system Matrix.X = B with when Matrix is factored in LU form The Array is an seen as an Array[1..N][1..ArrayDimension] with N = the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension If HomogeneousFlag == 0 the Poles are multiplied by the Weights uppon Entry and once interpolation is carried over the result of the poles are divided by the result of the interpolation of the weights. Otherwise if HomogenousFlag == 1 the Poles and Weigths are treated homogenously that is that those are interpolated as they are and result is returned without division by the interpolated weigths.
Parameters:
  • Matrix (math_Matrix &) –
  • UpperBandWidth (int) –
  • LowerBandWidth (int) –
  • HomogeneousFlag (bool) –
  • Array (TColgp_Array1OfPnt) –
  • Weights (TColStd_Array1OfReal &) –
Return type:

int
bsplclib_TangExtendToConstraint()
  • Extend a BSpline nD using the tangency map <C1Coefficient> is the coefficient of reparametrisation <Continuity> must be equal to 1, 2 or 3. <Degree> must be greater or equal than <Continuity> + 1. //! Warning: <KnotsResult> and <PolesResult> must be dimensionned properly.
Parameters:
  • FlatKnots (TColStd_Array1OfReal &) –
  • C1Coefficient (float) –
  • NumPoles (int) –
  • Poles (float &) –
  • Dimension (int) –
  • Degree (int) –
  • ConstraintPoint (TColStd_Array1OfReal &) –
  • Continuity (int) –
  • After (bool) –
  • NbPolesResult (int &) –
  • NbKnotsRsult (int &) –
  • KnotsResult (float &) –
  • PolesResult (float &) –
Return type:

void
bsplclib_Trimming()
Parameters:
  • Degree (int) –
  • Periodic (bool) –
  • Dimension (int) –
  • Knots (TColStd_Array1OfReal &) –
  • Mults (TColStd_Array1OfInteger &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • U1 (float) –
  • U2 (float) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewMults (TColStd_Array1OfInteger &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Degree –
  • Periodic –
  • Knots –
  • Mults –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • U1 –
  • U2 –
  • NewKnots –
  • NewMults –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • Degree –
  • Periodic –
  • Knots –
  • Mults –
  • Poles –
  • Weights –
  • U1 –
  • U2 –
  • NewKnots –
  • NewMults –
  • NewPoles –
  • NewWeights –
Return type:

void
Return type:

void
Return type:

void
bsplclib_Unperiodize()
Parameters:
  • Degree (int) –
  • Dimension (int) –
  • Mults (TColStd_Array1OfInteger &) –
  • Knots (TColStd_Array1OfReal &) –
  • Poles (TColgp_Array1OfPnt2d) –
  • NewMults (TColStd_Array1OfInteger &) –
  • NewKnots (TColStd_Array1OfReal &) –
  • NewPoles (TColgp_Array1OfPnt2d) –
  • Degree –
  • Mults –
  • Knots –
  • Poles –
  • Weights (TColStd_Array1OfReal &) –
  • NewMults –
  • NewKnots –
  • NewPoles –
  • NewWeights (TColStd_Array1OfReal &) –
  • Degree –
  • Mults –
  • Knots –
  • Poles –
  • Weights –
  • NewMults –
  • NewKnots –
  • NewPoles –
  • NewWeights –
Return type:

void
Return type:

void
Return type:

void
new_instancemethod(func, inst, cls)
register_handle(handle, base_object)

Inserts the handle into the base object to prevent memory corruption in certain cases