OCC.Core.BSplCLib module

BSplCLib module, see official documentation at https://www.opencascade.com/doc/occt-7.4.0/refman/html/package_bsplclib.html

class BSplCLib_Cache(*args)

Bases: OCC.Core.Standard.Standard_Transient

• Constructor, prepares data structures for caching values on a 2d curve. param theDegree degree of the curve param thePeriodic identify whether the curve is periodic param theFlatKnots knots of Bezier/B-spline curve (with repetitions) param thePoles2d array of poles of 2D curve param theWeights array of weights of corresponding poles

  param theDegree

  type theDegree

  int

  param thePeriodic

  type thePeriodic

  bool

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  param thePoles2d

  type thePoles2d

  TColgp_Array1OfPnt2d

  param theWeights

  default value is NULL

  type theWeights

  TColStd_Array1OfReal *

  rtype

  None* Constructor, prepares data structures for caching values on a 3d curve. param theDegree degree of the curve param thePeriodic identify whether the curve is periodic param theFlatKnots knots of Bezier/B-spline curve (with repetitions) param thePoles array of poles of 3D curve param theWeights array of weights of corresponding poles

  param theDegree

  type theDegree

  int

  param thePeriodic

  type thePeriodic

  bool

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  param thePoles

  type thePoles

  TColgp_Array1OfPnt

  param theWeights

  default value is NULL

  type theWeights

  TColStd_Array1OfReal *

  rtype

  None

BuildCache()

• Recomputes the cache data for 2D curves. Does not verify validity of the cache param theParameter the value on the knot’s axis to identify the span param theFlatKnots knots of Bezier/B-spline curve (with repetitions) param thePoles2d array of poles of 2D curve param theWeights array of weights of corresponding poles

  param theParameter

  type theParameter

  float

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  param thePoles2d

  type thePoles2d

  TColgp_Array1OfPnt2d

  param theWeights

  type theWeights

  TColStd_Array1OfReal *

  rtype

  None* Recomputes the cache data for 3D curves. Does not verify validity of the cache param theParameter the value on the knot’s axis to identify the span param theFlatKnots knots of Bezier/B-spline curve (with repetitions) param thePoles array of poles of 3D curve param theWeights array of weights of corresponding poles

  param theParameter

  type theParameter

  float

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  param thePoles

  type thePoles

  TColgp_Array1OfPnt

  param theWeights

  default value is NULL

  type theWeights

  TColStd_Array1OfReal *

  rtype

  None

D0()

• Calculates the point on the curve in the specified parameter param[in] theParameter parameter of calculation of the value param[out] thePoint the result of calculation (the point on the curve)

  param theParameter

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt2d

  rtype

  None:param theParameter:

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt

  rtype

  None

D1()

• Calculates the point on the curve and its first derivative in the specified parameter param[in] theParameter parameter of calculation of the value param[out] thePoint the result of calculation (the point on the curve) param[out] theTangent tangent vector (first derivatives) for the curve in the calculated point

  param theParameter

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt2d

  param theTangent

  type theTangent

  gp_Vec2d

  rtype

  None:param theParameter:

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt

  param theTangent

  type theTangent

  gp_Vec

  rtype

  None

D2()

• Calculates the point on the curve and two derivatives in the specified parameter param[in] theParameter parameter of calculation of the value param[out] thePoint the result of calculation (the point on the curve) param[out] theTangent tangent vector (1st derivatives) for the curve in the calculated point param[out] theCurvature curvature vector (2nd derivatives) for the curve in the calculated point

  param theParameter

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt2d

  param theTangent

  type theTangent

  gp_Vec2d

  param theCurvature

  type theCurvature

  gp_Vec2d

  rtype

  None:param theParameter:

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt

  param theTangent

  type theTangent

  gp_Vec

  param theCurvature

  type theCurvature

  gp_Vec

  rtype

  None

D3()

• Calculates the point on the curve and three derivatives in the specified parameter param[in] theParameter parameter of calculation of the value param[out] thePoint the result of calculation (the point on the curve) param[out] theTangent tangent vector (1st derivatives) for the curve in the calculated point param[out] theCurvature curvature vector (2nd derivatives) for the curve in the calculated point param[out] theTorsion second curvature vector (3rd derivatives) for the curve in the calculated point

  param theParameter

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt2d

  param theTangent

  type theTangent

  gp_Vec2d

  param theCurvature

  type theCurvature

  gp_Vec2d

  param theTorsion

  type theTorsion

  gp_Vec2d

  rtype

  None:param theParameter:

  type theParameter

  float

  param thePoint

  type thePoint

  gp_Pnt

  param theTangent

  type theTangent

  gp_Vec

  param theCurvature

  type theCurvature

  gp_Vec

  param theTorsion

  type theTorsion

  gp_Vec

  rtype

  None

static DownCast(t)

IsCacheValid()

• Verifies validity of the cache using flat parameter of the point param theParameter parameter of the point placed in the span

  param theParameter

  type theParameter

  float

  rtype

  bool

property thisown

The membership flag

class BSplCLib_CacheParams(*args)

Bases: object

• ///< index of the span Constructor, prepares data structures for caching. param theDegree degree of the B-spline (or Bezier) param thePeriodic identify whether the B-spline is periodic param theFlatKnots knots of Bezier / B-spline parameterization

  param theDegree

  type theDegree

  int

  param thePeriodic

  type thePeriodic

  bool

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  rtype

  None

IsCacheValid()

• Verifies validity of the cache using flat parameter of the point param theParameter parameter of the point placed in the span

  param theParameter

  type theParameter

  float

  rtype

  bool

LocateParameter()

• Computes span for the specified parameter param theParameter parameter of the point placed in the span param theFlatKnots knots of Bezier / B-spline parameterization

  param theParameter

  type theParameter

  float

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  rtype

  None

PeriodicNormalization()

• Normalizes the parameter for periodic B-splines param theParameter the value to be normalized into the knots array

  param theParameter

  type theParameter

  float

  rtype

  float

property SpanIndex

property SpanLength

property SpanStart

property thisown

The membership flag

class SwigPyIterator(*args, **kwargs)

Bases: object

advance()

copy()

decr()

distance()

equal()

incr()

next()

previous()

property 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.

  param U

  type U

  float

  param Degree

  type Degree

  int

  param Knots

  type Knots

  float

  param Dimension

  type Dimension

  int

  param Poles

  type Poles

  float

  param Depth

  type Depth

  int

  param Length

  type Length

  int

  param Tolerance

  type Tolerance

  float

  rtype

  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.

  param U

  type U

  float

  param Degree

  type Degree

  int

  param N

  type N

  int

  param Knots

  type Knots

  float

  param Dimension

  type Dimension

  int

  param Poles

  type Poles

  float

  rtype

  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>.

  param Index

  type Index

  int

  param Length

  type Length

  int

  param Depth

  type Depth

  int

  rtype

  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).

  param U

  type U

  float

  param Degree

  type Degree

  int

  param Knots

  type Knots

  float

  param Dimension

  type Dimension

  int

  param Poles

  type Poles

  float

  param Depth

  type Depth

  int

  param Length

  type Length

  int

  rtype

  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

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  param OrderArray

  type OrderArray

  TColStd_Array1OfInteger

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Degree

  type Degree

  int

  param Matrix

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  rtype

  int

static BuildBoor()

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

  param Index

  type Index

  int

  param Length

  type Length

  int

  param Dimension

  type Dimension

  int

  param Poles

  type Poles

  TColStd_Array1OfReal

  param LP

  type LP

  float

  rtype

  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

  param U

  type U

  float

  param InverseOfSpanDomain

  type InverseOfSpanDomain

  float

  param PeriodicFlag

  type PeriodicFlag

  bool

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param CachePoles

  type CachePoles

  TColgp_Array1OfPnt

  param CacheWeights

  type CacheWeights

  TColStd_Array1OfReal *

  rtype

  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

  param U

  type U

  float

  param InverseOfSpanDomain

  type InverseOfSpanDomain

  float

  param PeriodicFlag

  type PeriodicFlag

  bool

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param CachePoles

  type CachePoles

  TColgp_Array1OfPnt2d

  param CacheWeights

  type CacheWeights

  TColStd_Array1OfReal *

  rtype

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

  param theParameter

  type theParameter

  float

  param theSpanDomain

  type theSpanDomain

  float

  param thePeriodicFlag

  type thePeriodicFlag

  bool

  param theDegree

  type theDegree

  int

  param theSpanIndex

  type theSpanIndex

  int

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  param thePoles

  type thePoles

  TColgp_Array1OfPnt

  param theWeights

  type theWeights

  TColStd_Array1OfReal *

  param theCacheArray

  type theCacheArray

  TColStd_Array2OfReal

  rtype

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

  param theParameter

  type theParameter

  float

  param theSpanDomain

  type theSpanDomain

  float

  param thePeriodicFlag

  type thePeriodicFlag

  bool

  param theDegree

  type theDegree

  int

  param theSpanIndex

  type theSpanIndex

  int

  param theFlatKnots

  type theFlatKnots

  TColStd_Array1OfReal

  param thePoles

  type thePoles

  TColgp_Array1OfPnt2d

  param theWeights

  type theWeights

  TColStd_Array1OfReal *

  param theCacheArray

  type theCacheArray

  TColStd_Array2OfReal

  rtype

  void

static BuildEval()

Parameters

Degree –

type Degree

int

param Index

type Index

int

param Poles

type Poles

TColStd_Array1OfReal

param Weights

type Weights

TColStd_Array1OfReal *

param LP

type LP

float

rtype

void:param Degree:

type Degree

int

param Index

type Index

int

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param LP

type LP

float

rtype

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

param Degree

type Degree

int

param Index

type Index

int

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param LP

type LP

float

rtype

void

static BuildKnots()

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

  param Degree

  type Degree

  int

  param Index

  type Index

  int

  param Periodic

  type Periodic

  bool

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger *

  param LK

  type LK

  float

  rtype

  void

static BuildSchoenbergPoints()

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

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  param Vec

  type Vec

  gp_Vec

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  param Vec

  type Vec

  gp_Vec2d

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  param Vec1

  type Vec1

  gp_Vec

  param Vec2

  type Vec2

  gp_Vec

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  param Vec1

  type Vec1

  gp_Vec2d

  param Vec2

  type Vec2

  gp_Vec2d

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  param Vec1

  type Vec1

  gp_Vec

  param Vec2

  type Vec2

  gp_Vec

  param Vec3

  type Vec3

  gp_Vec

  rtype

  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

  param U

  type U

  float

  param Degree

  type Degree

  int

  param CacheParameter

  type CacheParameter

  float

  param SpanLenght

  type SpanLenght

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  param Vec1

  type Vec1

  gp_Vec2d

  param Vec2

  type Vec2

  gp_Vec2d

  param Vec3

  type Vec3

  gp_Vec2d

  rtype

  void

static CoefsD0()

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

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  rtype

  None* Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  rtype

  None

static CoefsD1()

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

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  param Vec

  type Vec

  gp_Vec

  rtype

  None* Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  param Vec

  type Vec

  gp_Vec2d

  rtype

  None

static CoefsD2()

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

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  param Vec1

  type Vec1

  gp_Vec

  param Vec2

  type Vec2

  gp_Vec

  rtype

  None* Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  param Vec1

  type Vec1

  gp_Vec2d

  param Vec2

  type Vec2

  gp_Vec2d

  rtype

  None

static CoefsD3()

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

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt

  param Vec1

  type Vec1

  gp_Vec

  param Vec2

  type Vec2

  gp_Vec

  param Vec3

  type Vec3

  gp_Vec

  rtype

  None* Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!!

  param U

  type U

  float

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param Point

  type Point

  gp_Pnt2d

  param Vec1

  type Vec1

  gp_Vec2d

  param Vec2

  type Vec2

  gp_Vec2d

  param Vec3

  type Vec3

  gp_Vec2d

  rtype

  None

static D0()

Parameters

U –

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColStd_Array1OfReal

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

float

rtype

void:param U:

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt

rtype

void:param U:

type U

float

param UIndex

type UIndex

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt2d

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt2d

rtype

void

static D1()

Parameters

U –

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColStd_Array1OfReal

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

float

param V

type V

float

rtype

void:param U:

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt

param V

type V

gp_Vec

rtype

void:param U:

type U

float

param UIndex

type UIndex

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt2d

param V

type V

gp_Vec2d

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt

param V

type V

gp_Vec

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt2d

param V

type V

gp_Vec2d

rtype

void

static D2()

Parameters

U –

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColStd_Array1OfReal

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

float

param V1

type V1

float

param V2

type V2

float

rtype

void:param U:

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt

param V1

type V1

gp_Vec

param V2

type V2

gp_Vec

rtype

void:param U:

type U

float

param UIndex

type UIndex

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt2d

param V1

type V1

gp_Vec2d

param V2

type V2

gp_Vec2d

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt

param V1

type V1

gp_Vec

param V2

type V2

gp_Vec

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt2d

param V1

type V1

gp_Vec2d

param V2

type V2

gp_Vec2d

rtype

void

static D3()

Parameters

U –

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColStd_Array1OfReal

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

float

param V1

type V1

float

param V2

type V2

float

param V3

type V3

float

rtype

void:param U:

type U

float

param Index

type Index

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt

param V1

type V1

gp_Vec

param V2

type V2

gp_Vec

param V3

type V3

gp_Vec

rtype

void:param U:

type U

float

param UIndex

type UIndex

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger *

param P

type P

gp_Pnt2d

param V1

type V1

gp_Vec2d

param V2

type V2

gp_Vec2d

param V3

type V3

gp_Vec2d

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt

param V1

type V1

gp_Vec

param V2

type V2

gp_Vec

param V3

type V3

gp_Vec

rtype

void:param U:

type U

float

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param P

type P

gp_Pnt2d

param V1

type V1

gp_Vec2d

param V2

type V2

gp_Vec2d

param V3

type V3

gp_Vec2d

rtype

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).

  param Degree

  type Degree

  int

  param Knots

  type Knots

  float

  param Dimension

  type Dimension

  int

  param Length

  type Length

  int

  param Order

  type Order

  int

  param Poles

  type Poles

  float

  rtype

  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.

  param U

  type U

  float

  param Degree

  type Degree

  int

  param Knots

  type Knots

  float

  param Dimension

  type Dimension

  int

  param Poles

  type Poles

  float

  rtype

  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

  param U

  type U

  float

  param PeriodicFlag

  type PeriodicFlag

  bool

  param DerivativeRequest

  type DerivativeRequest

  int

  param ExtrapMode

  type ExtrapMode

  int

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param ArrayDimension

  type ArrayDimension

  int

  param Poles

  type Poles

  float

  param Result

  type Result

  float

  rtype

  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.

  param U

  type U

  float

  param PeriodicFlag

  type PeriodicFlag

  bool

  param DerivativeRequest

  type DerivativeRequest

  int

  param ExtrapMode

  type ExtrapMode

  int

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param ArrayDimension

  type ArrayDimension

  int

  param Poles

  type Poles

  float

  param Weights

  type Weights

  float

  param PolesResult

  type PolesResult

  float

  param WeightsResult

  type WeightsResult

  float

  rtype

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

  param U

  type U

  float

  param PeriodicFlag

  type PeriodicFlag

  bool

  param HomogeneousFlag

  type HomogeneousFlag

  bool

  param ExtrapMode

  type ExtrapMode

  int

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal

  param Point

  type Point

  gp_Pnt

  param Weight

  type Weight

  float

  rtype

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

  param U

  type U

  float

  param PeriodicFlag

  type PeriodicFlag

  bool

  param HomogeneousFlag

  type HomogeneousFlag

  bool

  param ExtrapMode

  type ExtrapMode

  int

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal

  param Point

  type Point

  gp_Pnt2d

  param Weight

  type Weight

  float

  rtype

  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

  param DerivativeOrder

  type DerivativeOrder

  int

  param Order

  type Order

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameter

  type Parameter

  float

  param FirstNonZeroBsplineIndex

  type FirstNonZeroBsplineIndex

  int

  param BsplineBasis

  type BsplineBasis

  math_Matrix

  param isPeriodic

  default value is Standard_False

  type isPeriodic

  bool

  rtype

  int

static FactorBandedMatrix()

• this factors the Banded Matrix in the LU form with a Banded storage of components of the L matrix WARNINGdo not use if the Matrix is totally positive (It is the case for Bspline matrices build as above with parameters being the Schoenberg points

  param Matrix

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  param PivotIndexProblem

  type PivotIndexProblem

  int

  rtype

  int

static FirstUKnotIndex()

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

  param Degree

  type Degree

  int

  param Mults

  type Mults

  TColStd_Array1OfInteger

  rtype

  int

static FlatBezierKnots()

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

  param Degree

  type Degree

  int

  rtype

  float

static FlatIndex()

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

  param Degree

  type Degree

  int

  param Index

  type Index

  int

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param Periodic

  type Periodic

  bool

  rtype

  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 following1. 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 satisfiedno check whatsoever is made in this method theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSplinethe method used is interpolation at Schoenenberg points of a(t)*F(t)

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param PolesDimension

  type PolesDimension

  int

  param Poles

  type Poles

  float

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  float

  param theStatus

  type theStatus

  int

  rtype

  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 theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColStd_Array1OfReal

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  TColStd_Array1OfReal

  param theStatus

  type theStatus

  int

  rtype

  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 theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt2d

  param theStatus

  type theStatus

  int

  rtype

  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 theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of a(t)*F(t)

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt

  param theStatus

  type theStatus

  int

  rtype

  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 satisfiedno check whatsoever is made in this method //! theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSplinethe method used is interpolation at Schoenenberg points of F(a(t))

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param PolesDimension

  type PolesDimension

  int

  param Poles

  type Poles

  float

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  float

  param theStatus

  type theStatus

  int

  rtype

  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 //! theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColStd_Array1OfReal

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  TColStd_Array1OfReal

  param theStatus

  type theStatus

  int

  rtype

  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 theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt

  param theStatus

  type theStatus

  int

  rtype

  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 theStatus will return 0 if OK else it will return the pivot index of the matrix that was inverted to compute the multiplied BSpline : the method used is interpolation at Schoenenberg points of F(a(t))

  param Function

  type Function

  BSplCLib_EvaluatorFunction

  param BSplineDegree

  type BSplineDegree

  int

  param BSplineFlatKnots

  type BSplineFlatKnots

  TColStd_Array1OfReal

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewDegree

  type NewDegree

  int

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt2d

  param theStatus

  type theStatus

  int

  rtype

  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.

  param Index

  type Index

  int

  param Length

  type Length

  int

  param Depth

  type Depth

  int

  param Dimension

  type Dimension

  int

  param LocPoles

  type LocPoles

  float

  param Position

  type Position

  int

  param Pole

  type Pole

  TColStd_Array1OfReal

  rtype

  void

static Hunt()

• This routine searches the position of the real value theX in the monotonically increasing set of real values theArray using bisection algorithm. //! If the given value is out of range or array values, algorithm returns either theArray.Lower()-1 or theArray.Upper()+1 depending on theX position in the ordered set. //! This routine is used to locate a knot value in a set of knots.

  param theArray

  type theArray

  TColStd_Array1OfReal

  param theX

  type theX

  float

  param theXPos

  type theXPos

  int

  rtype

  void

static IncreaseDegree()

Parameters

Degree –

type Degree

int

param NewDegree

type NewDegree

int

param Periodic

type Periodic

bool

param Dimension

type Dimension

int

param Poles

type Poles

TColStd_Array1OfReal

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColStd_Array1OfReal

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

rtype

void:param Degree:

type Degree

int

param NewDegree

type NewDegree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

rtype

void:param Degree:

type Degree

int

param NewDegree

type NewDegree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

rtype

void:param NewDegree:

type NewDegree

int

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

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.

param NewDegree

type NewDegree

int

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

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.

  param Degree

  type Degree

  int

  param NewDegree

  type NewDegree

  int

  param Periodic

  type Periodic

  bool

  param Mults

  type Mults

  TColStd_Array1OfInteger

  rtype

  int

static InsertKnot()

Parameters

UIndex –

type UIndex

int

param U

type U

float

param UMult

type UMult

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

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.

param UIndex

type UIndex

int

param U

type U

float

param UMult

type UMult

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

void

static InsertKnots()

Parameters

Degree –

type Degree

int

param Periodic

type Periodic

bool

param Dimension

type Dimension

int

param Poles

type Poles

TColStd_Array1OfReal

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param AddKnots

type AddKnots

TColStd_Array1OfReal

param AddMults

type AddMults

TColStd_Array1OfInteger *

param NewPoles

type NewPoles

TColStd_Array1OfReal

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param Epsilon

type Epsilon

float

param Add

default value is Standard_True

type Add

bool

rtype

void:param Degree:

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param AddKnots

type AddKnots

TColStd_Array1OfReal

param AddMults

type AddMults

TColStd_Array1OfInteger *

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param Epsilon

type Epsilon

float

param Add

default value is Standard_True

type Add

bool

rtype

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.

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param AddKnots

type AddKnots

TColStd_Array1OfReal

param AddMults

type AddMults

TColStd_Array1OfInteger *

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param Epsilon

type Epsilon

float

param Add

default value is Standard_True

type Add

bool

rtype

void

static Interpolate()

• Performs the interpolation of the data given in the Poles array according to the requests in ContactOrderArray that isif 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 sameParameters, 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

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  param ContactOrderArray

  type ContactOrderArray

  TColStd_Array1OfInteger

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param InversionProblem

  type InversionProblem

  int

  rtype

  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

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  param ContactOrderArray

  type ContactOrderArray

  TColStd_Array1OfInteger

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param InversionProblem

  type InversionProblem

  int

  rtype

  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

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  param ContactOrderArray

  type ContactOrderArray

  TColStd_Array1OfInteger

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal

  param InversionProblem

  type InversionProblem

  int

  rtype

  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

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  param ContactOrderArray

  type ContactOrderArray

  TColStd_Array1OfInteger

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal

  param InversionProblem

  type InversionProblem

  int

  rtype

  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

  param Degree

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  param ContactOrderArray

  type ContactOrderArray

  TColStd_Array1OfInteger

  param ArrayDimension

  type ArrayDimension

  int

  param Poles

  type Poles

  float

  param InversionProblem

  type InversionProblem

  int

  rtype

  void:param Degree:

  type Degree

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Parameters

  type Parameters

  TColStd_Array1OfReal

  param ContactOrderArray

  type ContactOrderArray

  TColStd_Array1OfInteger

  param ArrayDimension

  type ArrayDimension

  int

  param Poles

  type Poles

  float

  param Weights

  type Weights

  float

  param InversionProblem

  type InversionProblem

  int

  rtype

  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.

  param Weights

  type Weights

  TColStd_Array1OfReal

  param I1

  type I1

  int

  param I2

  type I2

  int

  param Epsilon

  default value is 0.0

  type Epsilon

  float

  rtype

  bool

static KnotAnalysis()

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

  param Degree

  type Degree

  int

  param Periodic

  type Periodic

  bool

  param CKnots

  type CKnots

  TColStd_Array1OfReal

  param CMults

  type CMults

  TColStd_Array1OfInteger

  param KnotForm

  type KnotForm

  GeomAbs_BSplKnotDistribution

  param MaxKnotMult

  type MaxKnotMult

  int

  rtype

  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>.

  param Knots

  type Knots

  TColStd_Array1OfReal

  param FromK1

  type FromK1

  int

  param ToK2

  type ToK2

  int

  rtype

  BSplCLib_KnotDistribution

static KnotSequence()

Parameters

Knots –

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param KnotSeq

type KnotSeq

TColStd_Array1OfReal

param Periodic

default value is Standard_False

type Periodic

bool

rtype

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)

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param Degree

type Degree

int

param Periodic

type Periodic

bool

param KnotSeq

type KnotSeq

TColStd_Array1OfReal

rtype

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

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param Degree

  type Degree

  int

  param Periodic

  type Periodic

  bool

  rtype

  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)

  param KnotSeq

  type KnotSeq

  TColStd_Array1OfReal

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param Periodic

  default value is Standard_False

  type Periodic

  bool

  rtype

  void

static KnotsLength()

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

  param KnotSeq

  type KnotSeq

  TColStd_Array1OfReal

  param Periodic

  default value is Standard_False

  type Periodic

  bool

  rtype

  int

static LastUKnotIndex()

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

  param Degree

  type Degree

  int

  param Mults

  type Mults

  TColStd_Array1OfInteger

  rtype

  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’

  param Degree

  type Degree

  int

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param U

  type U

  float

  param IsPeriodic

  type IsPeriodic

  bool

  param FromK1

  type FromK1

  int

  param ToK2

  type ToK2

  int

  param KnotIndex

  type KnotIndex

  int

  param NewU

  type NewU

  float

  rtype

  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’

  param Degree

  type Degree

  int

  param Knots

  type Knots

  TColStd_Array1OfReal

  param U

  type U

  float

  param IsPeriodic

  type IsPeriodic

  bool

  param FromK1

  type FromK1

  int

  param ToK2

  type ToK2

  int

  param KnotIndex

  type KnotIndex

  int

  param NewU

  type NewU

  float

  rtype

  void:param Degree:

  type Degree

  int

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger *

  param U

  type U

  float

  param Periodic

  type Periodic

  bool

  param Index

  type Index

  int

  param NewU

  type NewU

  float

  rtype

  void

static MaxDegree()

• returns the degree maxima for a BSplineCurve.

  rtype

  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.

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param K1

  type K1

  int

  param K2

  type K2

  int

  rtype

  int

static MergeBSplineKnots()

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

  param Tolerance

  type Tolerance

  float

  param StartValue

  type StartValue

  float

  param EndValue

  type EndValue

  float

  param Degree1

  type Degree1

  int

  param Knots1

  type Knots1

  TColStd_Array1OfReal

  param Mults1

  type Mults1

  TColStd_Array1OfInteger

  param Degree2

  type Degree2

  int

  param Knots2

  type Knots2

  TColStd_Array1OfReal

  param Mults2

  type Mults2

  TColStd_Array1OfInteger

  param NumPoles

  type NumPoles

  int

  param NewKnots

  type NewKnots

  TColStd_HArray1OfReal

  param NewMults

  type NewMults

  TColStd_HArray1OfInteger

  rtype

  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.

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param K1

  type K1

  int

  param K2

  type K2

  int

  rtype

  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

  param U

  type U

  float

  param Displ

  type Displ

  gp_Vec2d

  param Index1

  type Index1

  int

  param Index2

  type Index2

  int

  param Degree

  type Degree

  int

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param FirstIndex

  type FirstIndex

  int

  param LastIndex

  type LastIndex

  int

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt2d

  rtype

  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

  param U

  type U

  float

  param Displ

  type Displ

  gp_Vec

  param Index1

  type Index1

  int

  param Index2

  type Index2

  int

  param Degree

  type Degree

  int

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param FirstIndex

  type FirstIndex

  int

  param LastIndex

  type LastIndex

  int

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt

  rtype

  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 not NULL NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.

  param U

  type U

  float

  param ArrayDimension

  type ArrayDimension

  int

  param Delta

  type Delta

  float

  param DeltaDerivative

  type DeltaDerivative

  float

  param Tolerance

  type Tolerance

  float

  param Degree

  type Degree

  int

  param StartingCondition

  type StartingCondition

  int

  param EndingCondition

  type EndingCondition

  int

  param Poles

  type Poles

  float

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewPoles

  type NewPoles

  float

  param ErrorStatus

  type ErrorStatus

  int

  rtype

  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 not NULL NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.

  param U

  type U

  float

  param Delta

  type Delta

  gp_Vec

  param DeltaDerivative

  type DeltaDerivative

  gp_Vec

  param Tolerance

  type Tolerance

  float

  param Degree

  type Degree

  int

  param StartingCondition

  type StartingCondition

  int

  param EndingCondition

  type EndingCondition

  int

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt

  param ErrorStatus

  type ErrorStatus

  int

  rtype

  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 not NULL NewPoles are the poles of the deformed curve ErrorStatus will be 0 if no error happened 1 if there are not enough knots/poles the imposed conditions The way to solve this problem is to add knots to the BSpline If StartCondition = 1 and EndCondition = 1 then you need at least 4 + 2 = 6 poles so for example to have a C1 cubic you will need have at least 2 internal knots.

  param U

  type U

  float

  param Delta

  type Delta

  gp_Vec2d

  param DeltaDerivative

  type DeltaDerivative

  gp_Vec2d

  param Tolerance

  type Tolerance

  float

  param Degree

  type Degree

  int

  param StartingCondition

  type StartingCondition

  int

  param EndingCondition

  type EndingCondition

  int

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param NewPoles

  type NewPoles

  TColgp_Array1OfPnt2d

  param ErrorStatus

  type ErrorStatus

  int

  rtype

  void

static MultForm()

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

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param FromK1

  type FromK1

  int

  param ToK2

  type ToK2

  int

  rtype

  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.

  param Degree

  type Degree

  int

  param Periodic

  type Periodic

  bool

  param Mults

  type Mults

  TColStd_Array1OfInteger

  rtype

  int

static NoMults()

• Used as argument for a flatknots evaluation.

  rtype

  TColStd_Array1OfInteger *

static NoWeights()

• Used as argument for a non rational curve.

  rtype

  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().

  param Degree

  type Degree

  int

  param Index

  type Index

  int

  param Periodic

  type Periodic

  bool

  param Mults

  type Mults

  TColStd_Array1OfInteger

  rtype

  int

static PolesCoefficients()

Parameters

Poles –

type Poles

TColgp_Array1OfPnt2d

param CachePoles

type CachePoles

TColgp_Array1OfPnt2d

rtype

None:param Poles:

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param CachePoles

type CachePoles

TColgp_Array1OfPnt2d

param CacheWeights

type CacheWeights

TColStd_Array1OfReal *

rtype

void:param Poles:

type Poles

TColgp_Array1OfPnt

param CachePoles

type CachePoles

TColgp_Array1OfPnt

rtype

None* Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziercurves at parameter 0. Warning: To be used for Beziercurves ONLY!!!

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param CachePoles

type CachePoles

TColgp_Array1OfPnt

param CacheWeights

type CacheWeights

TColStd_Array1OfReal *

rtype

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 ifThe knew knots are knot increasing. The new knots are not in the range.

  param Degree

  type Degree

  int

  param Periodic

  type Periodic

  bool

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param AddKnots

  type AddKnots

  TColStd_Array1OfReal

  param AddMults

  type AddMults

  TColStd_Array1OfInteger *

  param NbPoles

  type NbPoles

  int

  param NbKnots

  type NbKnots

  int

  param Epsilon

  type Epsilon

  float

  param Add

  default value is Standard_True

  type Add

  bool

  rtype

  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>

  param Degree

  type Degree

  int

  param Periodic

  type Periodic

  bool

  param Knots

  type Knots

  TColStd_Array1OfReal

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param U1

  type U1

  float

  param U2

  type U2

  float

  param NbKnots

  type NbKnots

  int

  param NbPoles

  type NbPoles

  int

  rtype

  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>.

  param Degree

  type Degree

  int

  param Mults

  type Mults

  TColStd_Array1OfInteger

  param NbKnots

  type NbKnots

  int

  param NbPoles

  type NbPoles

  int

  rtype

  void

static RaiseMultiplicity()

Parameters

KnotIndex –

type KnotIndex

int

param Mult

type Mult

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

void* Raise the multiplicity of knot to <UMult>. //! The new control points are returned. Knots and Mults are not updated.

param KnotIndex

type KnotIndex

int

param Mult

type Mult

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

void

static RemoveKnot()

Parameters

Index –

type Index

int

param Mult

type Mult

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Dimension

type Dimension

int

param Poles

type Poles

TColStd_Array1OfReal

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColStd_Array1OfReal

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param Tolerance

type Tolerance

float

rtype

bool:param Index:

type Index

int

param Mult

type Mult

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param Tolerance

type Tolerance

float

rtype

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.

param Index

type Index

int

param Mult

type Mult

int

param Degree

type Degree

int

param Periodic

type Periodic

bool

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param Tolerance

type Tolerance

float

rtype

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. WarningsIn the array Knots the values must be in ascending order. U1 must not be equal to U2 to avoid division by zero.

  param U1

  type U1

  float

  param U2

  type U2

  float

  param Knots

  type Knots

  TColStd_Array1OfReal

  rtype

  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

  param PolesArray

  type PolesArray

  float

  param ArrayDimension

  type ArrayDimension

  int

  param NumPoles

  type NumPoles

  int

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Degree

  type Degree

  int

  param Tolerance3D

  type Tolerance3D

  float

  param UTolerance

  type UTolerance

  float

  rtype

  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

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param NumPoles

  type NumPoles

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Degree

  type Degree

  int

  param Tolerance3D

  type Tolerance3D

  float

  param UTolerance

  type UTolerance

  float

  rtype

  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

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal *

  param NumPoles

  type NumPoles

  int

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param Degree

  type Degree

  int

  param Tolerance3D

  type Tolerance3D

  float

  param UTolerance

  type UTolerance

  float

  rtype

  void

static Reverse()

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

  param Knots

  type Knots

  TColStd_Array1OfReal

  rtype

  void* Reverses the array of multiplicities.

  param Mults

  type Mults

  TColStd_Array1OfInteger

  rtype

  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)

  param Poles

  type Poles

  TColgp_Array1OfPnt

  param Last

  type Last

  int

  rtype

  void* Reverses the array of poles.

  param Poles

  type Poles

  TColgp_Array1OfPnt2d

  param Last

  type Last

  int

  rtype

  void* Reverses the array of poles.

  param Weights

  type Weights

  TColStd_Array1OfReal

  param Last

  type Last

  int

  rtype

  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

  param Matrix

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  param ArrayDimension

  type ArrayDimension

  int

  param Array

  type Array

  float

  rtype

  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

  param Matrix

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  param Array

  type Array

  TColgp_Array1OfPnt2d

  rtype

  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

  param Matrix

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  param Array

  type Array

  TColgp_Array1OfPnt

  rtype

  int:param Matrix:

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  param HomogenousFlag

  type HomogenousFlag

  bool

  param ArrayDimension

  type ArrayDimension

  int

  param Array

  type Array

  float

  param Weights

  type Weights

  float

  rtype

  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.

  param Matrix

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  param HomogenousFlag

  type HomogenousFlag

  bool

  param Array

  type Array

  TColgp_Array1OfPnt2d

  param Weights

  type Weights

  TColStd_Array1OfReal

  rtype

  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.

  param Matrix

  type Matrix

  math_Matrix

  param UpperBandWidth

  type UpperBandWidth

  int

  param LowerBandWidth

  type LowerBandWidth

  int

  param HomogeneousFlag

  type HomogeneousFlag

  bool

  param Array

  type Array

  TColgp_Array1OfPnt

  param Weights

  type Weights

  TColStd_Array1OfReal

  rtype

  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.

  param FlatKnots

  type FlatKnots

  TColStd_Array1OfReal

  param C1Coefficient

  type C1Coefficient

  float

  param NumPoles

  type NumPoles

  int

  param Poles

  type Poles

  float

  param Dimension

  type Dimension

  int

  param Degree

  type Degree

  int

  param ConstraintPoint

  type ConstraintPoint

  TColStd_Array1OfReal

  param Continuity

  type Continuity

  int

  param After

  type After

  bool

  param NbPolesResult

  type NbPolesResult

  int

  param NbKnotsRsult

  type NbKnotsRsult

  int

  param KnotsResult

  type KnotsResult

  float

  param PolesResult

  type PolesResult

  float

  rtype

  void

static Trimming()

Parameters

Degree –

type Degree

int

param Periodic

type Periodic

bool

param Dimension

type Dimension

int

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param Poles

type Poles

TColStd_Array1OfReal

param U1

type U1

float

param U2

type U2

float

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColStd_Array1OfReal

rtype

void:param Degree:

type Degree

int

param Periodic

type Periodic

bool

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param U1

type U1

float

param U2

type U2

float

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

void:param Degree:

type Degree

int

param Periodic

type Periodic

bool

param Knots

type Knots

TColStd_Array1OfReal

param Mults

type Mults

TColStd_Array1OfInteger

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param U1

type U1

float

param U2

type U2

float

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

void

static Unperiodize()

Parameters

Degree –

type Degree

int

param Dimension

type Dimension

int

param Mults

type Mults

TColStd_Array1OfInteger

param Knots

type Knots

TColStd_Array1OfReal

param Poles

type Poles

TColStd_Array1OfReal

param NewMults

type NewMults

TColStd_Array1OfInteger

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewPoles

type NewPoles

TColStd_Array1OfReal

rtype

void:param Degree:

type Degree

int

param Mults

type Mults

TColStd_Array1OfInteger

param Knots

type Knots

TColStd_Array1OfReal

param Poles

type Poles

TColgp_Array1OfPnt

param Weights

type Weights

TColStd_Array1OfReal *

param NewMults

type NewMults

TColStd_Array1OfInteger

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewPoles

type NewPoles

TColgp_Array1OfPnt

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

void:param Degree:

type Degree

int

param Mults

type Mults

TColStd_Array1OfInteger

param Knots

type Knots

TColStd_Array1OfReal

param Poles

type Poles

TColgp_Array1OfPnt2d

param Weights

type Weights

TColStd_Array1OfReal *

param NewMults

type NewMults

TColStd_Array1OfInteger

param NewKnots

type NewKnots

TColStd_Array1OfReal

param NewPoles

type NewPoles

TColgp_Array1OfPnt2d

param NewWeights

type NewWeights

TColStd_Array1OfReal *

rtype

void

property thisown

The membership flag