Defines 3D B-Spline curve. More...

Inheritance diagram for cadex.Geom.BSplineCurve:

Public Member Functions
	BSplineCurve (global::System.IntPtr cPtr, bool cMemoryOwn)

	BSplineCurve (cadex.Collections.PointList thePoles, cadex.Collections.DoubleList theKnots, cadex.Collections.IntList theMultiplicities, int theDegree, bool theIsPeriodic)
	Constructor.

	BSplineCurve (cadex.Collections.PointList thePoles, cadex.Collections.DoubleList theKnots, cadex.Collections.IntList theMultiplicities, int theDegree)

	BSplineCurve (cadex.Collections.PointList thePoles, cadex.Collections.DoubleList thePoleWeights, cadex.Collections.DoubleList theKnots, cadex.Collections.IntList theMultiplicities, int theDegree, bool theIsPeriodic)
	Constructor.

	BSplineCurve (cadex.Collections.PointList thePoles, cadex.Collections.DoubleList thePoleWeights, cadex.Collections.DoubleList theKnots, cadex.Collections.IntList theMultiplicities, int theDegree)

int	Degree ()
	Returns degree.

int	NumberOfKnots ()
	Returns number of unique knots.

int	NumberOfPoles ()
	Returns number of poles.

double	Knot (int theIndex)
	Returns a knot value.

cadex.Collections.DoubleList	Knots ()
	Populates a vector of knots.

int	Multiplicity (int theIndex)
	Returns a knot multiplicity.

cadex.Collections.IntList	Multiplicities ()
	Populates a vector of knot multiplicities.

cadex.Geom.Point	Pole (int theIndex)
	Returns a pole value.

cadex.Collections.PointList	Poles ()
	Populates a vector of poles.

double	Weight (int theIndex)
	Returns a weight value.

cadex.Collections.DoubleList	Weights ()
	Populates a vector of weights.

bool	IsRational ()
	Returns true if the B-Spline curve is rational (i.e. has weights).

Public Member Functions inherited from cadex.Geom.Curve
	Curve (global::System.IntPtr cPtr, bool cMemoryOwn)

cadex.Geom.CurveType	Type ()

cadex.Geom.Continuity	Continuity ()
	Returns a continuity type of the curve.

cadex.Geom.Point	Value (double theParameter)
	Evaluates a point on the curve.

cadex.Geom.Direction	Normal (double theParameter)
	Returns the normal direction theNormal of parameter theParam.

double	Curvature (double theParameter)
	Returns the curvature value of parameter theParam.

bool	IsPeriodic ()
	Returns true if the curve is periodic.

double	UMin ()
	Returns a minimum parameter of a definition domain.

double	UMax ()
	Returns a maximum parameter of a definition domain.

void	Domain (out double theUMin, out double theUMax)
	Returns a definition domain.

bool	IsTrimmed ()
	Returns whether curve is trimmed or not.

void	SetTrim (double theFirst, double theLast)
	Trims curve with [theFirst, theLast] section.

void	Transform (cadex.Geom.Transformation theTransformation)
	Applies transformation matrix to this object.

cadex.Geom.Curve	Transformed (cadex.Geom.Transformation theTransformation)
	Returns a copy this object after applying transformation.

void	D0 (double theParameter, cadex.Geom.Point theValue)
	Returns the point theValue of parameter theParam.

void	D1 (double theParameter, cadex.Geom.Point theValue, cadex.Geom.Vector theD1)

void	D2 (double theParameter, cadex.Geom.Point theValue, cadex.Geom.Vector theD1, cadex.Geom.Vector theD2)
	Returns the point theValue of parameter theParam, the first theD1 and second theD2 derivatives.

bool	DN (double theParameter, uint theDerivativeOrder, cadex.Geom.Point theValue, cadex.Collections.VectorList theD)

void	Mirror (cadex.Geom.Point thePoint)

void	Mirror (cadex.Geom.Axis1d theAxis)

void	Mirror (cadex.Geom.Axis3d theAxis)

cadex.Geom.Curve	Mirrored (cadex.Geom.Point theRef)

cadex.Geom.Curve	Mirrored (cadex.Geom.Axis1d theAxis)

cadex.Geom.Curve	Mirrored (cadex.Geom.Axis3d theAxis)

void	Rotate (cadex.Geom.Axis1d theAxis, double theAngle)

cadex.Geom.Curve	Rotated (cadex.Geom.Axis1d theAxis, double theAngle)

void	Translate (cadex.Geom.Vector theVector)

cadex.Geom.Curve	Translated (cadex.Geom.Vector theVector)

void	Scale (cadex.Geom.Point thePoint, double theScale)

cadex.Geom.Curve	Scaled (cadex.Geom.Point thePoint, double theScale)

Public Member Functions inherited from cadex.Geom.Geometry
	Geometry (global::System.IntPtr cPtr, bool cMemoryOwn)

Public Member Functions inherited from cadex.BaseObject
	BaseObject (global::System.IntPtr cPtr, bool cMemoryOwn)

void	Dispose ()

bool	IsNull ()

ulong	Id ()
	Return unique identifier of public object.

bool	IsEqual (cadex.BaseObject theObj)

override int	GetHashCode ()

override bool	Equals (System.Object o)

Static Public Member Functions
static new bool	CompareType (cadex.BaseObject theObject)

static cadex.Geom.BSplineCurve	Cast (cadex.Geom.Curve theBase)

Static Public Member Functions inherited from cadex.Geom.Curve
static new bool	CompareType (cadex.BaseObject theObject)

static cadex.Geom.Curve	Cast (cadex.Geom.Geometry theBase)

Static Public Member Functions inherited from cadex.Geom.Geometry
static bool	CompareType (cadex.BaseObject theObject)

static cadex.Geom.Geometry	Cast (cadex.BaseObject theBase)

Protected Member Functions
override void	Dispose (bool disposing)

Protected Member Functions inherited from cadex.Geom.Curve
override void	Dispose (bool disposing)

Protected Member Functions inherited from cadex.Geom.Geometry
override void	Dispose (bool disposing)

Detailed Description

Defines 3D B-Spline curve.

B-Spline curve is defined by degree, control points (poles), their weights, unique knots and their multiplicities. The following image depicts an example of a B-Spline curve:

B-Spline curve

For introduction to and mathematical definition of NURBS please refer to external resources, for instance:

A rational B-Spline contains an explicit vector of weights, whereas polynomial does not.

The number of poles must equal the number of weights. The number of poles is defined via the following formulas:

for non-periodic B-Spline: number_of_poles = sum_of_knot_multiplicities - degree - 1;
for periodic B-Spline: number_of_poles = sum_of_knot_multiplicities - start_multiplicity.

B-Splines of degree up to 25 are supported.

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

Constructor & Destructor Documentation

◆ BSplineCurve() [1/2]

cadex.Geom.BSplineCurve.BSplineCurve	(	cadex.Collections.PointList	thePoles,
		cadex.Collections.DoubleList	theKnots,
		cadex.Collections.IntList	theMultiplicities,
		int	theDegree,
		bool	theIsPeriodic )

inline

Constructor.

Creates a polynomial B-Spline curve.

Parameters:

theNumberOfPoles defines the length of thePoles and must be >=2;
theNumberOfKnots defines the length of theKnots and theMultiplicities and must be >=2;
theDegree must belong to range [1, 25];
theIsPeriodic specifies if the B-Spline is periodic.

theNumberOfPoles must meet the requirements described above.

◆ BSplineCurve() [2/2]

cadex.Geom.BSplineCurve.BSplineCurve	(	cadex.Collections.PointList	thePoles,
		cadex.Collections.DoubleList	thePoleWeights,
		cadex.Collections.DoubleList	theKnots,
		cadex.Collections.IntList	theMultiplicities,
		int	theDegree,
		bool	theIsPeriodic )

inline

Constructor.

Creates a rational B-Spline curve.

Parameters:

theNumberOfPoles defines the length of thePoles and thePoleWeights and must be >=2;
theNumberOfKnots defines the length of theKnots and theMultiplicities and must be >=2;
theDegree must belong to range [1, 25];
theIsPeriodic specifies if the B-Spline is periodic.

theNumberOfPoles must meet the requirements described above.

Poles are to be provided after division by their weights.

Member Function Documentation

◆ Degree()

int cadex.Geom.BSplineCurve.Degree ( )

inline

Returns degree.

Returns the value specified in the constructor.

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ Dispose()

override void cadex.Geom.BSplineCurve.Dispose ( bool disposing )

inlineprotectedvirtual

Reimplemented from cadex.BaseObject.

◆ IsRational()

bool cadex.Geom.BSplineCurve.IsRational ( )

inline

Returns true if the B-Spline curve is rational (i.e. has weights).

See also: Weight().

◆ Knot()

double cadex.Geom.BSplineCurve.Knot ( int theIndex )

inline

Returns a knot value.

theIndex must be in the range [1, NumberOfKnots()].

See also: Multiplicity().

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ Knots()

cadex.Collections.DoubleList cadex.Geom.BSplineCurve.Knots ( )

inline

Populates a vector of knots.

theKnots must point to a buffer in memory with at least NumberOfKnots() preallocated values.

Returns NumberOfKnots().

See also: Multiplicities().

◆ Multiplicities()

cadex.Collections.IntList cadex.Geom.BSplineCurve.Multiplicities ( )

inline

Populates a vector of knot multiplicities.

theMultiplicities must point to a buffer in memory with at least NumberOfKnots() preallocated values.

Returns NumberOfKnots().

See also: Knots().

◆ Multiplicity()

int cadex.Geom.BSplineCurve.Multiplicity ( int theIndex )

inline

Returns a knot multiplicity.

theIndex must be in the range [1, NumberOfKnots()].

See also: Knot().

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ NumberOfKnots()

int cadex.Geom.BSplineCurve.NumberOfKnots ( )

inline

Returns number of unique knots.

Returns the value specified in the constructor.

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ NumberOfPoles()

int cadex.Geom.BSplineCurve.NumberOfPoles ( )

inline

Returns number of poles.

Returns the value specified in the constructor.

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ Pole()

cadex.Geom.Point cadex.Geom.BSplineCurve.Pole ( int theIndex )

inline

Returns a pole value.

theIndex must be in the range [1, NumberOfPoles()].

See also: Weight().

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ Poles()

cadex.Collections.PointList cadex.Geom.BSplineCurve.Poles ( )

inline

Populates a vector of poles.

thePoles must point to a buffer in memory with at least NumberOfPoles() preallocated values.

Returns NumberOfPoles().

See also: Weights().

◆ Weight()

double cadex.Geom.BSplineCurve.Weight ( int theIndex )

inline

Returns a weight value.

theIndex must be in the range [1, NumberOfPoles()].

For polynomial B-Spline behavior is undefined.

See also: Pole(), IsRational().

Examples: exploring/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

◆ Weights()

cadex.Collections.DoubleList cadex.Geom.BSplineCurve.Weights ( )

inline

Populates a vector of weights.

theWeights must point to a buffer in memory with at least NumberOfPoles() preallocated values.

Returns NumberOfPoles().

For polynomial B-Spline does nothing and returns 0.

See also: Poles(), IsRational().

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ BSplineCurve() [1/2]

◆ BSplineCurve() [2/2]

Member Function Documentation

◆ Degree()

◆ Dispose()

◆ IsRational()

◆ Knot()

◆ Knots()

◆ Multiplicities()

◆ Multiplicity()

◆ NumberOfKnots()

◆ NumberOfPoles()

◆ Pole()

◆ Poles()

◆ Weight()

◆ Weights()