Defines a B-Spline surface. More...

Inheritance diagram for cadex.Geom.BSplineSurface:

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

	BSplineSurface (cadex.Collections.PointList thePoles, int theNumberOfUPoles, int theNumberOfVPoles, cadex.Collections.DoubleList theUKnots, cadex.Collections.DoubleList theVKnots, cadex.Collections.IntList theUMults, cadex.Collections.IntList theVMults, int theUDegree, int theVDegree, bool theIsUPeriodic, bool theIsVPeriodic)

	BSplineSurface (cadex.Collections.PointList thePoles, int theNumberOfUPoles, int theNumberOfVPoles, cadex.Collections.DoubleList theUKnots, cadex.Collections.DoubleList theVKnots, cadex.Collections.IntList theUMults, cadex.Collections.IntList theVMults, int theUDegree, int theVDegree, bool theIsUPeriodic)

	BSplineSurface (cadex.Collections.PointList thePoles, int theNumberOfUPoles, int theNumberOfVPoles, cadex.Collections.DoubleList theUKnots, cadex.Collections.DoubleList theVKnots, cadex.Collections.IntList theUMults, cadex.Collections.IntList theVMults, int theUDegree, int theVDegree)

	BSplineSurface (cadex.Collections.PointList thePoles, cadex.Collections.DoubleList theWeights, int theNumberOfUPoles, int theNumberOfVPoles, cadex.Collections.DoubleList theUKnots, cadex.Collections.DoubleList theVKnots, cadex.Collections.IntList theUMults, cadex.Collections.IntList theVMults, int theUDegree, int theVDegree, bool theIsUPeriodic, bool theIsVPeriodic)

	BSplineSurface (cadex.Collections.PointList thePoles, cadex.Collections.DoubleList theWeights, int theNumberOfUPoles, int theNumberOfVPoles, cadex.Collections.DoubleList theUKnots, cadex.Collections.DoubleList theVKnots, cadex.Collections.IntList theUMults, cadex.Collections.IntList theVMults, int theUDegree, int theVDegree, bool theIsUPeriodic)

	BSplineSurface (cadex.Collections.PointList thePoles, cadex.Collections.DoubleList theWeights, int theNumberOfUPoles, int theNumberOfVPoles, cadex.Collections.DoubleList theUKnots, cadex.Collections.DoubleList theVKnots, cadex.Collections.IntList theUMults, cadex.Collections.IntList theVMults, int theUDegree, int theVDegree)

int	UDegree ()
	Returns U-degree.

int	VDegree ()
	Returns V-degree.

int	NumberOfUPoles ()
	Returns number of U-poles.

int	NumberOfVPoles ()
	Returns number of V-poles.

int	NumberOfUKnots ()
	Returns number of unique U-knots.

int	NumberOfVKnots ()
	Returns number of unique V-knots.

cadex.Geom.Point	Pole (int theUIndex, int theVIndex)
	theUIndex must be in the range [1, NumberOfUPoles()], theVIndex in the range [1, NumberOfVPoles()].

cadex.Collections.PointList	Poles ()
	thePoles must point to a buffer in memory with at least NumberOfUPoles() * NumberOfVPoles() preallocated values.

double	Weight (int theUIndex, int theVIndex)
	theUIndex must be in the range [1, NumberOfUPoles()], theVIndex in the range [1, NumberOfVPoles()].

cadex.Collections.DoubleList	Weights ()
	theWeights must point to a buffer in memory with at least NumberOfUPoles() * NumberOfVPoles() preallocated values.

double	UKnot (int theUIndex)
	theIndex must be in the range [1, NumberOfUKnots()].

double	VKnot (int theVIndex)
	theIndex must be in the range [1, NumberOfVKnots()].

cadex.Collections.DoubleList	UKnots ()
	theUKnots must point to a buffer in memory with at least NumberOfUKnots() preallocated values.

cadex.Collections.DoubleList	VKnots ()
	theVKnots must point to a buffer in memory with at least NumberOfVKnots() preallocated values.

int	UMultiplicity (int theUIndex)
	theIndex must be in the range [1, NumberOfUKnots()].

int	VMultiplicity (int theVIndex)
	theIndex must be in the range [1, NumberOfVKnots()].

cadex.Collections.IntList	UMultiplicities ()
	theUMults must point to a buffer in memory with at least NumberOfUKnots() preallocated values.

cadex.Collections.IntList	VMultiplicities ()
	theVMults must point to a buffer in memory with at least NumberOfVKnots() preallocated values.

bool	IsURational ()
	Returns true if the B-Spline curve is rational in U direction.

bool	IsVRational ()
	Returns true if the B-Spline curve is rational in V direction.

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

cadex.Geom.SurfaceType	Type ()
	Returns a surface type.

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

cadex.Geom.Point	Value (double theParameterU, double theParameterV)
	theParameterU must be within [UMin(), UMax()] if the surface is not U-periodic.

cadex.Geom.Direction	Normal (double theParameterU, double theParameterV)

bool	IsUPeriodic ()
	Examples include sphere, torus or a surface of revolution.

bool	IsVPeriodic ()
	Examples include torus or a V-periodic B-Spline.

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

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

double	VMin ()
	Returns a minimum parameter of a definition domain in V direction.

double	VMax ()
	Returns a maximum parameter of a definition domain in V direction.

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

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

void	SetTrim (double theUFirst, double theULast, double theVFirst, double theVLast)
	Trims surface with [theUFirst, theULast] x [theVFirst, theVLast] section.

void	Transform (cadex.Geom.Transformation theTransformation)
	Results depends on the actual surface type.

cadex.Geom.Surface	Transformed (cadex.Geom.Transformation theTransformation)
	The contents of this object is not modified.

void	D0 (double theParameterU, double theParameterV, cadex.Geom.Point theValue)

void	D1 (double theParameterU, double theParameterV, cadex.Geom.Point theValue, cadex.Geom.Vector theD1U, cadex.Geom.Vector theD1V)

void	D2 (double theParameterU, double theParameterV, cadex.Geom.Point theValue, cadex.Geom.Vector theD1U, cadex.Geom.Vector theD1V, cadex.Geom.Vector theD2U, cadex.Geom.Vector theD2V, cadex.Geom.Vector theD2UV)

bool	DN (double theParameterU, double theParameterV, uint theDerivativeOrder, cadex.Geom.Point theValue, cadex.Collections.VectorList theD)
	Returns true if calculation was passed succsesfully, the returned vectors gives the value of the derivative for the order of derivation theDerivativeOrder.

void	Curvature (double theParameterU, double theParameterV, cadex.Geom.Direction thePrincipalMaxDirection, cadex.Geom.Direction thePrincipalMinDirection)

void	Curvature (double theParameterU, double theParameterV, cadex.Geom.Direction thePrincipalMaxDirection, cadex.Geom.Direction thePrincipalMinDirection, out double theMaxCurvature, out double theMinCurvature)

void	Mirror (cadex.Geom.Point thePoint)

void	Mirror (cadex.Geom.Axis1d theAxis)

void	Mirror (cadex.Geom.Axis3d theAxis)

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

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

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

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

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

void	Translate (cadex.Geom.Vector theVector)

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

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

cadex.Geom.Surface	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.BSplineSurface	Cast (cadex.Geom.Surface theBase)

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

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.Surface
override void	Dispose (bool disposing)

Detailed Description

Defines a B-Spline surface.

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

B-Spline surface

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 in each direction (U or V) 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.

Member Function Documentation

◆ Dispose()

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

inlineprotectedvirtual

Reimplemented from cadex.BaseObject.

◆ IsURational()

bool cadex.Geom.BSplineSurface.IsURational ( )

inline

Returns true if the B-Spline curve is rational in U direction.

◆ IsVRational()

bool cadex.Geom.BSplineSurface.IsVRational ( )

inline

Returns true if the B-Spline curve is rational in V direction.

◆ NumberOfUKnots()

int cadex.Geom.BSplineSurface.NumberOfUKnots ( )

inline

Returns number of unique U-knots.

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

◆ NumberOfUPoles()

int cadex.Geom.BSplineSurface.NumberOfUPoles ( )

inline

Returns number of U-poles.

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

◆ NumberOfVKnots()

int cadex.Geom.BSplineSurface.NumberOfVKnots ( )

inline

Returns number of unique V-knots.

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

◆ NumberOfVPoles()

int cadex.Geom.BSplineSurface.NumberOfVPoles ( )

inline

Returns number of V-poles.

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

◆ Pole()

cadex.Geom.Point cadex.Geom.BSplineSurface.Pole	(	int	theUIndex,
		int	theVIndex )

inline

theUIndex must be in the range [1, NumberOfUPoles()], theVIndex in the range [1, NumberOfVPoles()].

See also: Weight(). Returns a pole value.

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

◆ Poles()

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

inline

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

Returns NumberOfUPoles() * NumberOfVPoles().

See also: Weights(). Populates a 2D table of poles.

◆ UDegree()

int cadex.Geom.BSplineSurface.UDegree ( )

inline

Returns U-degree.

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

◆ UKnot()

double cadex.Geom.BSplineSurface.UKnot ( int theUIndex )

inline

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

See also: UMultiplicity(). Returns a U-knot value.

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

◆ UKnots()

cadex.Collections.DoubleList cadex.Geom.BSplineSurface.UKnots ( )

inline

theUKnots must point to a buffer in memory with at least NumberOfUKnots() preallocated values.

Returns NumberOfUKnots().

See also: UMultiplicities(). Populates a vector of U-knots.

◆ UMultiplicities()

cadex.Collections.IntList cadex.Geom.BSplineSurface.UMultiplicities ( )

inline

theUMults must point to a buffer in memory with at least NumberOfUKnots() preallocated values.

Returns NumberOfUKnots().

See also: UKnots(). Populates a vector of U knot multiplicities.

◆ UMultiplicity()

int cadex.Geom.BSplineSurface.UMultiplicity ( int theUIndex )

inline

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

See also: UKnot(). Returns a U knot multiplicity.

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

◆ VDegree()

int cadex.Geom.BSplineSurface.VDegree ( )

inline

Returns V-degree.

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

◆ VKnot()

double cadex.Geom.BSplineSurface.VKnot ( int theVIndex )

inline

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

See also: VMultiplicity(). Returns a V-knot value.

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

◆ VKnots()

cadex.Collections.DoubleList cadex.Geom.BSplineSurface.VKnots ( )

inline

theVKnots must point to a buffer in memory with at least NumberOfVKnots() preallocated values.

Returns NumberOfVKnots().

See also: VMultiplicities(). Populates a vector of V-knots.

◆ VMultiplicities()

cadex.Collections.IntList cadex.Geom.BSplineSurface.VMultiplicities ( )

inline

theVMults must point to a buffer in memory with at least NumberOfVKnots() preallocated values.

Returns NumberOfVKnots().

See also: VKnots(). Populates a vector of V knot multiplicities.

◆ VMultiplicity()

int cadex.Geom.BSplineSurface.VMultiplicity ( int theVIndex )

inline

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

See also: VKnot(). Returns a V knot multiplicity.

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

◆ Weight()

double cadex.Geom.BSplineSurface.Weight	(	int	theUIndex,
		int	theVIndex )

inline

theUIndex must be in the range [1, NumberOfUPoles()], theVIndex in the range [1, NumberOfVPoles()].

For polynomial B-Spline behavior is undefined.

See also: Pole(), IsURational(), IsVRational(). Returns a weight value.

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

◆ Weights()

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

inline

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

Returns NumberOfUPoles() * NumberOfVPoles().

For polynomial B-Spline does nothing and returns 0.

See also: Poles(), IsURational(), IsVRational(). Populates a 2D table of weights.

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Member Function Documentation

◆ Dispose()

◆ IsURational()

◆ IsVRational()

◆ NumberOfUKnots()

◆ NumberOfUPoles()

◆ NumberOfVKnots()

◆ NumberOfVPoles()

◆ Pole()

◆ Poles()

◆ UDegree()

◆ UKnot()

◆ UKnots()

◆ UMultiplicities()

◆ UMultiplicity()

◆ VDegree()

◆ VKnot()

◆ VKnots()

◆ VMultiplicities()

◆ VMultiplicity()

◆ Weight()

◆ Weights()