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)
	Constructor.

	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)
	Constructor.

	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)
	Returns a pole value.

cadex.Collections.PointList	Poles ()
	Populates a 2D table of poles.

double	Weight (int theUIndex, int theVIndex)
	Returns a weight value.

cadex.Collections.DoubleList	Weights ()
	Populates a 2D table of weights.

double	UKnot (int theUIndex)
	Returns a U-knot value.

double	VKnot (int theVIndex)
	Returns a V-knot value.

cadex.Collections.DoubleList	UKnots ()
	Populates a vector of U-knots.

cadex.Collections.DoubleList	VKnots ()
	Populates a vector of V-knots.

int	UMultiplicity (int theUIndex)
	Returns a U knot multiplicity.

int	VMultiplicity (int theVIndex)
	Returns a V knot multiplicity.

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

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

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)
	Evaluates a point on the surface.

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

bool	IsUPeriodic ()
	Returns true if the surface is periodic in U direction.

bool	IsVPeriodic ()
	Returns true if the surface is periodic in V direction.

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)
	Applies transformation matrix to this object.

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

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)

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.

Constructor & Destructor Documentation

◆ BSplineSurface() [1/2]

cadex.Geom.BSplineSurface.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 )

inline

Constructor.

Creates a polynomial B-Spline surface.

Parameters:

thePoles contains a 2D table of poles, with size equal to theNumberOfUPoles * theNumberOfVPoles; theNumberOfUPoles and theNumberOfVPoles must be >=2 each;
theNumberOfUKnots defines the length of theUKnots and theUMults and must be >=2;
theNumberOfVKnots defines the length of theVKnots and theVMults and must be >=2;
theUDegree and theVDegree must belong to range [1, 25];
theIsUPeriodic and theIsVPeriodic specify if the B-Spline is periodic in U and/or V direction respectively.

Number of poles in U and V direction must meet the requirements described above.

◆ BSplineSurface() [2/2]

cadex.Geom.BSplineSurface.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 )

inline

Constructor.

Creates a rational B-Spline surface.

Parameters:

thePoles contains a 2D table of poles, with size equal to theNumberOfUPoles * theNumberOfVPoles; theNumberOfUPoles and theNumberOfVPoles must be >=2 each;
thePoleWeights defines pole weights and must have the same size and layout as thePoles;
theNumberOfUKnots defines the length of theUKnots and theUMults and must be >=2;
theNumberOfVKnots defines the length of theVKnots and theVMults and must be >=2;
theUDegree and theVDegree must belong to range [1, 25];
theIsUPeriodic and theIsVPeriodic specify if the B-Spline is periodic in U and/or V direction respectively.

Number of poles in U and V direction must meet the requirements described above.

Poles are to be provided after division by their weights.

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.

See also: Weights(), IsVRational().

◆ IsVRational()

bool cadex.Geom.BSplineSurface.IsVRational ( )

inline

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

See also: Weights(), IsURational().

◆ NumberOfUKnots()

int cadex.Geom.BSplineSurface.NumberOfUKnots ( )

inline

Returns number of unique U-knots.

Returns the value specified in the constructor.

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

◆ NumberOfUPoles()

int cadex.Geom.BSplineSurface.NumberOfUPoles ( )

inline

Returns number of U-poles.

Returns the value specified in the constructor.

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.

Returns the value specified in the constructor.

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

◆ NumberOfVPoles()

int cadex.Geom.BSplineSurface.NumberOfVPoles ( )

inline

Returns number of V-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.BSplineSurface.Pole	(	int	theUIndex,
		int	theVIndex )

inline

Returns a pole value.

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

See also: Weight().

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

◆ Poles()

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

inline

Populates a 2D table of poles.

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

Returns NumberOfUPoles() * NumberOfVPoles().

See also: Weights().

◆ UDegree()

int cadex.Geom.BSplineSurface.UDegree ( )

inline

Returns U-degree.

Returns the value specified in the constructor.

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

◆ UKnot()

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

inline

Returns a U-knot value.

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

See also: UMultiplicity().

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

◆ UKnots()

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

inline

Populates a vector of U-knots.

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

Returns NumberOfUKnots().

See also: UMultiplicities().

◆ UMultiplicities()

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

inline

Populates a vector of U knot multiplicities.

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

Returns NumberOfUKnots().

See also: UKnots().

◆ UMultiplicity()

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

inline

Returns a U knot multiplicity.

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

See also: UKnot().

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

◆ VDegree()

int cadex.Geom.BSplineSurface.VDegree ( )

inline

Returns V-degree.

Returns the value specified in the constructor.

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

◆ VKnot()

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

inline

Returns a V-knot value.

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

See also: VMultiplicity().

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

◆ VKnots()

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

inline

Populates a vector of V-knots.

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

Returns NumberOfVKnots().

See also: VMultiplicities().

◆ VMultiplicities()

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

inline

Populates a vector of V knot multiplicities.

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

Returns NumberOfVKnots().

See also: VKnots().

◆ VMultiplicity()

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

inline

Returns a V knot multiplicity.

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

See also: VKnot().

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

◆ Weight()

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

inline

Returns a weight value.

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().

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

◆ Weights()

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

inline

Populates a 2D table of weights.

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().

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ BSplineSurface() [1/2]

◆ BSplineSurface() [2/2]

Member Function Documentation

◆ Dispose()

◆ IsURational()

◆ IsVRational()

◆ NumberOfUKnots()

◆ NumberOfUPoles()

◆ NumberOfVKnots()

◆ NumberOfVPoles()

◆ Pole()

◆ Poles()

◆ UDegree()

◆ UKnot()

◆ UKnots()

◆ UMultiplicities()

◆ UMultiplicity()

◆ VDegree()

◆ VKnot()

◆ VKnots()

◆ VMultiplicities()

◆ VMultiplicity()

◆ Weight()

◆ Weights()