Defines a B-Spline surface. More...

#include <cadex/ModelData_BSplineSurface.hxx>

Inheritance diagram for cadex::ModelData_BSplineSurface:

Public Types
typedef cadex::internal::ModelData_BSplineSurfaceImpl	ImplType

Public Member Functions
	ModelData_BSplineSurface ()
	Constructor.

	ModelData_BSplineSurface (const ModelData_Point thePoles[], int theNumberOfUPoles, int theNumberOfVPoles, const double theUKnots[], const double theVKnots[], int theNumberOfUKnots, int theNumberOfVKnots, const int theUMults[], const int theVMults[], int theUDegree, int theVDegree, bool theIsUPeriodic=false, bool theIsVPeriodic=false)
	Constructor.

	ModelData_BSplineSurface (const ModelData_Point thePoles[], const double thePoleWeights[], int theNumberOfUPoles, int theNumberOfVPoles, const double theUKnots[], const double theVKnots[], int theNumberOfUKnots, int theNumberOfVKnots, const int theUMults[], const int theVMults[], int theUDegree, int theVDegree, bool theIsUPeriodic=false, bool theIsVPeriodic=false)
	Constructor.

	ModelData_BSplineSurface (const Handle_C &)
	Constructor.

int	UDegree () const
	Returns U-degree.

int	VDegree () const
	Returns V-degree.

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

int	NumberOfUPoles () const
	Returns number of U-poles.

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

int	NumberOfVPoles () const
	Returns number of V-poles.

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

int	UKnots (double theUKnots[]) const
	Populates a vector of U-knots.

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

int	VKnots (double theVKnots[]) const
	Populates a vector of V-knots.

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

int	UMultiplicities (int theUMultiplicities[]) const
	Populates a vector of U knot multiplicities.

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

int	VMultiplicities (int theVMultiplicities[]) const
	Populates a vector of V knot multiplicities.

ModelData_Point	Pole (int theUIndex, int theVIndex) const
	Returns a pole value.

int	Poles (ModelData_Point thePoles[]) const
	Populates a 2D table of poles.

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

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

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

int	Weights (double theWeights[]) const
	Populates a 2D table of weights.

Public Member Functions inherited from cadex::ModelData_Surface
	ModelData_Surface ()
	Constructor.

	ModelData_Surface (const ModelData_Surface &theOther)
	Constructor.

	ModelData_Surface (ModelData_Surface &&theOther)
	Constructor.

	~ModelData_Surface ()
	Destructor.

ModelData_Surface &	operator= (const ModelData_Surface &theOther)
	Assignment operator.

ModelData_Surface &	operator= (ModelData_Surface &&theOther)
	Move assignment operator.

ModelData_SurfaceType	Type () const
	Returns a surface type.

bool	IsNull () const
	Returns true if the object has not been initialized yet.

void	Nullify ()
	Resets the object.

	operator bool () const

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

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

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

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

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

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

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

ModelData_Point	Value (double theParameterU, double theParameterV) const
	Evaluates a point on the surface.

void	Transform (const ModelData_Transformation &theTransformation)
	Applies transformation matrix to this object.

ModelData_Surface	Transformed (const ModelData_Transformation &theTransformation) const
	Returns a copy this object after applying transformation.

ModelData_Continuity	Continuity () const
	Returns a continuity type of the surface.

void	D0 (double theParameterU, double theParameterV, ModelData_Point &theValue) const
	Returns the point theValue of parameter theU, theV on the surface.

void	D1 (double theParameterU, double theParameterV, ModelData_Point &theValue, ModelData_Vector &theD1U, ModelData_Vector &theD1V) const
	Returns the point theValue and the first derivatives in the directions U theD1U and V theD1V at this point.

void	D2 (double theParameterU, double theParameterV, ModelData_Point &theValue, ModelData_Vector &theD1U, ModelData_Vector &theD1V, ModelData_Vector &theD2U, ModelData_Vector &theD2V, ModelData_Vector &theD2UV) const
	Returns the point theValue, the first and the second derivatives in the directions U and V at this point.

bool	DN (double theParameterU, double theParameterV, size_t theDerivativeOrder, ModelData_Point &theValue, ModelData_Vector theD[]) const

void	Curvature (double theParameterU, double theParameterV, ModelData_Vector &thePrincipalMaxDirection, ModelData_Vector &thePrincipalMinDirection) const
	Returns the max and min principal curvature directions multiplied by max and min value of curvature respectively.

void	Curvature (double theParameterU, double theParameterV, ModelData_Direction &thePrincipalMaxDirection, ModelData_Direction &thePrincipalMinDirection, double &theMaxCurvature, double &theMinCurvature) const
	Returns the max and min principal curvature directions and their values.

void	Normal (double theParameterU, double theParameterV, ModelData_Direction &theNormal) const
	Returns the normal direction theNormal at the current point.

void	Mirror (const ModelData_Point &thePoint)
	Mirrors the surface relative to the point.

void	Mirror (const ModelData_Axis1Placement &theAxis)
	Mirrors the surface relative to the axis placement.

void	Mirror (const ModelData_Axis2Placement &theAxis)
	Mirrors the surface relative to the axis placement.

ModelData_Surface	Mirrored (const ModelData_Point &theRef) const
	Returns a copy this surface mirrored along the object.

ModelData_Surface	Mirrored (const ModelData_Axis1Placement &theAxis) const
	Returns a copy this surface mirrored along the object.

ModelData_Surface	Mirrored (const ModelData_Axis2Placement &theAxis) const
	Returns a copy this surface mirrored along the object.

void	Rotate (const ModelData_Axis1Placement &theAxis, double theAngle)
	Rotates the surface around the axis.

ModelData_Surface	Rotated (const ModelData_Axis1Placement &theAxis, double theAngle) const
	Returns a copy this surface rotated along the axis.

void	Translate (const ModelData_Vector &theVector)
	Translates the surface along the vector.

ModelData_Surface	Translated (const ModelData_Vector &theVector) const
	Returns a copy this surface translated along the vector.

void	Scale (const ModelData_Point &thePoint, double theScale)
	Scales the surface with respect to the point.

ModelData_Surface	Scaled (const ModelData_Point &thePoint, double theScale) const
	Returns a copy this surface scaled with respect to the point.

Public Attributes
	operator Handle_C const

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/brepgeometry/Program.cs, exploring/brepgeometry/main.cxx, modeling/brep/Program.cs, and modeling/brep/main.cxx.

Constructor & Destructor Documentation

◆ ModelData_BSplineSurface() [1/3]

cadex::ModelData_BSplineSurface::ModelData_BSplineSurface ( )

inline

Constructor.

Empty constructor.

◆ ModelData_BSplineSurface() [2/3]

cadex::ModelData_BSplineSurface::ModelData_BSplineSurface	(	const ModelData_Point	thePoles[],
		int	theNumberOfUPoles,
		int	theNumberOfVPoles,
		const double	theUKnots[],
		const double	theVKnots[],
		int	theNumberOfUKnots,
		int	theNumberOfVKnots,
		const int	theUMults[],
		const int	theVMults[],
		int	theUDegree,
		int	theVDegree,
		bool	theIsUPeriodic = `false`,
		bool	theIsVPeriodic = `false`
	)

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.

◆ ModelData_BSplineSurface() [3/3]

cadex::ModelData_BSplineSurface::ModelData_BSplineSurface	(	const ModelData_Point	thePoles[],
		const double	thePoleWeights[],
		int	theNumberOfUPoles,
		int	theNumberOfVPoles,
		const double	theUKnots[],
		const double	theVKnots[],
		int	theNumberOfUKnots,
		int	theNumberOfVKnots,
		const int	theUMults[],
		const int	theVMults[],
		int	theUDegree,
		int	theVDegree,
		bool	theIsUPeriodic = `false`,
		bool	theIsVPeriodic = `false`
	)

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

◆ IsURational()

bool cadex::ModelData_BSplineSurface::IsURational ( ) const

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

See also: Weights(), IsVRational().

◆ IsVRational()

bool cadex::ModelData_BSplineSurface::IsVRational ( ) const

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

See also: Weights(), IsURational().

◆ NumberOfUKnots()

int cadex::ModelData_BSplineSurface::NumberOfUKnots ( ) const

Returns number of unique U-knots.

Returns the value specified in the constructor.

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

◆ NumberOfUPoles()

int cadex::ModelData_BSplineSurface::NumberOfUPoles ( ) const

Returns number of U-poles.

Returns the value specified in the constructor.

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

◆ NumberOfVKnots()

int cadex::ModelData_BSplineSurface::NumberOfVKnots ( ) const

Returns number of unique V-knots.

Returns the value specified in the constructor.

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

◆ NumberOfVPoles()

int cadex::ModelData_BSplineSurface::NumberOfVPoles ( ) const

Returns number of V-poles.

Returns the value specified in the constructor.

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

◆ Pole()

ModelData_Point cadex::ModelData_BSplineSurface::Pole	(	int	theUIndex,
		int	theVIndex
	)		const

Returns a pole value.

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

See also: Weight().

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

◆ Poles()

int cadex::ModelData_BSplineSurface::Poles ( ModelData_Point thePoles[] ) const

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::ModelData_BSplineSurface::UDegree ( ) const

Returns U-degree.

Returns the value specified in the constructor.

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

◆ UKnot()

double cadex::ModelData_BSplineSurface::UKnot ( int theUIndex ) const

Returns a U-knot value.

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

See also: UMultiplicity().

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

◆ UKnots()

int cadex::ModelData_BSplineSurface::UKnots ( double theUKnots[] ) const

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()

int cadex::ModelData_BSplineSurface::UMultiplicities ( int theUMults[] ) const

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::ModelData_BSplineSurface::UMultiplicity ( int theUIndex ) const

Returns a U knot multiplicity.

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

See also: UKnot().

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

◆ VDegree()

int cadex::ModelData_BSplineSurface::VDegree ( ) const

Returns V-degree.

Returns the value specified in the constructor.

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

◆ VKnot()

double cadex::ModelData_BSplineSurface::VKnot ( int theVIndex ) const

Returns a V-knot value.

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

See also: VMultiplicity().

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

◆ VKnots()

int cadex::ModelData_BSplineSurface::VKnots ( double theVKnots[] ) const

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()

int cadex::ModelData_BSplineSurface::VMultiplicities ( int theVMults[] ) const

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::ModelData_BSplineSurface::VMultiplicity ( int theVIndex ) const

Returns a V knot multiplicity.

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

See also: VKnot().

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

◆ Weight()

double cadex::ModelData_BSplineSurface::Weight	(	int	theUIndex,
		int	theVIndex
	)		const

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/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

◆ Weights()

int cadex::ModelData_BSplineSurface::Weights ( double theWeights[] ) const

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 Types

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ ModelData_BSplineSurface() [1/3]

◆ ModelData_BSplineSurface() [2/3]

◆ ModelData_BSplineSurface() [3/3]

Member Function Documentation

◆ IsURational()

◆ IsVRational()

◆ NumberOfUKnots()

◆ NumberOfUPoles()

◆ NumberOfVKnots()

◆ NumberOfVPoles()

◆ Pole()

◆ Poles()

◆ UDegree()

◆ UKnot()

◆ UKnots()

◆ UMultiplicities()

◆ UMultiplicity()

◆ VDegree()

◆ VKnot()

◆ VKnots()

◆ VMultiplicities()

◆ VMultiplicity()

◆ Weight()

◆ Weights()