Defines a B-Spline surface. More...

#include <cadex/Geom/BSplineSurface.hxx>

Inheritance diagram for cadex::Geom::BSplineSurface:

Public Member Functions
	BSplineSurface ()
	Constructor.

	BSplineSurface (const std::vector< Point > &thePoles, int theNumberOfUPoles, int theNumberOfVPoles, const std::vector< double > &theUKnots, const std::vector< double > &theVKnots, const std::vector< int > &theUMults, const std::vector< int > &theVMults, int theUDegree, int theVDegree, bool theIsUPeriodic=false, bool theIsVPeriodic=false)
	Constructor.

	BSplineSurface (const std::vector< Point > &thePoles, const std::vector< double > &theWeights, int theNumberOfUPoles, int theNumberOfVPoles, const std::vector< double > &theUKnots, const std::vector< double > &theVKnots, const std::vector< int > &theUMults, const std::vector< int > &theVMults, int theUDegree, int theVDegree, bool theIsUPeriodic=false, bool theIsVPeriodic=false)
	Constructor.

int	UDegree () const
	Returns U-degree.

int	VDegree () const
	Returns V-degree.

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

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

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

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

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

std::vector< Point >	Poles () const
	Populates a 2D table of poles.

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

std::vector< double >	Weights () const
	Populates a 2D table of weights.

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

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

std::vector< double >	UKnots () const
	Populates a vector of U-knots.

std::vector< double >	VKnots () const
	Populates a vector of V-knots.

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

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

std::vector< int >	UMultiplicities () const
	Populates a vector of U knot multiplicities.

std::vector< int >	VMultiplicities () const
	Populates a vector of V knot multiplicities.

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.

Public Member Functions inherited from cadex::Geom::Surface
	Surface ()
	Constructor.

SurfaceType	Type () const
	Returns a surface type.

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

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

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

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.

bool	IsTrimmed () const
	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 (const Transformation &theTransformation)
	Applies transformation matrix to this object.

Surface	Transformed (const Transformation &theTransformation) const
	Returns a copy this object after applying transformation.

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

void	D1 (double theParameterU, double theParameterV, Point &theValue, Vector &theD1U, 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, Point &theValue, Vector &theD1U, Vector &theD1V, Vector &theD2U, Vector &theD2V, 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, Geom::Point &theValue, std::vector< Geom::Vector > &theD) const

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

void	Mirror (const Point &thePoint)

void	Mirror (const Axis1d &theAxis)

void	Mirror (const Axis3d &theAxis)

Surface	Mirrored (const Point &theRef) const

Surface	Mirrored (const Axis1d &theAxis) const

Surface	Mirrored (const Axis3d &theAxis) const

void	Rotate (const Axis1d &theAxis, double theAngle)

Surface	Rotated (const Axis1d &theAxis, double theAngle) const

void	Translate (const Vector &theVector)

Surface	Translated (const Vector &theVector) const

void	Scale (const Point &thePoint, double theScale)

Surface	Scaled (const Point &thePoint, double theScale) const

Public Member Functions inherited from cadex::BaseObject
size_t	Id () const
	Return unique identifier of public object.

internal::BaseObjectImpl *	Impl () const

bool	IsNull () const

	operator bool () const

template<typename T >
bool	IsOfType () const

template<typename T >
T *	Impl () const
	Reserved for internal use.

Static Public Member Functions
static bool	CompareType (const BaseObject &theObject)

Static Public Member Functions inherited from cadex::Geom::Surface
static bool	CompareType (const BaseObject &theObject)

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

Additional Inherited Members
Public Types inherited from cadex::BaseObject
typedef std::shared_ptr< internal::BaseObjectImpl >	ImplType

Protected Member Functions inherited from cadex::Geom::Surface
	Surface (const ImplType &theImpl)

Protected Member Functions inherited from cadex::Geom::Geometry
	Geometry (const ImplType &theImpl)

Protected Member Functions inherited from cadex::BaseObject
	BaseObject (const ImplType &theImpl)

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.

Constructor & Destructor Documentation

◆ BSplineSurface() [1/2]

cadex::Geom::BSplineSurface::BSplineSurface	(	const std::vector< Point > &	thePoles,
		int	theNumberOfUPoles,
		int	theNumberOfVPoles,
		const std::vector< double > &	theUKnots,
		const std::vector< double > &	theVKnots,
		const std::vector< int > &	theUMults,
		const std::vector< 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.

◆ BSplineSurface() [2/2]

cadex::Geom::BSplineSurface::BSplineSurface	(	const std::vector< Point > &	thePoles,
		const std::vector< double > &	theWeights,
		int	theNumberOfUPoles,
		int	theNumberOfVPoles,
		const std::vector< double > &	theUKnots,
		const std::vector< double > &	theVKnots,
		const std::vector< int > &	theUMults,
		const std::vector< 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::Geom::BSplineSurface::IsURational ( ) const

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

See also: Weights(), IsVRational().

◆ IsVRational()

bool cadex::Geom::BSplineSurface::IsVRational ( ) const

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

See also: Weights(), IsURational().

◆ NumberOfUKnots()

int cadex::Geom::BSplineSurface::NumberOfUKnots ( ) const

Returns number of unique U-knots.

Returns the value specified in the constructor.

◆ NumberOfUPoles()

int cadex::Geom::BSplineSurface::NumberOfUPoles ( ) const

Returns number of U-poles.

Returns the value specified in the constructor.

◆ NumberOfVKnots()

int cadex::Geom::BSplineSurface::NumberOfVKnots ( ) const

Returns number of unique V-knots.

Returns the value specified in the constructor.

◆ NumberOfVPoles()

int cadex::Geom::BSplineSurface::NumberOfVPoles ( ) const

Returns number of V-poles.

Returns the value specified in the constructor.

◆ Pole()

Point cadex::Geom::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().

◆ Poles()

std::vector< Point > cadex::Geom::BSplineSurface::Poles ( ) 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::Geom::BSplineSurface::UDegree ( ) const

Returns U-degree.

Returns the value specified in the constructor.

◆ UKnot()

double cadex::Geom::BSplineSurface::UKnot ( int theUIndex ) const

Returns a U-knot value.

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

See also: UMultiplicity().

◆ UKnots()

std::vector< double > cadex::Geom::BSplineSurface::UKnots ( ) 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()

std::vector< int > cadex::Geom::BSplineSurface::UMultiplicities ( ) 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::Geom::BSplineSurface::UMultiplicity ( int theUIndex ) const

Returns a U knot multiplicity.

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

See also: UKnot().

◆ VDegree()

int cadex::Geom::BSplineSurface::VDegree ( ) const

Returns V-degree.

Returns the value specified in the constructor.

◆ VKnot()

double cadex::Geom::BSplineSurface::VKnot ( int theVIndex ) const

Returns a V-knot value.

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

See also: VMultiplicity().

◆ VKnots()

std::vector< double > cadex::Geom::BSplineSurface::VKnots ( ) 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()

std::vector< int > cadex::Geom::BSplineSurface::VMultiplicities ( ) 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::Geom::BSplineSurface::VMultiplicity ( int theVIndex ) const

Returns a V knot multiplicity.

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

See also: VKnot().

◆ Weight()

double cadex::Geom::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().

◆ Weights()

std::vector< double > cadex::Geom::BSplineSurface::Weights ( ) 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 Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BSplineSurface() [1/2]

◆ BSplineSurface() [2/2]

Member Function Documentation

◆ IsURational()

◆ IsVRational()

◆ NumberOfUKnots()

◆ NumberOfUPoles()

◆ NumberOfVKnots()

◆ NumberOfVPoles()

◆ Pole()

◆ Poles()

◆ UDegree()

◆ UKnot()

◆ UKnots()

◆ UMultiplicities()

◆ UMultiplicity()

◆ VDegree()

◆ VKnot()

◆ VKnots()

◆ VMultiplicities()

◆ VMultiplicity()

◆ Weight()

◆ Weights()