Defines a Bezier surface. More...

#include <cadex/Geom/BezierSurface.hxx>

Inheritance diagram for cadex::Geom::BezierSurface:

Public Member Functions
	BezierSurface ()
	Constructor.

	BezierSurface (const std::vector< Point > &thePoles, int theNumberOfUPoles, int theNumberOfVPoles)
	Constructor.

	BezierSurface (const std::vector< Point > &thePoles, const std::vector< double > &thePoleWeights, int theNumberOfUPoles, int theNumberOfVPoles)
	Constructor.

int	UDegree () const
	Returns degree.

int	VDegree () const
	Returns degree.

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

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

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.

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 Bezier surface.

Bezier surface is defined by control points (poles) and their weights. The following image depicts an example of a Bezier surface:

Bezier surface

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

A rational Bezier surface contains an explicit vector of weights, whereas polynomial does not.

The surface degree equals number of poles minus one. Degree up to 25 is supported.

The Bezier surface is always considered non-periodic.

Constructor & Destructor Documentation

◆ BezierSurface() [1/2]

cadex::Geom::BezierSurface::BezierSurface	(	const std::vector< Point > &	thePoles,
		int	theNumberOfUPoles,
		int	theNumberOfVPoles )

Constructor.

Creates a polynomial Bezier surface.

thePoles contains a 2D table of poles, with size equal to theNumberOfUPoles * theNumberOfVPoles. theNumberOfUPoles and theNumberOfVPoles must be >=2 each.

◆ BezierSurface() [2/2]

cadex::Geom::BezierSurface::BezierSurface	(	const std::vector< Point > &	thePoles,
		const std::vector< double > &	theWeights,
		int	theNumOfUPoles,
		int	theNumOfVPoles )

Constructor.

Creates a rational Bezier surface.

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;

Member Function Documentation

◆ NumberOfUPoles()

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

Returns number of U-poles.

Returns the value specified in the constructor.

◆ NumberOfVPoles()

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

Returns number of V-poles.

Returns the value specified in the constructor.

◆ Pole()

Point cadex::Geom::BezierSurface::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::BezierSurface::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::BezierSurface::UDegree ( ) const

Returns degree.

Returns the value equal to NumberOfUPoles() - 1.

◆ VDegree()

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

Returns degree.

Returns the value equal to NumberOfVPoles() - 1.

◆ Weight()

double cadex::Geom::BezierSurface::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 Bezier surface behavior is undefined.

See also: Pole().

◆ Weights()

std::vector< double > cadex::Geom::BezierSurface::Weights ( ) const

Populates a 2D table of weights.