Defines a toroidal surface. More...

Inheritance diagram for cadex::ModelData_ToroidalSurface:

Public Types
typedef cadex::internal::ModelData_ToroidalSurfaceImpl	ImplType

Public Types inherited from cadex::ModelData_ElementarySurface
typedef cadex::internal::ModelData_ElementarySurfaceImpl	ImplType

Public Member Functions
	ModelData_ToroidalSurface ()
	Constructor.

	ModelData_ToroidalSurface (const ModelData_Axis3Placement &thePosition, double theMajorRadius, double theMinorRadius)
	Constructor.

	ModelData_ToroidalSurface (const Handle_C &)

double	MajorRadius () const
	Returns major radius.

double	MinorRadius () const
	Returns minor radius.

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

const ModelData_Axis3Placement &	Position () const
	Returns a surface axis.

const ModelData_Point &	Location () const
	Returns origin point.

const ModelData_Direction &	Direction () const
	Returns Z direction of the axis placement.

ModelData_Point2d	Parameter (const ModelData_Point &thePoint) const
	Returns UV-point in surface parametric space for a 3D point.

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

Public Attributes inherited from cadex::ModelData_ElementarySurface
	operator Handle_C const

Detailed Description

Defines a toroidal surface.

A toroidal surface is defined by an axis placement and a major and minor radius. The following image depicts a toroidal surface example:

Toroidal surface

A toroidal surface is parametrized as follows: \(\mathbf{S}(u,v) = \mathbf{P} + (R_1 + R_2\cos(v))(\cos(u)\mathbf{D}_x + \sin(u)\mathbf{D}_y) + R_2\sin(v)\mathbf{D}_z\), where

\(\mathbf{P}\) is an origin point,
\(\mathbf{D}_x\), \(\mathbf{D}_y\) and \(\mathbf{D}_z\) are directions (unit vectors) of X, Y and Z axes respectively,
\(R_1\) is a major radius,
\(R_2\) is a minor radius,
\(u\) belongs to \([0, 2\pi]\),
\(v\) belongs to \([0, 2\pi]\),

U-parameter is an angle when rotating around the \(\mathbf{D}_z\) axis counterclockwise, and V-parameter is an angle in circular section at a given parameter U. Thus, U-isolines circles lying in the plane containing Z axis and V-isolines are circles in the planes perpendicular to Z axis.

V-isoline at \(v=0\) is a circle of radius \(R_1+R_2\) in the plane defined by an axis placement. U-isoline at \(u=0\) is a circle of radius \(R_2\) in the plane containing Z and X axes.

Radii \(R_1\) and \(R_2\) must be positive. If \(R_2>R_1\) then toroidal surface will be self-intersecting.

Toroidal surface is both U- and V-periodical with periods \(2\pi\).

If a face lies on a full toroidal surface its boundary wire will contain two seam-edges, corresponding to \(u=0\) and \(u=2\pi\), and \(v=0\) and \(v=2\pi\) respectively.

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

Constructor & Destructor Documentation

◆ ModelData_ToroidalSurface() [1/2]

cadex::ModelData_ToroidalSurface::ModelData_ToroidalSurface ( )

inline

Constructor.

Empty constructor.

◆ ModelData_ToroidalSurface() [2/2]

cadex::ModelData_ToroidalSurface::ModelData_ToroidalSurface	(	const ModelData_Axis3Placement &	thePosition,
		double	theMajorRadius,
		double	theMinorRadius
	)

Constructor.

Creates a toroidal surface from an axis placement, major radius and minor radius.

theMajorRadius and theMinorRadius must be positive.

Member Function Documentation

◆ MajorRadius()

double cadex::ModelData_ToroidalSurface::MajorRadius ( ) const

Returns major radius.

Returns the value specified in the constructor.

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

◆ MinorRadius()

double cadex::ModelData_ToroidalSurface::MinorRadius ( ) const

Returns minor radius.