Defines a toroidal surface. More...

#include <cadex/Geom/ToroidalSurface.hxx>

Inheritance diagram for cadex::Geom::ToroidalSurface:

Public Member Functions
	ToroidalSurface ()
	Constructor.

	ToroidalSurface (const Axis3d &thePosition, double theMajorRadius, double theMinorRadius)
	Constructor.

double	MajorRadius () const
	Returns major radius.

double	MinorRadius () const
	Returns minor radius.

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

Geom::Axis3d	Position () const
	Returns a surface axis.

Geom::Point	Location () const
	Returns origin point.

Geom::Direction	Direction () const
	Returns Z direction of the axis placement.

Geom::Point2d	Parameter (const Geom::Point &thePoint) const
	Returns UV-point in surface parametric space for a 3D point.

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::ElementarySurface
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::ElementarySurface
	ElementarySurface (const ImplType &theImpl)

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 toroidal surface.

A toroidal surface is defined by an axis 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/brep_geometry/Program.cs, and exploring/brep_geometry/main.cxx.

Constructor & Destructor Documentation

◆ ToroidalSurface()

cadex::Geom::ToroidalSurface::ToroidalSurface	(	const Axis3d &	thePosition,
		double	theMajorRadius,
		double	theMinorRadius )

Constructor.

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

theMajorRadius and theMinorRadius must be positive.

Member Function Documentation

◆ MajorRadius()

double cadex::Geom::ToroidalSurface::MajorRadius ( ) const

Returns major radius.

Returns the value specified in the constructor.

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

◆ MinorRadius()

double cadex::Geom::ToroidalSurface::MinorRadius ( ) const

Returns minor radius.