Defines a toroidal surface. More...

Inheritance diagram for cadex.Geom.ToroidalSurface:

Public Member Functions
	ToroidalSurface (global::System.IntPtr cPtr, bool cMemoryOwn)

	ToroidalSurface (cadex.Geom.Axis3d thePosition, double theMajorRadius, double theMinorRadius)
	Constructor.

double	MajorRadius ()
	Returns major radius.

double	MinorRadius ()
	Returns minor radius.

Public Member Functions inherited from cadex.Geom.ElementarySurface
	ElementarySurface (global::System.IntPtr cPtr, bool cMemoryOwn)

cadex.Geom.Axis3d	Position ()
	Returns a surface axis.

cadex.Geom.Point	Location ()
	Returns origin point.

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

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

Public Member Functions inherited from cadex.Geom.Surface
	Surface (global::System.IntPtr cPtr, bool cMemoryOwn)

cadex.Geom.SurfaceType	Type ()
	Returns a surface type.

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

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

cadex.Geom.Direction	Normal (double theParameterU, double theParameterV)

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

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

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

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

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

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

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

bool	IsTrimmed ()
	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 (cadex.Geom.Transformation theTransformation)
	Applies transformation matrix to this object.

cadex.Geom.Surface	Transformed (cadex.Geom.Transformation theTransformation)
	Returns a copy this object after applying transformation.

void	D0 (double theParameterU, double theParameterV, cadex.Geom.Point theValue)

void	D1 (double theParameterU, double theParameterV, cadex.Geom.Point theValue, cadex.Geom.Vector theD1U, cadex.Geom.Vector theD1V)

void	D2 (double theParameterU, double theParameterV, cadex.Geom.Point theValue, cadex.Geom.Vector theD1U, cadex.Geom.Vector theD1V, cadex.Geom.Vector theD2U, cadex.Geom.Vector theD2V, cadex.Geom.Vector theD2UV)

bool	DN (double theParameterU, double theParameterV, uint theDerivativeOrder, cadex.Geom.Point theValue, cadex.Collections.VectorList theD)

void	Curvature (double theParameterU, double theParameterV, cadex.Geom.Direction thePrincipalMaxDirection, cadex.Geom.Direction thePrincipalMinDirection)

void	Curvature (double theParameterU, double theParameterV, cadex.Geom.Direction thePrincipalMaxDirection, cadex.Geom.Direction thePrincipalMinDirection, out double theMaxCurvature, out double theMinCurvature)

void	Mirror (cadex.Geom.Point thePoint)

void	Mirror (cadex.Geom.Axis1d theAxis)

void	Mirror (cadex.Geom.Axis3d theAxis)

cadex.Geom.Surface	Mirrored (cadex.Geom.Point theRef)

cadex.Geom.Surface	Mirrored (cadex.Geom.Axis1d theAxis)

cadex.Geom.Surface	Mirrored (cadex.Geom.Axis3d theAxis)

void	Rotate (cadex.Geom.Axis1d theAxis, double theAngle)

cadex.Geom.Surface	Rotated (cadex.Geom.Axis1d theAxis, double theAngle)

void	Translate (cadex.Geom.Vector theVector)

cadex.Geom.Surface	Translated (cadex.Geom.Vector theVector)

void	Scale (cadex.Geom.Point thePoint, double theScale)

cadex.Geom.Surface	Scaled (cadex.Geom.Point thePoint, double theScale)

Public Member Functions inherited from cadex.Geom.Geometry
	Geometry (global::System.IntPtr cPtr, bool cMemoryOwn)

Public Member Functions inherited from cadex.BaseObject
	BaseObject (global::System.IntPtr cPtr, bool cMemoryOwn)

void	Dispose ()

bool	IsNull ()

ulong	Id ()
	Return unique identifier of public object.

bool	IsEqual (cadex.BaseObject theObj)

override int	GetHashCode ()

override bool	Equals (System.Object o)

Static Public Member Functions
static new bool	CompareType (cadex.BaseObject theObject)

static new cadex.Geom.ToroidalSurface	Cast (cadex.Geom.Surface theBase)

Static Public Member Functions inherited from cadex.Geom.ElementarySurface
static new bool	CompareType (cadex.BaseObject theObject)

static cadex.Geom.ElementarySurface	Cast (cadex.Geom.Surface theBase)

Static Public Member Functions inherited from cadex.Geom.Surface
static new bool	CompareType (cadex.BaseObject theObject)

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

static cadex.Geom.Geometry	Cast (cadex.BaseObject theBase)

Protected Member Functions
override void	Dispose (bool disposing)

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	(	cadex.Geom.Axis3d	thePosition,
		double	theMajorRadius,
		double	theMinorRadius )

inline

Constructor.

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

theMajorRadius and theMinorRadius must be positive.

Member Function Documentation

◆ Dispose()

override void cadex.Geom.ToroidalSurface.Dispose ( bool disposing )

inlineprotectedvirtual

Reimplemented from cadex.Geom.ElementarySurface.

◆ MajorRadius()

double cadex.Geom.ToroidalSurface.MajorRadius ( )

inline

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 ( )

inline

Returns minor radius.

Returns the value specified in the constructor.

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ ToroidalSurface()

Member Function Documentation

◆ Dispose()

◆ MajorRadius()

◆ MinorRadius()