Defines a spherical surface. More...

Inheritance diagram for cadex.Geom.SphericalSurface:

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

	SphericalSurface (cadex.Geom.Axis3d thePosition, double theRadius)
	Constructor.

double	Radius ()
	Returns 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.SphericalSurface	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)

Protected Member Functions inherited from cadex.Geom.Surface
override void	Dispose (bool disposing)

Detailed Description

Defines a spherical surface.

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

Spherical surface

A spherical surface is parametrized as follows: \(\mathbf{S}(u,v) = \mathbf{P} + R\cos(v)(\cos(u)\mathbf{D}_x + \sin(u)\mathbf{D}_y) + R\sin(v)\mathbf{D}_z\), 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,
\(R\) is a radius,
\(u\) belongs to \([0, 2\pi]\),
\(v\) belongs to \([-\frac{\pi}{2}, \frac{\pi}{2}]\).

U-parameter is an angle of rotation around the Dz axis counterclockwise (i.e. similar to longitude on the Earth), and V-parameter is an angle between plane defined by an axis placement and line from P to a point on a sphere (i.e. latitude). Thus, U-isolines are semi-circles and V-isoline are circles.

V-isoline at \(v=0\) is a circle of radius \(R\) in the plane defined by an axis placement. U-isoline at \(u=0\) corresponds to a semi-circle from south to north pole.

Spherical surface is U-periodical with period \(2\pi\).

If a face lies on a full spherical surface its boundary wire will contain two a degenerated edges corresponding to the south and north poles (V equals \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) respectively), and a seam-edge.

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

Constructor & Destructor Documentation

◆ SphericalSurface()

cadex.Geom.SphericalSurface.SphericalSurface	(	cadex.Geom.Axis3d	thePosition,
		double	theRadius )

inline

Constructor.

Creates a spherical surface from an axis and radius.

theRadius must be positive.

Member Function Documentation

◆ Dispose()

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

inlineprotectedvirtual

Reimplemented from cadex.Geom.ElementarySurface.

◆ Radius()

double cadex.Geom.SphericalSurface.Radius ( )

inline

Returns radius.

Returns the value specified in the constructor.

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

Public Member Functions