cadex.Geom.SurfaceOfRevolution Class Reference

Defines a surface of revolution. More...

Inheritance diagram for cadex.Geom.SurfaceOfRevolution:

Public Member Functions
	SurfaceOfRevolution (global::System.IntPtr cPtr, bool cMemoryOwn)
	SurfaceOfRevolution (cadex.Geom.Curve theBasisCurve, cadex.Geom.Point theLocation, cadex.Geom.Direction theDirection)
	Constructor.
cadex.Geom.Point	Location ()
	Returns an origin point of a rotation axis.
Public Member Functions inherited from cadex.Geom.SweptSurface
	SweptSurface (global::System.IntPtr cPtr, bool cMemoryOwn)
cadex.Geom.Curve	BasisCurve ()
cadex.Geom.Direction	Direction ()
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.SurfaceOfRevolution	Cast (cadex.Geom.Surface theBase)
Static Public Member Functions inherited from cadex.Geom.SweptSurface
static new bool	CompareType (cadex.BaseObject theObject)
static cadex.Geom.SweptSurface	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.SweptSurface
override void	Dispose (bool disposing)

Detailed Description

Defines a surface of revolution.

Surface of revolution is defined by a basis curve and a rotation axis. The following image depicts an example of a surface of revolution:

Surface of revolution

A surface of revolution is parametrized as follows: \(\mathbf{S}(u,v) = \mathbf{Z}(v) + \cos(u)(\mathbf{B}(v) - \mathbf{Z}(v)) + \mathbf{D}\times\sin(u)(\mathbf{B}(v) - \mathbf{Z}(v))\), where:

• \(\mathbf{P}\) is an origin point specifying rotation axis,
• \(\mathbf{D}\) is unit vector specifying rotation axis,
• \(\mathbf{B}(v)\) is a basis curve,
• \(\mathbf{Z}(v)\) is a projection of a point on the basis curve onto a rotation axis, \(\mathbf{Z}(v) = \mathbf{P} + ((\mathbf{B}(v) - \mathbf{P})\cdot\mathbf{D})\mathbf{D}\),
• \(u\) belongs to \([0, 2\pi]\),
• \(v\) belongs to a basis curve definition domain.

U-parameter is an angle of rotation around the axis counterclockwise, and V-parameter is s a parameter along the curve \(\mathbf{B}(v)\). Thus, U-isolines are correspond to curve \(\mathbf{B}(v)\) rotated around the rotation axis and V-isolines are circles perpendicular to rotation axis with radius equal to distance from the axis to a point on the basis curve at parameter V. U-isoline at \(u=0\) is the basis curve itself.

The curve \(\mathbf{B}(v)\) should be planar although this is not enforced. It should not cross the rotation axis, except possibly at the end points.

Surface or revolution is periodic along U with period \(2\pi\). It is V-periodic if the basis curve is periodic itself.

If a face lies on a full range of U its boundary wire will contain two seam-edges at parameters UMin() and UMax(). Likewise, if the surface is V-periodic the wire will contain two seam-edges at parameters VMin() and VMax(). If the basis curve has end point(s) lying on a rotation axis then the wire will contain degenerated edge(s) at respective point(s).

Examples

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

Constructor & Destructor Documentation

SurfaceOfRevolution()

cadex.Geom.SurfaceOfRevolution.SurfaceOfRevolution ( cadex.Geom.Curve theBasisCurve, cadex.Geom.Point theLocation, cadex.Geom.Direction theDirection )

inline

Constructor.

Creates a surface of revolution from a basis curve and a rotation axis.

Member Function Documentation

Dispose()

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

inlineprotectedvirtual

Reimplemented from cadex.Geom.Surface.

Location()

cadex.Geom.Point cadex.Geom.SurfaceOfRevolution.Location ( )

inline

Returns an origin point of a rotation axis.

Returns the value specified in the constructor.

Examples

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