Base class for geometrical surfaces. More...

Inheritance diagram for cadex.Geom.Surface:

Public Member Functions
	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 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

Base class for geometrical surfaces.

Surfaces in 3D space are used to represent boundaries of a body (e.g. solid or sheet body). Each face must refer to a surface.

Types

Refer to Surface Types for the list of supported surface types. Type() returns a surface type as enumeration value which can be used to downcast to a respective subclass type, for instance:

Surface aSurface = ...;
if (aSurface.Type() == Geom::ShapeType::Cylinder) {
    const CylindricalSurface& aCylSurf = static_cast<const CylindricalSurface&> (aSurface);
    double aRadius = aCylSurf.Radius();
    ...
}

Parametric Definition

Surface is defined using parametric definition as \(\mathbf{S}(u,v)\) where \(\mathbf{S}\) is a 3D radius-vector \((x,y,z)\) and \((u, v)\) are parameters from a definition domain \([u_{min}, u_{max}]\times[v_{min}, v_{max}]\).

UMin(), UMax() and VMin(), VMax(), and Domain() return parametric definition range. Parametric range can be bounded (e.g. \([0, 1]\times[0, 1]\) for Bezier surface), unbounded (e.g. \((-\infty, +\infty)\times(-\infty, +\infty)\) for a plane), or semi-unbounded (e.g. \([0, 2\pi]\times(-\infty, +\infty)\) for cylindrical surface).

Evaluation

At any parameter u and v within a definition domain, the surface can be evaluated as follows:

Value() and D0() return a 3D point;
D1(), D2() and DN() return a derivative of a respective order;
Curvature() returns a curvature;
Normal() returns a normal to the surface (i.e. perpendicular to a tangential plane).

The following example demonstrates computation of a point on a sphere at parameters \(u=\frac{\pi}{4}\), \(v=\frac{\pi}{6}\):

CylindricalSurface aSphere = ...;

Point aPoint = aSphere.Value (M_PI / 4, M_PI / 6);

cadex.Geom.Point

Defines a 3D point.

Definition Point.cs:17

If the surface is periodic in U and/or V (IsUPeriodic() and/or IsVPeriodic() return true) then the surface can be evaluated at any parameter U and/or V, otherwise behavior is undefined (e.g. an exception can be thrown or a weird value can be returned).

Continuity

Continuity() returns continuity (C0, C1, C2, CN) of the surface, minimum of U- and V- continuities, where C0 indicates continuity of the surface only, C1 - of its first derivative and so on.

Transformation

The surface can be modified using the following operations:

translation (Translate() and Translated());
rotation (Rotate() and Rotated());
mirroring (Mirror() and Mirrored());
scaling (Scale() and Scaled());
arbitrary transformation using 3x4 matrix (Transform() and Transformed()).

Warning: As the surface data is shared via internal pointer modification of the surface may affect other users of the surface (e.g. a face referring to it). So you might want to use method returning a modified copy of the surface (such as Transformed()).

See also: Surfaces, Curve, ModelData.Face.

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

Member Function Documentation

◆ Dispose()

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

inlineprotectedvirtual

Reimplemented from cadex.Geom.Geometry.

◆ DN()

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

inline

Returns true if calculation was passed succsesfully, the returned vectors gives the value of the derivative for the order of derivation theDerivativeOrder. Otherwise returns false. Throws exception if the continuity of the surface is not CN.

Parameters:

theDerivativeOrder must belong to range [0, 3].
theD should have enough size to store 2 for D1(), 5 for D2() or 9 for D3() derivatives.

◆ Domain()

void cadex.Geom.Surface.Domain	(	out double	theUMin,
		out double	theUMax,
		out double	theVMin,
		out double	theVMax )

inline

Returns a definition domain.

See also: UMin(), UMax(), VMin(), VMax().

◆ IsUPeriodic()

bool cadex.Geom.Surface.IsUPeriodic ( )

inline

Returns true if the surface is periodic in U direction.

Examples include sphere, torus or a surface of revolution

◆ IsVPeriodic()

bool cadex.Geom.Surface.IsVPeriodic ( )

inline

Returns true if the surface is periodic in V direction.

Examples include torus or a V-periodic B-Spline.

◆ Transform()

void cadex.Geom.Surface.Transform ( cadex.Geom.Transformation theTransformation )

inline

Applies transformation matrix to this object.

Results depends on the actual surface type.

See also: Transformed().

◆ Transformed()

cadex.Geom.Surface cadex.Geom.Surface.Transformed ( cadex.Geom.Transformation theTransformation )

inline

Returns a copy this object after applying transformation.

The contents of this object is not modified.

See also: Transform().

◆ UMax()

double cadex.Geom.Surface.UMax ( )

inline

Returns a maximum parameter of a definition domain in U direction.

See also: UMin(), Domain().

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

◆ UMin()

double cadex.Geom.Surface.UMin ( )

inline

Returns a minimum parameter of a definition domain in U direction.

See also: UMax(), Domain().

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

◆ Value()

cadex.Geom.Point cadex.Geom.Surface.Value	(	double	theParameterU,
		double	theParameterV )

inline

Evaluates a point on the surface.

theParameterU must be within [UMin(), UMax()] if the surface is not U-periodic. theParameterV must be within [VMin(), VMax()] if the surface is not V-periodic.

◆ VMax()

double cadex.Geom.Surface.VMax ( )

inline

Returns a maximum parameter of a definition domain in V direction.

See also: VMin(), Domain().

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

◆ VMin()

double cadex.Geom.Surface.VMin ( )

inline

Returns a minimum parameter of a definition domain in V direction.

See also: VMax(), Domain().

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Types

Parametric Definition

Evaluation

Continuity

Transformation

Member Function Documentation

◆ Dispose()

◆ DN()

◆ Domain()

◆ IsUPeriodic()

◆ IsVPeriodic()

◆ Transform()

◆ Transformed()

◆ UMax()

◆ UMin()

◆ Value()

◆ VMax()

◆ VMin()