Base class for geometrical surfaces. More...

#include <cadex/Geom/Surface.hxx>

Inheritance diagram for cadex::Geom::Surface:

Public Member Functions
	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::Geometry
static bool	CompareType (const BaseObject &theObject)

Protected Member Functions
	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)

Additional Inherited Members
Public Types inherited from cadex::BaseObject
typedef std::shared_ptr< internal::BaseObjectImpl >	ImplType

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.hxx:35

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.

Member Function Documentation

◆ D0()

void cadex::Geom::Surface::D0	(	double	theU,
		double	theV,
		Point &	theValue ) const

Returns the point theValue of parameter theU, theV on the surface.

Throws exception only for the Geom::OffsetSurface if it is not possible to compute the current point.

◆ D1()

void cadex::Geom::Surface::D1	(	double	theU,
		double	theV,
		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.

Throws exception if the continuity of the surface is not C1.

◆ D2()

void cadex::Geom::Surface::D2	(	double	theU,
		double	theV,
		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.

Throws exception if the continuity of the surface is not C2.

◆ DN()

bool cadex::Geom::Surface::DN	(	double	theParameterU,
		double	theParameterV,
		size_t	theDerivativeOrder,
		Geom::Point &	theValue,
		std::vector< Geom::Vector > &	theD ) const

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	(	double &	theUMin,
		double &	theUMax,
		double &	theVMin,
		double &	theVMax ) const

Returns a definition domain.

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

◆ IsUPeriodic()

bool cadex::Geom::Surface::IsUPeriodic ( ) const

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 ( ) const

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 ( const Transformation & theTransformation )

Applies transformation matrix to this object.

Results depends on the actual surface type.

See also: Transformed().

◆ Transformed()

Surface cadex::Geom::Surface::Transformed ( const Transformation & theTransformation ) const

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 ( ) const

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

See also: UMin(), Domain().

◆ UMin()

double cadex::Geom::Surface::UMin ( ) const

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

See also: UMax(), Domain().

◆ Value()

Point cadex::Geom::Surface::Value	(	double	theParameterU,
		double	theParameterV ) const

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 ( ) const

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

See also: VMin(), Domain().

◆ VMin()

double cadex::Geom::Surface::VMin ( ) const

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

See also: VMax(), Domain().

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members