Describes the common behavior of surfaces which have a simple parametric equation in a local coordinate system. The Geom package provides several implementations of concrete elementary surfaces: More...

#include <Geom_ElementarySurface.hxx>

Inheritance diagram for Geom_ElementarySurface:

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Public Member Functions
void	SetAxis (const gp_Ax1 &theA1)
	Changes the main axis (ZAxis) of the elementary surface.

void	SetLocation (const gp_Pnt &theLoc)
	Changes the location of the local coordinates system of the surface.

void	SetPosition (const gp_Ax3 &theAx3)
	Changes the local coordinates system of the surface.

const gp_Ax1 &	Axis () const
	Returns the main axis of the surface (ZAxis).

const gp_Pnt &	Location () const
	Returns the location point of the local coordinate system of the surface.

const gp_Ax3 &	Position () const
	Returns the local coordinates system of the surface.

virtual void	UReverse () override
	Reverses the U parametric direction of the surface.

virtual Standard_Real	UReversedParameter (const Standard_Real U) const override=0
	Return the parameter on the Ureversed surface for the point of parameter U on <me>.

virtual void	VReverse () override
	Reverses the V parametric direction of the surface.

virtual Standard_Real	VReversedParameter (const Standard_Real V) const override=0
	Return the parameter on the Vreversed surface for the point of parameter V on <me>.

GeomAbs_Shape	Continuity () const override
	Returns GeomAbs_CN, the global continuity of any elementary surface.

Standard_Boolean	IsCNu (const Standard_Integer N) const override
	Returns True.

Standard_Boolean	IsCNv (const Standard_Integer N) const override
	Returns True.

virtual void	DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override
	Dumps the content of me into the stream.

Public Member Functions inherited from Geom_Surface
Handle< Geom_Surface >	UReversed () const
	Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.

Handle< Geom_Surface >	VReversed () const
	Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.

virtual void	TransformParameters (Standard_Real &U, Standard_Real &V, const gp_Trsf &T) const
	Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.

virtual gp_GTrsf2d	ParametricTransformation (const gp_Trsf &T) const
	Returns a 2d transformation used to find the new parameters of a point on the transformed surface.

virtual void	Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const =0
	Returns the parametric bounds U1, U2, V1 and V2 of this surface. If the surface is infinite, this function can return a value equal to Precision::Infinite: instead of Standard_Real::LastReal.

virtual Standard_Boolean	IsUClosed () const =0
	Checks whether this surface is closed in the u parametric direction. Returns true if, in the u parametric direction: taking uFirst and uLast as the parametric bounds in the u parametric direction, for each parameter v, the distance between the points P(uFirst, v) and P(uLast, v) is less than or equal to gp::Resolution().

virtual Standard_Boolean	IsVClosed () const =0
	Checks whether this surface is closed in the u parametric direction. Returns true if, in the v parametric direction: taking vFirst and vLast as the parametric bounds in the v parametric direction, for each parameter u, the distance between the points P(u, vFirst) and P(u, vLast) is less than or equal to gp::Resolution().

virtual Standard_Boolean	IsUPeriodic () const =0
	Checks if this surface is periodic in the u parametric direction. Returns true if:

virtual Standard_Real	UPeriod () const
	Returns the period of this surface in the u parametric direction. Raises if the surface is not uperiodic.

virtual Standard_Boolean	IsVPeriodic () const =0
	Checks if this surface is periodic in the v parametric direction. Returns true if:

virtual Standard_Real	VPeriod () const
	Returns the period of this surface in the v parametric direction. raises if the surface is not vperiodic.

virtual Handle< Geom_Curve >	UIso (const Standard_Real U) const =0
	Computes the U isoparametric curve.

virtual Handle< Geom_Curve >	VIso (const Standard_Real V) const =0
	Computes the V isoparametric curve.

virtual void	D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const =0
	Computes the point of parameter U,V on the surface.

virtual void	D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const =0
	Computes the point P and the first derivatives in the directions U and V at this point. Raised if the continuity of the surface is not C1.

virtual void	D2 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const =0
	Computes the point P, the first and the second derivatives in the directions U and V at this point. Raised if the continuity of the surface is not C2.

virtual void	D3 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV, gp_Vec &D3U, gp_Vec &D3V, gp_Vec &D3UUV, gp_Vec &D3UVV) const =0
	Computes the point P, the first,the second and the third derivatives in the directions U and V at this point. Raised if the continuity of the surface is not C2.

virtual gp_Vec	DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const =0
	Computes the derivative of order Nu in the direction U and Nv in the direction V at the point P(U, V).

gp_Pnt	Value (const Standard_Real U, const Standard_Real V) const
	Computes the point of parameter (U, V) on the surface.

Public Member Functions inherited from Geom_Geometry
void	Mirror (const gp_Pnt &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry.

void	Mirror (const gp_Ax1 &A1)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.

void	Mirror (const gp_Ax2 &A2)
	Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection).

void	Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians.

void	Scale (const gp_Pnt &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value.

void	Translate (const gp_Vec &V)
	Translates a Geometry. V is the vector of the translation.

void	Translate (const gp_Pnt &P1, const gp_Pnt &P2)
	Translates a Geometry from the point P1 to the point P2.

virtual void	Transform (const gp_Trsf &T)=0
	Transformation of a geometric object. This tansformation can be a translation, a rotation, a symmetry, a scaling or a complex transformation obtained by combination of the previous elementaries transformations. (see class Transformation of the package Geom).

Handle< Geom_Geometry >	Mirrored (const gp_Pnt &P) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax1 &A1) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax2 &A2) const

Handle< Geom_Geometry >	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle< Geom_Geometry >	Scaled (const gp_Pnt &P, const Standard_Real S) const

Handle< Geom_Geometry >	Transformed (const gp_Trsf &T) const

Handle< Geom_Geometry >	Translated (const gp_Vec &V) const

Handle< Geom_Geometry >	Translated (const gp_Pnt &P1, const gp_Pnt &P2) const

virtual Handle< Geom_Geometry >	Copy () const =0
	Creates a new object which is a copy of this geometric object.

Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor.

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing.

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter.

virtual	~Standard_Transient ()
	Destructor must be virtual.

virtual const opencascade::handle< Standard_Type > &	DynamicType () const
	Returns a type descriptor about this object.

Standard_Boolean	IsInstance (const opencascade::handle< Standard_Type > &theType) const
	Returns a true value if this is an instance of Type.

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName.

Standard_Boolean	IsKind (const opencascade::handle< Standard_Type > &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Boolean	IsKind (const Standard_CString theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Transient *	This () const
	Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero.

Standard_Integer	GetRefCount () const noexcept
	Get the reference counter of this object.

void	IncrementRefCounter () noexcept
	Increments the reference counter of this object.

Standard_Integer	DecrementRefCounter () noexcept
	Decrements the reference counter of this object; returns the decremented value.

virtual void	Delete () const
	Memory deallocator for transient classes.

Protected Attributes
gp_Ax3	pos

Additional Inherited Members
Public Types inherited from Standard_Transient
typedef void	base_type
	Returns a type descriptor about this object.

Static Public Member Functions inherited from Standard_Transient
static constexpr const char *	get_type_name ()
	Returns a type descriptor about this object.

static const opencascade::handle< Standard_Type > &	get_type_descriptor ()
	Returns type descriptor of Standard_Transient class.

Detailed Description

Describes the common behavior of surfaces which have a simple parametric equation in a local coordinate system. The Geom package provides several implementations of concrete elementary surfaces:

the plane, and
four simple surfaces of revolution: the cylinder, the cone, the sphere and the torus. An elementary surface inherits the common behavior of Geom_Surface surfaces. Furthermore, it is located in 3D space by a coordinate system (a gp_Ax3 object) which is also its local coordinate system. Any elementary surface is oriented, i.e. the normal vector is always defined, and gives the same orientation to the surface, at any point on the surface. In topology this property is referred to as the "outside region of the surface". This orientation is related to the two parametric directions of the surface. Rotation of a surface around the "main Axis" of its coordinate system, in the trigonometric sense given by the "X Direction" and the "Y Direction" of the coordinate system, defines the u parametric direction of that elementary surface of revolution. This is the default construction mode. It is also possible, however, to change the orientation of a surface by reversing one of the two parametric directions: use the UReverse or VReverse functions to change the orientation of the normal at any point on the surface. Warning The local coordinate system of an elementary surface is not necessarily direct:
if it is direct, the trigonometric sense defined by its "main Direction" is the same as the trigonometric sense defined by its two vectors "X Direction" and "Y Direction": "main Direction" = "X Direction" ^ "Y Direction"
if it is indirect, the two definitions of trigonometric sense are opposite: "main Direction" = - "X Direction" ^ "Y Direction"

Member Function Documentation

◆ Axis()

const gp_Ax1 & Geom_ElementarySurface::Axis ( ) const

inline

Returns the main axis of the surface (ZAxis).

◆ Continuity()

GeomAbs_Shape Geom_ElementarySurface::Continuity ( ) const

overridevirtual

Returns GeomAbs_CN, the global continuity of any elementary surface.

Implements Geom_Surface.

◆ DumpJson()

virtual void Geom_ElementarySurface::DumpJson	(	Standard_OStream &	theOStream,
		Standard_Integer	theDepth = `-1`
	)		const

overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Surface.

Reimplemented in Geom_ConicalSurface, Geom_CylindricalSurface, Geom_Plane, Geom_SphericalSurface, and Geom_ToroidalSurface.

◆ IsCNu()

Standard_Boolean Geom_ElementarySurface::IsCNu ( const Standard_Integer N ) const

overridevirtual

Returns True.

Implements Geom_Surface.

◆ IsCNv()

Standard_Boolean Geom_ElementarySurface::IsCNv ( const Standard_Integer N ) const

overridevirtual

Returns True.

Implements Geom_Surface.

◆ Location()

const gp_Pnt & Geom_ElementarySurface::Location ( ) const

inline

Returns the location point of the local coordinate system of the surface.

◆ Position()

const gp_Ax3 & Geom_ElementarySurface::Position ( ) const

inline

Returns the local coordinates system of the surface.

◆ SetAxis()

void Geom_ElementarySurface::SetAxis ( const gp_Ax1 & theA1 )

inline

Changes the main axis (ZAxis) of the elementary surface.

Raised if the direction of A1 is parallel to the XAxis of the coordinate system of the surface.

◆ SetLocation()

void Geom_ElementarySurface::SetLocation ( const gp_Pnt & theLoc )

inline

Changes the location of the local coordinates system of the surface.

◆ SetPosition()

void Geom_ElementarySurface::SetPosition ( const gp_Ax3 & theAx3 )

inline

Changes the local coordinates system of the surface.

◆ UReverse()

virtual void Geom_ElementarySurface::UReverse ( )

overridevirtual

Reverses the U parametric direction of the surface.

Implements Geom_Surface.

Reimplemented in Geom_Plane.

◆ UReversedParameter()

virtual Standard_Real Geom_ElementarySurface::UReversedParameter ( const Standard_Real U ) const

overridepure virtual

Return the parameter on the Ureversed surface for the point of parameter U on <me>.

me->UReversed()->Value(me->UReversedParameter(U),V) is the same point as me->Value(U,V)

Implements Geom_Surface.

Implemented in Geom_ConicalSurface, Geom_CylindricalSurface, Geom_Plane, Geom_SphericalSurface, and Geom_ToroidalSurface.

◆ VReverse()

virtual void Geom_ElementarySurface::VReverse ( )

overridevirtual

Reverses the V parametric direction of the surface.

Implements Geom_Surface.

Reimplemented in Geom_ConicalSurface, and Geom_Plane.

◆ VReversedParameter()

virtual Standard_Real Geom_ElementarySurface::VReversedParameter ( const Standard_Real V ) const

overridepure virtual

Return the parameter on the Vreversed surface for the point of parameter V on <me>.

me->VReversed()->Value(U,me->VReversedParameter(V)) is the same point as me->Value(U,V)

Implements Geom_Surface.

Implemented in Geom_ToroidalSurface, Geom_ConicalSurface, Geom_CylindricalSurface, Geom_Plane, and Geom_SphericalSurface.

Field Documentation

◆ pos

gp_Ax3 Geom_ElementarySurface::pos

protected

The documentation for this class was generated from the following file:

Geom_ElementarySurface.hxx

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Axis()

◆ Continuity()

◆ DumpJson()

◆ IsCNu()

◆ IsCNv()

◆ Location()

◆ Position()

◆ SetAxis()

◆ SetLocation()

◆ SetPosition()

◆ UReverse()

◆ UReversedParameter()

◆ VReverse()

◆ VReversedParameter()

Field Documentation

◆ pos