Describes a torus. A torus is defined by its major and minor radii, and positioned in space with a coordinate system (a gp_Ax3 object) as follows: More...

#include <Geom_ToroidalSurface.hxx>

Inheritance diagram for Geom_ToroidalSurface:

[legend]

Public Member Functions
	Geom_ToroidalSurface (const gp_Ax3 &A3, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
	A3 is the local coordinate system of the surface. The orientation of increasing V parametric value is defined by the rotation around the main axis (ZAxis) in the trigonometric sense. The parametrization of the surface in the U direction is defined such as the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface. Warnings : It is not forbidden to create a toroidal surface with MajorRadius = MinorRadius = 0.0.

	Geom_ToroidalSurface (const gp_Torus &T)
	Creates a ToroidalSurface from a non transient Torus from package gp.

void	SetMajorRadius (const Standard_Real MajorRadius)
	Modifies this torus by changing its major radius. Exceptions Standard_ConstructionError if:

void	SetMinorRadius (const Standard_Real MinorRadius)
	Modifies this torus by changing its minor radius. Exceptions Standard_ConstructionError if:

void	SetTorus (const gp_Torus &T)
	Converts the gp_Torus torus T into this torus.

gp_Torus	Torus () const
	Returns the non transient torus with the same geometric properties as <me>.

Standard_Real	UReversedParameter (const Standard_Real U) const override
	Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.

Standard_Real	VReversedParameter (const Standard_Real U) const override
	Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.

Standard_Real	Area () const
	Computes the aera of the surface.

void	Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const override
	Returns the parametric bounds U1, U2, V1 and V2 of this torus. For a torus: U1 = V1 = 0 and U2 = V2 = 2*PI .

void	Coefficients (TColStd_Array1OfReal &Coef) const
	Returns the coefficients of the implicit equation of the surface in the absolute cartesian coordinate system : Coef(1) * X*4 + Coef(2) Y*4 + Coef(3) Z*4 + Coef(4) X*3 Y + Coef(5) * X*3 Z + Coef(6) * Y*3 X + Coef(7) * Y*3 Z + Coef(8) * Z*3 X + Coef(9) * Z*3 Y + Coef(10) * X*2 Y*2 + Coef(11) X*2 Z*2 + Coef(12) Y*2 Z*2 + Coef(13) X*3 + Coef(14) Y*3 + Coef(15) Z*3 + Coef(16) X*2 Y + Coef(17) * X*2 Z + Coef(18) * Y*2 X + Coef(19) * Y*2 Z + Coef(20) * Z*2 X + Coef(21) * Z*2 Y + Coef(22) * X*2 + Coef(23) Y*2 + Coef(24) Z*2 + Coef(25) X * Y + Coef(26) * X * Z + Coef(27) * Y * Z + Coef(28) * X + Coef(29) * Y + Coef(30) * Z + Coef(31) = 0.0 Raised if the length of Coef is lower than 31.

Standard_Real	MajorRadius () const
	Returns the major radius, or the minor radius, of this torus.

Standard_Real	MinorRadius () const
	Returns the major radius, or the minor radius, of this torus.

Standard_Real	Volume () const
	Computes the volume.

Standard_Boolean	IsUClosed () const override
	Returns True.

Standard_Boolean	IsVClosed () const override
	Returns True.

Standard_Boolean	IsUPeriodic () const override
	Returns True.

Standard_Boolean	IsVPeriodic () const override
	Returns True.

Handle< Geom_Curve >	UIso (const Standard_Real U) const override
	Computes the U isoparametric curve.

Handle< Geom_Curve >	VIso (const Standard_Real V) const override
	Computes the V isoparametric curve.

void	D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const override
	Computes the point P (U, V) on the surface. P (U, V) = Loc + MinorRadius * Sin (V) * Zdir + (MajorRadius + MinorRadius * Cos(V)) * (cos (U) * XDir + sin (U) * YDir) where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis and ZDir the direction of the ZAxis.

void	D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const override
	Computes the current point and the first derivatives in the directions U and V.

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 override
	Computes the current point, the first and the second derivatives in the directions U and V.

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 override
	Computes the current point, the first,the second and the third derivatives in the directions U and V.

gp_Vec	DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const override
	Computes the derivative of order Nu in the direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.

void	Transform (const gp_Trsf &T) override
	Applies the transformation T to this torus.

Handle< Geom_Geometry >	Copy () const override
	Creates a new object which is a copy of this torus.

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

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.

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

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

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.

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

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.

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.

Protected Attributes inherited from Geom_ElementarySurface
gp_Ax3	pos

Detailed Description

Describes a torus. A torus is defined by its major and minor radii, and positioned in space with a coordinate system (a gp_Ax3 object) as follows:

The origin is the center of the torus.
The surface is obtained by rotating a circle around the "main Direction". This circle has a radius equal to the minor radius, and is located in the plane defined by the origin, "X Direction" and "main Direction". It is centered on the "X Axis", on its positive side, and positioned at a distance from the origin equal to the major radius. This circle is the "reference circle" of the torus.
The plane defined by the origin, the "X Direction" and the "Y Direction" is called the "reference plane" of the torus. This coordinate system is the "local coordinate system" of the torus. The following apply:
Rotation around its "main Axis", in the trigonometric sense given by "X Direction" and "Y Direction", defines the u parametric direction.
The "X Axis" gives the origin for the u parameter.
Rotation around an axis parallel to the "Y Axis" and passing through the center of the "reference circle" gives the v parameter on the "reference circle".
The "X Axis" gives the origin of the v parameter on the "reference circle".
The v parametric direction is oriented by the inverse of the "main Direction", i.e. near 0, as v increases, the Z coordinate decreases. (This implies that the "Y Direction" orients the reference circle only when the local coordinate system is direct.)
The u isoparametric curve is a circle obtained by rotating the "reference circle" of the torus through an angle u about the "main Axis". The parametric equation of the torus is : P(u, v) = O + (R + r*cos(v)) * (cos(u)*XDir + sin(u)*YDir ) + r*sin(v)*ZDir, where:
O, XDir, YDir and ZDir are respectively the origin, the "X Direction", the "Y Direction" and the "Z Direction" of the local coordinate system,
r and R are, respectively, the minor and major radius. The parametric range of the two parameters is:
[ 0, 2.*Pi ] for u
[ 0, 2.*Pi ] for v

Constructor & Destructor Documentation

◆ Geom_ToroidalSurface() [1/2]

Geom_ToroidalSurface::Geom_ToroidalSurface	(	const gp_Ax3 &	A3,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius
	)

A3 is the local coordinate system of the surface. The orientation of increasing V parametric value is defined by the rotation around the main axis (ZAxis) in the trigonometric sense. The parametrization of the surface in the U direction is defined such as the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface. Warnings : It is not forbidden to create a toroidal surface with MajorRadius = MinorRadius = 0.0.

Raised if MinorRadius < 0.0 or if MajorRadius < 0.0

◆ Geom_ToroidalSurface() [2/2]

Geom_ToroidalSurface::Geom_ToroidalSurface ( const gp_Torus & T )

Creates a ToroidalSurface from a non transient Torus from package gp.

Member Function Documentation

◆ Area()

Standard_Real Geom_ToroidalSurface::Area ( ) const

Computes the aera of the surface.

◆ Bounds()

void Geom_ToroidalSurface::Bounds	(	Standard_Real &	U1,
		Standard_Real &	U2,
		Standard_Real &	V1,
		Standard_Real &	V2
	)		const

overridevirtual

Returns the parametric bounds U1, U2, V1 and V2 of this torus. For a torus: U1 = V1 = 0 and U2 = V2 = 2*PI .

Implements Geom_Surface.

◆ Coefficients()

void Geom_ToroidalSurface::Coefficients ( TColStd_Array1OfReal & Coef ) const

Returns the coefficients of the implicit equation of the surface in the absolute cartesian coordinate system : Coef(1) * X**4 + Coef(2) * Y**4 + Coef(3) * Z**4 + Coef(4) * X**3 * Y + Coef(5) * X**3 * Z + Coef(6) * Y**3 * X + Coef(7) * Y**3 * Z + Coef(8) * Z**3 * X + Coef(9) * Z**3 * Y + Coef(10) * X**2 * Y**2 + Coef(11) * X**2 * Z**2 + Coef(12) * Y**2 * Z**2 + Coef(13) * X**3 + Coef(14) * Y**3 + Coef(15) * Z**3 + Coef(16) * X**2 * Y + Coef(17) * X**2 * Z + Coef(18) * Y**2 * X + Coef(19) * Y**2 * Z + Coef(20) * Z**2 * X + Coef(21) * Z**2 * Y + Coef(22) * X**2 + Coef(23) * Y**2 + Coef(24) * Z**2 + Coef(25) * X * Y + Coef(26) * X * Z + Coef(27) * Y * Z + Coef(28) * X + Coef(29) * Y + Coef(30) * Z + Coef(31) = 0.0 Raised if the length of Coef is lower than 31.

◆ Copy()

Handle< Geom_Geometry > Geom_ToroidalSurface::Copy ( ) const

overridevirtual

Creates a new object which is a copy of this torus.

Implements Geom_Geometry.

◆ D0()

void Geom_ToroidalSurface::D0	(	const Standard_Real	U,
		const Standard_Real	V,
		gp_Pnt &	P
	)		const

overridevirtual

Computes the point P (U, V) on the surface. P (U, V) = Loc + MinorRadius * Sin (V) * Zdir + (MajorRadius + MinorRadius * Cos(V)) * (cos (U) * XDir + sin (U) * YDir) where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis and ZDir the direction of the ZAxis.

Implements Geom_Surface.

◆ D1()

void Geom_ToroidalSurface::D1	(	const Standard_Real	U,
		const Standard_Real	V,
		gp_Pnt &	P,
		gp_Vec &	D1U,
		gp_Vec &	D1V
	)		const

overridevirtual

Computes the current point and the first derivatives in the directions U and V.

Implements Geom_Surface.

◆ D2()

void Geom_ToroidalSurface::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

overridevirtual

Computes the current point, the first and the second derivatives in the directions U and V.

Implements Geom_Surface.

◆ D3()

void Geom_ToroidalSurface::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

overridevirtual

Computes the current point, the first,the second and the third derivatives in the directions U and V.

Implements Geom_Surface.

◆ DN()

gp_Vec Geom_ToroidalSurface::DN	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	Nu,
		const Standard_Integer	Nv
	)		const

overridevirtual

Computes the derivative of order Nu in the direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.

Implements Geom_Surface.

◆ DumpJson()

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

overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom_ElementarySurface.

◆ IsUClosed()

Standard_Boolean Geom_ToroidalSurface::IsUClosed ( ) const

overridevirtual

Returns True.

Implements Geom_Surface.

◆ IsUPeriodic()

Standard_Boolean Geom_ToroidalSurface::IsUPeriodic ( ) const

overridevirtual

Returns True.

Implements Geom_Surface.

◆ IsVClosed()

Standard_Boolean Geom_ToroidalSurface::IsVClosed ( ) const

overridevirtual

Returns True.

Implements Geom_Surface.

◆ IsVPeriodic()

Standard_Boolean Geom_ToroidalSurface::IsVPeriodic ( ) const

overridevirtual

Returns True.

Implements Geom_Surface.

◆ MajorRadius()

Standard_Real Geom_ToroidalSurface::MajorRadius ( ) const

Returns the major radius, or the minor radius, of this torus.

◆ MinorRadius()

Standard_Real Geom_ToroidalSurface::MinorRadius ( ) const

Returns the major radius, or the minor radius, of this torus.

◆ SetMajorRadius()

void Geom_ToroidalSurface::SetMajorRadius ( const Standard_Real MajorRadius )

Modifies this torus by changing its major radius. Exceptions Standard_ConstructionError if:

MajorRadius is negative, or
MajorRadius - r is less than or equal to gp::Resolution(), where r is the minor radius of this torus.

◆ SetMinorRadius()

void Geom_ToroidalSurface::SetMinorRadius ( const Standard_Real MinorRadius )

Modifies this torus by changing its minor radius. Exceptions Standard_ConstructionError if:

MinorRadius is negative, or
R - MinorRadius is less than or equal to gp::Resolution(), where R is the major radius of this torus.

◆ SetTorus()

void Geom_ToroidalSurface::SetTorus ( const gp_Torus & T )

Converts the gp_Torus torus T into this torus.

◆ Torus()

gp_Torus Geom_ToroidalSurface::Torus ( ) const

Returns the non transient torus with the same geometric properties as <me>.

◆ Transform()

void Geom_ToroidalSurface::Transform ( const gp_Trsf & T )

overridevirtual

Applies the transformation T to this torus.

Implements Geom_Geometry.

◆ UIso()

Handle< Geom_Curve > Geom_ToroidalSurface::UIso ( const Standard_Real U ) const

overridevirtual

Computes the U isoparametric curve.

For a toroidal surface the UIso curve is a circle. The center of the Uiso circle is at the distance MajorRadius from the location point of the toroidal surface. Warnings : The radius of the circle can be zero if for the surface MinorRadius = 0.0

Implements Geom_Surface.

◆ UReversedParameter()

Standard_Real Geom_ToroidalSurface::UReversedParameter ( const Standard_Real U ) const

overridevirtual

Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.

Implements Geom_ElementarySurface.

◆ VIso()

Handle< Geom_Curve > Geom_ToroidalSurface::VIso ( const Standard_Real V ) const

overridevirtual

Computes the V isoparametric curve.

For a ToroidalSurface the VIso curve is a circle. The axis of the circle is the main axis (ZAxis) of the toroidal surface. Warnings : The radius of the circle can be zero if for the surface MajorRadius = MinorRadius

Implements Geom_Surface.

◆ Volume()

Standard_Real Geom_ToroidalSurface::Volume ( ) const

Computes the volume.

◆ VReversedParameter()

Standard_Real Geom_ToroidalSurface::VReversedParameter ( const Standard_Real U ) const

overridevirtual

Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.

Implements Geom_ElementarySurface.

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

Geom_ToroidalSurface.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geom_ToroidalSurface() [1/2]

◆ Geom_ToroidalSurface() [2/2]

Member Function Documentation

◆ Area()

◆ Bounds()

◆ Coefficients()

◆ Copy()

◆ D0()

◆ D1()

◆ D2()

◆ D3()

◆ DN()

◆ DumpJson()

◆ IsUClosed()

◆ IsUPeriodic()

◆ IsVClosed()

◆ IsVPeriodic()

◆ MajorRadius()

◆ MinorRadius()

◆ SetMajorRadius()

◆ SetMinorRadius()

◆ SetTorus()

◆ Torus()

◆ Transform()

◆ UIso()

◆ UReversedParameter()

◆ VIso()

◆ Volume()

◆ VReversedParameter()