Open CASCADE Technology  7.3.1.dev
Public Member Functions
Geom_ToroidalSurface Class Reference

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:
Inheritance graph
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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. More...
 
 Geom_ToroidalSurface (const gp_Torus &T)
 Creates a ToroidalSurface from a non transient Torus from package gp. More...
 
void SetMajorRadius (const Standard_Real MajorRadius)
 Modifies this torus by changing its major radius. Exceptions Standard_ConstructionError if: More...
 
void SetMinorRadius (const Standard_Real MinorRadius)
 Modifies this torus by changing its minor radius. Exceptions Standard_ConstructionError if: More...
 
void SetTorus (const gp_Torus &T)
 Converts the gp_Torus torus T into this torus. More...
 
gp_Torus Torus () const
 Returns the non transient torus with the same geometric properties as <me>. More...
 
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. More...
 
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. More...
 
Standard_Real Area () const
 Computes the aera of the surface. More...
 
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 . More...
 
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. More...
 
Standard_Real MajorRadius () const
 Returns the major radius, or the minor radius, of this torus. More...
 
Standard_Real MinorRadius () const
 Returns the major radius, or the minor radius, of this torus. More...
 
Standard_Real Volume () const
 Computes the volume. More...
 
Standard_Boolean IsUClosed () const override
 Returns True. More...
 
Standard_Boolean IsVClosed () const override
 Returns True. More...
 
Standard_Boolean IsUPeriodic () const override
 Returns True. More...
 
Standard_Boolean IsVPeriodic () const override
 Returns True. More...
 
Handle< Geom_CurveUIso (const Standard_Real U) const override
 Computes the U isoparametric curve. More...
 
Handle< Geom_CurveVIso (const Standard_Real V) const override
 Computes the V isoparametric curve. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
void Transform (const gp_Trsf &T) override
 Applies the transformation T to this torus. More...
 
Handle< Geom_GeometryCopy () const override
 Creates a new object which is a copy of this torus. More...
 
- Public Member Functions inherited from Geom_ElementarySurface
void SetAxis (const gp_Ax1 &A1)
 Changes the main axis (ZAxis) of the elementary surface. More...
 
void SetLocation (const gp_Pnt &Loc)
 Changes the location of the local coordinates system of the surface. More...
 
void SetPosition (const gp_Ax3 &A3)
 Changes the local coordinates system of the surface. More...
 
gp_Ax1 Axis () const
 Returns the main axis of the surface (ZAxis). More...
 
gp_Pnt Location () const
 Returns the location point of the local coordinate system of the surface. More...
 
const gp_Ax3Position () const
 Returns the local coordinates system of the surface. More...
 
virtual void UReverse () override
 Reverses the U parametric direction of the surface. More...
 
virtual void VReverse () override
 Reverses the V parametric direction of the surface. More...
 
GeomAbs_Shape Continuity () const override
 Returns GeomAbs_CN, the global continuity of any elementary surface. More...
 
Standard_Boolean IsCNu (const Standard_Integer N) const override
 Returns True. More...
 
Standard_Boolean IsCNv (const Standard_Integer N) const override
 Returns True. More...
 
- Public Member Functions inherited from Geom_Surface
Handle< Geom_SurfaceUReversed () const
 Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned. More...
 
Handle< Geom_SurfaceVReversed () const
 Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned. More...
 
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>. More...
 
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. More...
 
virtual Standard_Real UPeriod () const
 Returns the period of this surface in the u parametric direction. raises if the surface is not uperiodic. More...
 
virtual Standard_Real VPeriod () const
 Returns the period of this surface in the v parametric direction. raises if the surface is not vperiodic. More...
 
gp_Pnt Value (const Standard_Real U, const Standard_Real V) const
 Computes the point of parameter U on the surface. More...
 
- 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. More...
 
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. More...
 
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). More...
 
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. More...
 
void Scale (const gp_Pnt &P, const Standard_Real S)
 Scales a Geometry. S is the scaling value. More...
 
void Translate (const gp_Vec &V)
 Translates a Geometry. V is the vector of the tanslation. More...
 
void Translate (const gp_Pnt &P1, const gp_Pnt &P2)
 Translates a Geometry from the point P1 to the point P2. More...
 
Handle< Geom_GeometryMirrored (const gp_Pnt &P) const
 
Handle< Geom_GeometryMirrored (const gp_Ax1 &A1) const
 
Handle< Geom_GeometryMirrored (const gp_Ax2 &A2) const
 
Handle< Geom_GeometryRotated (const gp_Ax1 &A1, const Standard_Real Ang) const
 
Handle< Geom_GeometryScaled (const gp_Pnt &P, const Standard_Real S) const
 
Handle< Geom_GeometryTransformed (const gp_Trsf &T) const
 
Handle< Geom_GeometryTranslated (const gp_Vec &V) const
 
Handle< Geom_GeometryTranslated (const gp_Pnt &P1, const gp_Pnt &P2) const
 
- Public Member Functions inherited from Standard_Transient
 Standard_Transient ()
 Empty constructor. More...
 
 Standard_Transient (const Standard_Transient &)
 Copy constructor – does nothing. More...
 
Standard_Transientoperator= (const Standard_Transient &)
 Assignment operator, needed to avoid copying reference counter. More...
 
virtual ~Standard_Transient ()
 Destructor must be virtual. More...
 
virtual void Delete () const
 Memory deallocator for transient classes. More...
 
virtual const opencascade::handle< Standard_Type > & DynamicType () const
 Returns a type descriptor about this object. More...
 
Standard_Boolean IsInstance (const opencascade::handle< Standard_Type > &theType) const
 Returns a true value if this is an instance of Type. More...
 
Standard_Boolean IsInstance (const Standard_CString theTypeName) const
 Returns a true value if this is an instance of TypeName. More...
 
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. More...
 
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. More...
 
Standard_TransientThis () 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. More...
 
Standard_Integer GetRefCount () const
 Get the reference counter of this object. More...
 
void IncrementRefCounter () const
 Increments the reference counter of this object. More...
 
Standard_Integer DecrementRefCounter () const
 Decrements the reference counter of this object; returns the decremented value. More...
 

Additional Inherited Members

- Public Types inherited from Standard_Transient
typedef void base_type
 Returns a type descriptor about this object. More...
 
- Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()
 Returns a type descriptor about this object. More...
 
static const opencascade::handle< Standard_Type > & get_type_descriptor ()
 Returns type descriptor of Standard_Transient class. More...
 
- 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:

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.

◆ 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: