Open CASCADE Technology 6.6.0
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:
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#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
Raised if MinorRadius < 0.0 or if MajorRadius < 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
 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
 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
 Returns the parametric bounds U1, U2, V1 and V2 of this torus.
For a torus: U1 = V1 = 0 and V1 = 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
 Returns True.

Standard_Boolean IsVClosed () const
 Returns True.

Standard_Boolean IsUPeriodic () const
 Returns True.

Standard_Boolean IsVPeriodic () const
 Returns True.

Handle_Geom_Curve UIso (const Standard_Real U) const
 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

Handle_Geom_Curve VIso (const Standard_Real V) const
 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

void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const
 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
 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
 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
 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
 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)
 Applies the transformation T to this torus.

Handle_Geom_Geometry Copy () const
 Creates a new object which is a copy of this torus.


Detailed Description


Constructor & Destructor Documentation

Geom_ToroidalSurface::Geom_ToroidalSurface ( const gp_Ax3 A3,
const Standard_Real  MajorRadius,
const Standard_Real  MinorRadius 
)
Geom_ToroidalSurface::Geom_ToroidalSurface ( const gp_Torus T)

Member Function Documentation

Standard_Real Geom_ToroidalSurface::Area ( ) const
void Geom_ToroidalSurface::Bounds ( Standard_Real U1,
Standard_Real U2,
Standard_Real V1,
Standard_Real V2 
) const [virtual]

Implements Geom_Surface.

void Geom_ToroidalSurface::Coefficients ( TColStd_Array1OfReal Coef) const
Handle_Geom_Geometry Geom_ToroidalSurface::Copy ( ) const [virtual]

Implements Geom_Geometry.

void Geom_ToroidalSurface::D0 ( const Standard_Real  U,
const Standard_Real  V,
gp_Pnt P 
) const [virtual]

Implements Geom_Surface.

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

Implements Geom_Surface.

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 [virtual]

Implements Geom_Surface.

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 [virtual]

Implements Geom_Surface.

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

Implements Geom_Surface.

Standard_Boolean Geom_ToroidalSurface::IsUClosed ( ) const [virtual]

Implements Geom_Surface.

Standard_Boolean Geom_ToroidalSurface::IsUPeriodic ( ) const [virtual]

Implements Geom_Surface.

Standard_Boolean Geom_ToroidalSurface::IsVClosed ( ) const [virtual]

Implements Geom_Surface.

Standard_Boolean Geom_ToroidalSurface::IsVPeriodic ( ) const [virtual]

Implements Geom_Surface.

Standard_Real Geom_ToroidalSurface::MajorRadius ( ) const
Standard_Real Geom_ToroidalSurface::MinorRadius ( ) const
void Geom_ToroidalSurface::SetMajorRadius ( const Standard_Real  MajorRadius)
  • MajorRadius is negative, or
  • MajorRadius - r is less than or equal to
    gp::Resolution(), where r is the minor radius of this torus.
void Geom_ToroidalSurface::SetMinorRadius ( const Standard_Real  MinorRadius)
  • MinorRadius is negative, or
  • R - MinorRadius is less than or equal to
    gp::Resolution(), where R is the major radius of this torus.
void Geom_ToroidalSurface::SetTorus ( const gp_Torus T)
gp_Torus Geom_ToroidalSurface::Torus ( ) const
void Geom_ToroidalSurface::Transform ( const gp_Trsf T) [virtual]

Implements Geom_Geometry.

Handle_Geom_Curve Geom_ToroidalSurface::UIso ( const Standard_Real  U) const [virtual]

Implements Geom_Surface.

Standard_Real Geom_ToroidalSurface::UReversedParameter ( const Standard_Real  U) const [virtual]
Handle_Geom_Curve Geom_ToroidalSurface::VIso ( const Standard_Real  V) const [virtual]

Implements Geom_Surface.

Standard_Real Geom_ToroidalSurface::Volume ( ) const
Standard_Real Geom_ToroidalSurface::VReversedParameter ( const Standard_Real  U) const [virtual]

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