Open CASCADE Technology
6.5.4
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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>
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. |
Geom_ToroidalSurface::Geom_ToroidalSurface | ( | const gp_Ax3 & | A3, |
const Standard_Real | MajorRadius, | ||
const Standard_Real | MinorRadius | ||
) |
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.
void Geom_ToroidalSurface::SetMajorRadius | ( | const Standard_Real | MajorRadius | ) |
void Geom_ToroidalSurface::SetMinorRadius | ( | const Standard_Real | MinorRadius | ) |
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] |
Implements Geom_ElementarySurface.
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] |
Implements Geom_ElementarySurface.