Open CASCADE Technology 6.6.0
Public Member Functions
Geom_SphericalSurface Class Reference

Describes a sphere.
A sphere is defined by its radius, and is positioned in
space by a coordinate system (a gp_Ax3 object), the
origin of which is the center of the sphere.
This coordinate system is the "local coordinate <br> system" of the sphere. The following apply:
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#include <Geom_SphericalSurface.hxx>

Inheritance diagram for Geom_SphericalSurface:
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Public Member Functions

 Geom_SphericalSurface (const gp_Ax3 &A3, const Standard_Real Radius)
 A3 is the local coordinate system of the surface.
At the creation the parametrization of the surface is defined
such as the normal Vector (N = D1U ^ D1V) is directed away from
the center of the sphere.
The direction of increasing parametric value V is defined by the
rotation around the "YDirection" of A2 in the trigonometric sense
and the orientation of increasing parametric value U is defined
by the rotation around the main direction of A2 in the
trigonometric sense.
Warnings :
It is not forbidden to create a spherical surface with
Radius = 0.0
//! Raised if Radius < 0.0.

 Geom_SphericalSurface (const gp_Sphere &S)
 Creates a SphericalSurface from a non persistent Sphere from
package gp.

void SetRadius (const Standard_Real R)
 Assigns the value R to the radius of this sphere.
Exceptions Standard_ConstructionError if R is less than 0.0.

void SetSphere (const gp_Sphere &S)
 Converts the gp_Sphere S into this sphere.

gp_Sphere Sphere () const
 Returns a non persistent sphere with the same geometric
properties as <me>.

Standard_Real UReversedParameter (const Standard_Real U) const
 Computes the u parameter on the modified
surface, when reversing its u parametric
direction, for any point of u parameter U on this sphere.
In the case of a sphere, these functions returns 2.PI - U.

Standard_Real VReversedParameter (const Standard_Real V) const
 Computes the v parameter on the modified
surface, when reversing its v parametric
direction, for any point of v parameter V on this sphere.
In the case of a sphere, these functions returns -U.

Standard_Real Area () const
 Computes the aera of the spherical 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 sphere.
For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2.

void Coefficients (Standard_Real &A1, Standard_Real &A2, Standard_Real &A3, Standard_Real &B1, Standard_Real &B2, Standard_Real &B3, Standard_Real &C1, Standard_Real &C2, Standard_Real &C3, Standard_Real &D) const
 Returns the coefficients of the implicit equation of the
quadric in the absolute cartesian coordinates system :
These coefficients are normalized.
A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) +
2.(C1.X + C2.Y + C3.Z) + D = 0.0

Standard_Real Radius () const
 Computes the coefficients of the implicit equation of
this quadric in the absolute Cartesian coordinate system:
A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) +
2.(C1.X + C2.Y + C3.Z) + D = 0.0
An implicit normalization is applied (i.e. A1 = A2 = 1.
in the local coordinate system of this sphere).

Standard_Real Volume () const
 Computes the volume of the spherical surface.

Standard_Boolean IsUClosed () const
 Returns True.

Standard_Boolean IsVClosed () const
 Returns False.

Standard_Boolean IsUPeriodic () const
 Returns True.

Standard_Boolean IsVPeriodic () const
 Returns False.

Handle_Geom_Curve UIso (const Standard_Real U) const
 Computes the U isoparametric curve.
The U isoparametric curves of the surface are defined by the
section of the spherical surface with plane obtained by rotation
of the plane (Location, XAxis, ZAxis) around ZAxis. This plane
defines the origin of parametrization u.
For a SphericalSurface the UIso curve is a Circle.
Warnings : The radius of this circle can be zero.

Handle_Geom_Curve VIso (const Standard_Real V) const
 Computes the V isoparametric curve.
The V isoparametric curves of the surface are defined by
the section of the spherical surface with plane parallel to the
plane (Location, XAxis, YAxis). This plane defines the origin of
parametrization V.
Be careful if V is close to PI/2 or 3*PI/2 the radius of the
circle becomes tiny. It is not forbidden in this toolkit to
create circle with radius = 0.0
For a SphericalSurface the VIso curve is a Circle.
Warnings : The radius of this circle can be zero.

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 + Radius * Sin (V) * Zdir +
Radius * 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 sphere.

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


Detailed Description


Constructor & Destructor Documentation

Geom_SphericalSurface::Geom_SphericalSurface ( const gp_Ax3 A3,
const Standard_Real  Radius 
)
Geom_SphericalSurface::Geom_SphericalSurface ( const gp_Sphere S)

Member Function Documentation

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

Implements Geom_Surface.

void Geom_SphericalSurface::Coefficients ( Standard_Real A1,
Standard_Real A2,
Standard_Real A3,
Standard_Real B1,
Standard_Real B2,
Standard_Real B3,
Standard_Real C1,
Standard_Real C2,
Standard_Real C3,
Standard_Real D 
) const
Handle_Geom_Geometry Geom_SphericalSurface::Copy ( ) const [virtual]

Implements Geom_Geometry.

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

Implements Geom_Surface.

void Geom_SphericalSurface::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_SphericalSurface::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_SphericalSurface::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_SphericalSurface::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_SphericalSurface::IsUClosed ( ) const [virtual]

Implements Geom_Surface.

Standard_Boolean Geom_SphericalSurface::IsUPeriodic ( ) const [virtual]

Implements Geom_Surface.

Standard_Boolean Geom_SphericalSurface::IsVClosed ( ) const [virtual]

Implements Geom_Surface.

Standard_Boolean Geom_SphericalSurface::IsVPeriodic ( ) const [virtual]

Implements Geom_Surface.

Standard_Real Geom_SphericalSurface::Radius ( ) const
void Geom_SphericalSurface::SetRadius ( const Standard_Real  R)
void Geom_SphericalSurface::SetSphere ( const gp_Sphere S)
gp_Sphere Geom_SphericalSurface::Sphere ( ) const
void Geom_SphericalSurface::Transform ( const gp_Trsf T) [virtual]

Implements Geom_Geometry.

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

Implements Geom_Surface.

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

Implements Geom_Surface.

Standard_Real Geom_SphericalSurface::Volume ( ) const
Standard_Real Geom_SphericalSurface::VReversedParameter ( const Standard_Real  V) const [virtual]

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