Open CASCADE Technology
6.5.4
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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>
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. |
Geom_SphericalSurface::Geom_SphericalSurface | ( | const gp_Ax3 & | A3, |
const Standard_Real | Radius | ||
) |
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 |
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] |
Implements Geom_ElementarySurface.
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] |
Implements Geom_ElementarySurface.