Source: https://dev.opencascade.org/doc/refman/html/class_geom___spherical_surface.html
Timestamp: 2019-04-23 22:13:28+00:00

Document:
Rotation around its "main Axis", in the trigonometric sense given by the "X Direction" and the "Y Direction", defines the u parametric direction.
Its "X Axis" gives the origin for the u parameter.
The "reference meridian" of the sphere is a half-circle, of radius equal to the radius of the sphere. It is located in the plane defined by the origin, "X Direction" and "main Direction", centered on the origin, and positioned on the positive side of the "X Axis".
Rotation around the "Y Axis" gives the v parameter on the reference meridian.
The "X Axis" gives the origin of the v parameter on the reference meridian.
[ - Pi/2., + Pi/2. ] for v.
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.
Creates a SphericalSurface from a non persistent Sphere from package gp.
Computes the aera of the spherical surface.
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.
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.
Creates a new object which is a copy of this sphere.
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.
Computes the current point and the first derivatives in the directions U and V.
Computes the current point, the first and the second derivatives in the directions U and V.
Computes the current point, the first,the second and the third derivatives in the directions U and V.
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.
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).
Assigns the value R to the radius of this sphere. Exceptions Standard_ConstructionError if R is less than 0.0.
Converts the gp_Sphere S into this sphere.
Returns a non persistent sphere with the same geometric properties as <me>.
Applies the transformation T to this sphere.
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.
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.
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.
Computes the volume of the spherical surface.
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.

References: v.

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