| | 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:
- Rotation around its "main Axis", in the trigonometric
sense given by the "X Direction" and the "Y <br>
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.
- The v parametric direction is oriented by the "main <br>
Direction", i.e. when v increases, the Z coordinate
increases. (This implies that the "Y Direction"
orients the reference meridian only when the local
coordinate system is indirect.)
- The u isoparametric curve is a half-circle obtained
by rotating the reference meridian of the sphere
through an angle u around the "main Axis", in the
trigonometric sense defined by the "X Direction"
and the "Y Direction".
The parametric equation of the sphere is:
P(u,v) = O + R*cos(v)*(cos(u)*XDir + sin(u)*YDir)+R*sin(v)*ZDir
where:
- O, XDir, YDir and ZDir are respectively the
origin, the "X Direction", the "Y Direction" and the "Z <br>
Direction" of its local coordinate system, and
- R is the radius of the sphere.
The parametric range of the two parameters is:
- [ 0, 2.*Pi ] for u, and
- [ - Pi/2., + Pi/2. ] for v.
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1.6.3