Ellipsoid

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LiveGraphics3D, JavaView
The ellipsoids are a 3 parameter family of quadratic algebraic surfaces
that (up to a rigid motion) can be put into the form:

  (x/a)^2 + (y/b)^2 + (z/c)^2 = 1.

The three parameters a,b,c are called the semi-axes of the ellipsoid.
When two of them are,  the ellipsoid is called a spheroid and in 
this case the ellipsoid is a surface of revolution. Of course, when
all three are equal, the ellipsoid is a sphere. 

See QuadraticSurfaces.pdf. Other algebaric surfaces that has cross-sections of conic sections are: ellipsoid, paraboloid, hyperbolic paraboloid, hyperboloid of one sheet, hyperboloid of two sheets

   Ellipsoid Surface Parametric Equations

  x = aa * (cos(u) * sin(v))
  y = bb * (sin(u) * sin(v))
  z = cc * (cos(v))

3DXM-J for Ellipsoid vmm_ellipsoid.jnlp


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