Wasn't it David Cameron who wrote:
>Hi All,
>Do any of you know how to produce an elliptical torus?
>
>Given the general torus syntax is:
>torus { major_radius, minor_radius }
>
>How could I define:
>#macro elliptical_torus( x_major_radius, z_major_radius, minor_radius)
>  // which code goes here ?
>#end

You could do it as a parametric. Just replace the two instances of
major_radius in the usual parametric equations for the torus by
x_major_radius and z_major_radius.

#macro elliptical_torus( x_major_radius, z_major_radius, minor_radius)
  #declare Fx = function(u,v){cos(u)*(x_major_radius+minor_radius*cos(v))}
  #declare Fz = function(u,v){sin(u)*(z_major_radius+minor_radius*cos(v))}
  #declare Fy = function(u,v){minor_radius*sin(v)}

  #declare C = <x_major_radius+minor_radius, minor_radius,
         z_major_radius+minor_radius>*1.01;

  parametric {
    function {Fx(u,v)}
    function {Fy(u,v)}
    function {Fz(u,v)}
      <0,-2>,<2*pi,2*pi>
    contained_by{ box {-C,C}}
    precompute 18, x,y,z
}
#end

However, that's a bit slow, so I'd recommend using Ingo Janssen's param.inc
to approximate it. It runs about 20 times faster and the results are
virtually indistinguishable.

#macro elliptical_torus( x_major_radius, z_major_radius, minor_radius)
  #declare Fx = function(u,v){cos(u)*(x_major_radius+minor_radius*cos(v))}
  #declare Fz = function(u,v){sin(u)*(z_major_radius+minor_radius*cos(v))}
  #declare Fy = function(u,v){minor_radius*sin(v)}

  #include "param.inc"

  object{
    Parametric(
       Fx, Fy, Fz,
       <0,0>,<2*pi,2*pi>,
       100,40,""
    )
  }
#end

If you're not familiar with param.inc, see 
<http://www.econym.demon.co.uk/isotut/param.htm>

-- 
Mike Williams
Gentleman of Leisure

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