Whereupon Tor Olav Kristensen made a whopping follow-up post:

http://news.povray.org/povray.binaries.images/message/%3Cweb.5b5e768edce0719a79917fa00%40news.povray.org%3E/#%3Cweb.5b5
e768edce0719a79917fa00%40news.povray.org%3E


Especially interesting, with regard to the f_r function and fn_Gradient macro.
That ties in to the calculation of normals and using the object pattern in an
isosurface.


I suppose I'll also do a little light reading about the Laplacian operator and
the elliptic operator, since they are directly related.  ;)

With regard to the elliptical torus, I'm not exactly sure what throws off the 3D
shape.  With the standard circular torus, we just use R minus the length of the
x,z vector to get one side of the right triangle to evaluate the minor radius'
circle, and y becomes the other.

Generalizing this to an ellipse really seems like it should work without issue,
but obviously it doesn't.

It seems that any circle "drawn" ought to be in the plane bisecting the angle
formed by the two foci and the point on the ellipse.

It also seems like there's trend where the torus extends outward too much in the
direction of the longest semi-axis, and not enough in the shortest semi-axis.
Which leads me to intuitively believe that there ought to be a way to use a and
b to compensate for how the torus gets thrown off.

And that's all I have for now.

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