Well, I was able to get Mathematica to plot a half-ellipsoid, which is what
I am ultimately looking for. However, Mathematica's high-level functions do
all the work, so I still haven't gotten any insight into the actual formula
generating the ellipse.
Here's a screen shot of the Mathematica notebook, with slider adjustments
for the axes..
http://bit.ly/17Z2Ayo

I am able to rotate the view cube in real-time using my mouse, as well as
change the length of all the axes using the sliders. So I must have a
reasonable GPU in my Dell/Intel laptop. I think that Mathematica lets me
publish a "Live" version of this notebook on the web, with active sliders
and mouse view rotation, but I haven't figured out how to do that as yet.



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