Hi all,

I'm writing up my lecture notes for a differential geometry class and attempting
to render some of the more subtle graphics in PoVRay.

Here are two samples:

http://dl.dropbox.com/u/46424505/poinc_modelh.png

http://dl.dropbox.com/u/46424505/octo.png

The first example illustrates an issue.  As you can see in the picture, there is
a hyperboloid, and I'm attempting to draw some curves on the hyperboloid.

I'm wondering what are some more effective ways to do this.  One way to go would
be to make the curve on the surface just another hyperboloid, but I could crop
it by some planes to make it a thin-enough strip that it would approximate a
curve.  But ideally I want the curve to have a thickness.  In the linked file
poinc_modelh.png, the curve is a rather explicit parametric surface.  But with
radiosity, it can take my 8-core system 6 days to render an image like the one
above.  I'd like the render-time to be faster, just so tweaking the image
doesn't take so long. Even with low quality the render time is still fairly slow
with the parametric surface.

One option would be to make the curve out a sphere-cylinder-sphere chain, with
several hundred spheres.  This is pretty fast, but is there a tidy way to
automate the generation of that in PoV script?  When I was younger I'd just
write a C++ script to generate the PoV script but I'm hoping there's a tidy way
to do this in PoVRay itself.  Of course, a problem with this is I'd have to
appropriately crop the spheres if I wanted the effect to be seamless (and the
curves partially transparent).

Are there any other good options I should be thinking of?

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