"Shane" <shnkeply(at)gmail.com> wrote:
> I am a mathematician and I have been using povray for making pictures of 3D
> surfaces which are fairly complicated. The results are much more beautiful than
> what I can make using matlab or similar software but I feel like I am still
> missing a great deal of potential.

Welcome!  :)
I'm glad you're here - I dabble in your field as often as I'm able.
Planetary orbital mechanics, 1 and 2D Fourier transforms, parametrics,
isosurfaces, polynomials .....

> I typically choose things like lighting, camera angles, colors, refraction, etc
> etc almost arbitrarily. I lack the artistic training to have a good
> understanding of the choices involved and I typically just change these choices
> almost randomly to try and improve the picture. The resulting pictures are nice,
> but still lacking quality and I want to learn how to get better.

I'd start off with 3-point lighting
https://en.wikipedia.org/wiki/Three-point_lighting
http://warp.povusers.org/povtips/

Use a texture, even if it's a small and simple bumps or granite or agate.  I try
to keep my mathematical manifolds fairly matte, but I often use a finish
{specular 0.4} to give a slightly shiny plastic look.

> In this sample, the background sky, lighting, and essentially every choice other
> than camera placement is pretty much arbitrary. I don't have a great
> understanding of how to use transmittance, reflection, lighting, etc to make
> shadows and produce a nice texture. I can change these things and I get
> different pictures, but I don't know how to make "intentional" changes to create
> specific effects.

Check out
http://www.f-lohmueller.de/pov_tut/pov__eng.htm
it's an invaluable resource.
He's got great tutorials on realistic skies, water, media, etc.

Also - there are plenty of demo scenes in the subdirectories, and very useful
basic scene snippets in the drop-down Insert menu.

> The images themselves represent objects with some mathematical relevance (called
> manifolds for those interested). The green/red surfaces are generated as unions
> of triangles (about 500,000 in this picture). The blue curves are generated as
> unions of cylinders. There is probably a better way to use povray to generate
> both types of object but this is likely the least of my issues.

You absolutely have to check out Paul Nylander's page(s)
https://nylander.wordpress.com/2008/08/25/cross-section-of-the-quintic-calabi-yau-manifold/

He'll have lots of things you're interested in, and if you download the code
there, you'll see an excellent method of automating the triangular "mesh", which
vastly speeds up isosurface rendering.

And Mike Williams' isosurface tutorial.

Make sure you use an appropriate max_gradient, accuracy, and precompute.

> Just a couple examples of things I would like to learn how to improve:
>
> 1. There is a great deal of fine detail here. Both the red and green surfaces
> actually fold over themselves very sharply (like folding a piece of paper in
> half) many times. However, I can't see this detail because the surfaces lack
> texture or proper shadows.

I often draw a "line" - a showdowless cylinder from the light source to my
object or the origin, to see where it's shining from.

Put a thin box behind your object to give you some more visual cue from the
shadow it casts.

> 2. In several places the reflection seems to make a the picture completely
> white. Sometimes it looks cool but in other places it just looks washed out and
> "hazy". I think this is because I don't know how to properly choose and place
> lighting objects.
>
> If anyone has any advice or resources for me to read I would be very
> appreciative. I have read through much of the povray tutorials which covers the
> kinds of functionality included in povray, but obviously its up to me to decide
> how to use it and that is what I'm having trouble with. Thanks so much.

More to come - at work, and have to get back to it.   :|

Use the SEARCH at the top of the page, scroll through the image digest, and take
a tour back through the scene file section(s)  there are LOTS of great ideas
people have come up with --- too many to keep track of.

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