I'll take this:
- I'm sorry to ask such a vague and
generic question, but I need to
write a set of tools that will aid
people in creating 2D and 3D
geometric patterns.
You're not sorry, you are apologizing - there is a difference. The only dumb question is one you should have asked and didn't, see Smith's Law. There are a few tools, you will have to do some work if you want to write them yourself. I suggest Java as it's popularity as a research platform makes it likely good work is available plus is has run-time bumpers that make it useful as a sand-boxing tool for preliminary work.
- Does anyone know any good online
resources that discuss pattern logic
and algorithms (Wikipedia call it
tesselations)?
Looks like you already found it.