What's acceptable as far as tri's on my low poly? Should I aim for mostly quads and keep tri's hidden, or should I be super liberal with my tri's to keep my polycount low? What are the benefits of using all quads or quads and tri's other than taking the mesh to zbrush/mudbox?
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And when you talk about polycount we almost always mean triangles not quads.
So I always triangulate my low rez model. At least I do now. Use triangles as much as you want, it'll be triangulated in engine. So long as it can still deform correctly you'll be fine.
A) Your model is very low poly (something like a sign which is a Hexagon, or a Mobile MMO.
You need to correct shading errors because your engine doesn't triangulate a certain mesh correctly.
C) Your normal map bakes are giving you issues.
D) Your Specular is warped on the shading level.
Manually triangulating your model, while laborious, simply isn't worth it in the end. Engine nowadays already triangulate your models pretty well, and the few cases in which they don't usually are associated with N-gons or weird flat shapes that might be too big and relaxed, without even division for the mesh to correctly connect the vertices for a tri.
A model like a character, unless very low-poly and needs manual care, will never require manual triangulation, it's simply too much time spend on nothing at the end of the day. The payoff is too little.
Same with rocks and temples, on the other hand, there is a good chance, large walls say in a gas-station will little extrudes here and there might need triangulation...again, MIGHT need.
Also, while polycounts don't bottleneck games, Vertices do. It doesn't matter if your model is a tri or quads, vertices will add to performance, not to mention UV splits as well smoothing groups.
Optimization wise, I don't understand why Tri's or Quads would be any different in optimization. A Quad based spiral loop on your characters arm is just as bad, if not, worse then a loop that ends with a triangle as a cap-off.
I honestly can recommend one thing, go through Polycounts Wiki, this will answer alot of your questions.