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I think I've seen that... It's because the polygons are occupying the same space?
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Indeed, but as I said, I moved the polygons so there was a 1mm gap (or even more), but the Z-buffer, which decides which objects are in front of or behind each other in the render had trouble with it, most likely because of the way the smoothing algorithm works. The only way I could have overcome this problem would have been to either leave the stencils on the mesh, which would have caused all sorts of problems, or move the polygons for the decals about 5mm out, which would leave them noticeably "floating" over the mesh, and as you can see the stencils were blotching out unevenly, so there was something not aligning properly.
And it's actually a lot easier. I'd originally dismissed UV mapping because text and graphics will look distorted on a curved surface, and I don't know of a way to straighten out the curves properly and precisely, which I thought would have meant days of playing with warping options in Photoshop. I ended up just using the bend and rotate tools to try to straighten out the mesh, and I couldn't get it straight but it's close enough, and I can't tell the difference, and really you could never perfectly match the curve using the stencil tool anyway.
And now, if I notice something's off proportionately, I can just fiddle with it in photoshop and it's much faster because I don't have to go through the stencilling process again. To tell the truth, stencilling was a nightmare; it's simple to do in principle, but it takes ages to get it all bent and rotated to the right angle, and then I had to keep closing and re-opening modeler because there's a memory hole and if you do to many booleans operations it says "internal buffers too small". Then I had to worry about offsetting the polys, it was stupid.
And it looks fine:
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