Hello gordonp,
Textures are applied to surfaces, so maybe the problem is with the underlying surface integrity. What you describe reminds me of an STL tessilated (faceted) model. I'm not saying that's the problem but I would take a close look at the surfaces you are applying the texture to. A visual inspection using different types of surface contour plots should help, also try applying different different isoline values (contour lines) to the surfaces.
I've seen many surfaces that look otherwise perfectly perfect but then totally twisted and ugly when you look at the UV space of the same surfaces.
Good luck!
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