> Why try so hard to avoid using a triangle mesh? Any method you find will
> probably be much more CPU hungry and have artifacts that are harder to
> get rid of than faceting. The reason originally given for "curved smooth
> triangles" was the dark artifact seen when the normal points away from
> the camera, but there are other possible ways to fix that with flat
> smooth triangles.
> It seems like the best solution for curved triangles would be a cubic
> surface tesselated into triangles, something like a triangular bezier
> patch. It could even be tesselated on the fly to reduce memory
> requirements.
>
> Maybe subdivision surfaces would be a better solution.

I think another reason was that if not enough triangles are used, in
profile, the shape has a jagged edge rather than a smooth one.  Even though
the shading is smooth, the outline still follows the polygons.

-tgq

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