Um, Roland -- just curious -- have you seen
https://en.wikipedia.org/wiki/Bezier_triangle or
https://en.wikipedia.org/wiki/Bezier_surface ? It's a surface type with
pretty well-known implementation.

I'm just another user, but I agree too that Bezier
triangles/patches/surfaces would enable a modeling workflow not really
possible with NURBS or "flat" polygons.

Theoretically speaking, perhaps it can be implemented as a mesh modifier
that subdivides and deforms polygons based on specific properties of mesh
edges? (to not add a new kind of object data)
I'm not sure if there is a general solution for n-sided bezier polygon, but
at least triangles and quads can probably just use Catmull-Clark
subdivision scheme.
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