="Henry Baker" <hbaker1@pipeline.com> Good, but we have a convex surface modelled by a non-convex surface. Can we do better?
Well, how do we define "better"? On the one hand we seem to be talking about approximating surfaces ever more closely, but on the other we seem to be groping to converge on discovering some unstated intuitive definition.
Duality. I note that a triangulated surface in which every vertex has exactly 4 edges coming out (I believe) is dual to a quadrangulated surface where each vertex meets exactly 3 planar quadrilaterals.
Then you just get the dual of the problem: "all" one has to do is find an algorithm for triangulating with a net that's all degree-4. I think if the surface is genus 0 this implies an octahedral "skeleton". Anyway, why wouldn't this work: Make a cubic cage with square mesh sides, put a light inside, insert in the target shape, then take the quads defined by the shadows on the surface? If not close enough, or produces non-planar quads, use (locally) finer mesh. (If the shape is too lumpy or floppy or the like first smoothly deform it to be rounder, project as above, then deform back...)