Approximation Depth of Convex Polytopes
By: Egor Bakaev, Florestan Brunck, Amir Yehudayoff
Potential Business Impact:
Makes shapes simpler for computers to understand.
We study approximations of polytopes in the standard model for computing polytopes using Minkowski sums and (convex hulls of) unions. Specifically, we study the ability to approximate a target polytope by polytopes of a given depth. Our main results imply that simplices can only be ``trivially approximated''. On the way, we obtain a characterization of simplices as the only ``outer additive'' convex bodies.
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