Are there any theoretical results (including theorems, algorithms, etc) on representing a non-convex set as the union of a finite number of convex sets?
2026-03-29 12:11:16.1774786276
Conditions when a non-convex set can be represented as the union of a finite number of convex sets
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I think the general case is hopeless: I don't expect a "typical" set, even an open, connected one, to be representable as the finite union of convex sets.
If you are OK with approximating your set, you can try to compute an approximating triangulation; NB that triangulation in high dimensions is itself a nontrivial problem. Algorithms exists for computing approximate convex decompositions in two and three dimensions, which try to minimize the number of convex pieces. I don't have much hope for a computationally tractable approach in high dimensions as even the 3D case is an active area of research in computational geometry.