Testing roundness of a polytope and related problems
نویسنده
چکیده
In this paper we study the problem of computing the smallest-width annulus for a convex polytope in R d. This generalizes a topic from tolerancing metrology to higher dimensions, of which the planar case has been investigated by Swanson, Lee and Wu. We show this problem to be equivalent to the problem of computing diierent variants of Hausdorr-minimal spheres. We can formulate the latter problem as a LP-type problem with combinatorial dimension 2(d + 1) (for the planar case: 4) and prove the uniqueness of Hausdorr-minimal spheres for arbitrary convex bodies. The result is an expected linear-time algorithm in the size of the input, for all these problems. In conclusion we describe positive and negative results concerning an extension from spheres to ellipsoids.
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