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arXiv · 1311.6331

Compact families of Jordan curves and convex hulls in three dimensions

Colm Ó Dúnlaing
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Abstract

We prove that for certain families of semi-algebraic convex bodies in 3 dimensions, the convex hull of $n$ disjoint bodies has $O(n\lambda_s(n))$ features, where $s$ is a constant depending on the family: $\lambda_s(n)$ is the maximum length of order-$s$ Davenport-Schinzel sequences with $n$ letters. The argument is based on an apparently new idea of `compact families' of convex bodies or discs, and of `crossing content' of disc intersections.

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Colm Ó Dúnlaing. 2013-11-25. Compact families of Jordan curves and convex hulls in three dimensions. https://arxiv.org/abs/1311.6331

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