Approximating the Maximum Overlap of Polygons under Translation

Let $P$ and $Q$ be two simple polygons in the plane of total complexity $n$, each of which can be decomposed into at most $k$ convex parts. We present an $(1-\varepsilon)$-approximation algorithm, for finding the translation of $Q$, which maximizes its area of overlap with $P$. Our algorithm runs in $O(c n)$ time, where $c$ is a constant that depends only on $k$ and $\varepsilon$. This suggest that for polygons that are "close" to being convex, the problem can be solved (approximately), in near linear time

Overlap of convex polytopes under rigid motion

We present an algorithm to compute a rigid motion that approximately maximizes the volume of the intersection of two convex polytopes P-1 and P-2 in R-3. For all epsilon is an element of (0, 1/2] and for all n >= 1/epsilon, our algorithm runs in O(epsilon(-3) n log(3.5) n) time with probability 1 - n(-O(1)). The volume of the intersection guaranteed by the output rigid motion is a (1 - epsilon)-approximation of the optimum, provided that the optimum is at least lambda . max{vertical bar P-1 vertical bar . vertical bar P-2 vertical bar} for some given constant lambda is an element of (0, 1]. (C) 2013 Elsevier B.V. All rights reserved.X1155Ysciescopu

Maximizing the overlap of two planar convex sets under rigid motions

10.1145/1064092.1064146Proceedings of the Annual Symposium on Computational Geometry356-363PACG

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop