Efi Fogel's Minkowski Sums and Collision Detection Software
Given two convex polygons with m and n vertices respectively, it was shown that detecting collision and computing directional penetration depth can be done in optimal time O(log m + log n) [GS88], and that the (absolute) penetration depth can be computed in O(log(m + n)) time using the Minkowski sum computed a priori [DHK93]. It is well known that the Minkowski sum in this case consists of m + n edges when there are no degeneracies, and can be computed in linear time simply by merging the edges in slope order.
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This page last modified on 2008-07-10