Peeling Digital Potatoes

12/13/2018

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by   Loïc Crombez, et al.

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The potato-peeling problem (also known as convex skull) is a fundamental computational geometry problem and the fastest algorithm to date runs in O(n^8) time for a polygon with n vertices that may have holes. In this paper, we consider a digital version of the problem. A set K ⊂Z^2 is digital convex if conv(K) ∩Z^2 = K, where conv(K) denotes the convex hull of K. Given a set S of n lattice points, we present polynomial time algorithms to the problems of finding the largest digital convex subset K of S (digital potato-peeling problem) and the largest union of two digital convex subsets of S. The two algorithms take roughly O(n^3) and O(n^9) time, respectively. We also show that those algorithms provide an approximation to the continuous versions.