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• W3025561567 abstract "A set $$S subset mathbb {Z}^2$$ of integer points is digital convex if $${{,mathrm{conv},}}(S) cap mathbb {Z}^2 = S$$ , where $${{,mathrm{conv},}}(S)$$ denotes the convex hull of S. In this paper, we consider the following two problems. The first one is to test whether a given set S of n lattice points is digital convex. If the answer to the first problem is positive, then the second problem is to find a polygon $$Psubset mathbb {Z}^2$$ with minimum number of edges and whose intersection with the lattice $$Pcap mathbb {Z}^2$$ is exactly S. We provide linear-time algorithms for these two problems. The algorithm is based on the well-known quickhull algorithm. The time to solve both problems is $$O(n + h log r) = O(n + n^{1/3} log r)$$ , where $$h = min (|{{,mathrm{conv},}}(S)|, n^{1/3})$$ and r is the diameter of S." @default.
• W3025561567 created "2020-05-21" @default.
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• W3025561567 date "2020-05-11" @default.
• W3025561567 modified "2023-09-27" @default.
• W3025561567 title "Efficiently Testing Digital Convexity and Recognizing Digital Convex Polygons" @default.
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• W3025561567 doi "https://doi.org/10.1007/s10851-020-00957-6" @default.
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