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Finding Digital Convexity

Abstract : A set S⊂Zd is said \emph{digital convex} if \conv(S)∩Zd=S, where \conv(S) denotes the convex hull of S. Herein, we consider several algorithmic problems related to recognition of digital convex sets, as well as the detection of digital convex sets. We start by showing that the quickhull algorithm runs in linear time for digital convex sets. Then, based on this result, we propose an algorithm to test the digital convexiyty of a lattice set S⊂Z2 in O(n+hlogr) time, where h denotes the number of vertices of the convex hull of S, and r denotes the diameter of S. Then, We show how those results can be used to solve the digital polyhedra recognition problem. Finally, we propose a polynomial time algorithm to find the largest union of k digital convex subsets of S⊂Z2.
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https://theses.hal.science/tel-03870014
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Submitted on : Thursday, November 24, 2022 - 3:17:10 PM
Last modification on : Friday, November 25, 2022 - 4:01:34 AM

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  • HAL Id : tel-03870014, version 1

Citation

Loïc Crombez. Finding Digital Convexity. Computational Geometry [cs.CG]. Université Clermont Auvergne, 2021. English. ⟨NNT : 2021UCFAC110⟩. ⟨tel-03870014⟩

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