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arXiv · 2607.01423

On Reconstructing a Convex Polygon from Partial Information

Alexander Baumann·Therese Biedl·Mahmoud Elashmawi·Simon D. Fink·Maria Saumell·André Schulz
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Abstract

The reconstruction problem asks to construct a (convex) polygon that has a specified set of features, such as an ordered set of edge-lengths or an ordered set of polygon-angles. In this paper, we do a systematic exploration of the reconstruction problem in all scenarios where one or two sets of features have been specified. Some of these scenarios were well-studied already, for some we develop testing-algorithms and/or hardness results, and many give rise to interesting open problems for future study.

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Alexander Baumann, Therese Biedl, Mahmoud Elashmawi, Simon D. Fink, Maria Saumell, André Schulz. 2026-07-01. On Reconstructing a Convex Polygon from Partial Information. https://arxiv.org/abs/2607.01423

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