On Reconstructing a Convex Polygon from Partial Information

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

On Reconstructing a Convex Polygon from Partial Information

Computational Geometry 2026-07-01 v1 Discrete Mathematics

Authors: Alexander Baumann , Therese Biedl , Mahmoud Elashmawi , Simon D. Fink , Maria Saumell , André Schulz

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.

Cite

@article{arxiv.2607.01423,
  title  = {On Reconstructing a Convex Polygon from Partial Information},
  author = {Alexander Baumann and Therese Biedl and Mahmoud Elashmawi and Simon D. Fink and Maria Saumell and André Schulz},
  journal= {arXiv preprint arXiv:2607.01423},
  year   = {2026}
}

Comments

To appear at CCCG 2026