Reconstructing a Simple Polygon from Its Angles

Yann Disser, Matúš Mihalák, Peter Widmayer

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

We study the problem of reconstructing a simple polygon from angles measured at the vertices of the polygon. We assume that at each vertex, a sensing device returns the sequence of angles between each pair of vertices that are visible. We prove that the sequence of angle measurements at all vertices of a simple polygon in cyclic order uniquely determines the polygon up to similarity. Furthermore, we propose an algorithm that reconstructs the polygon from this information in polynomial time.
Original languageEnglish
Title of host publicationProceedings of the 12th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT)
Pages13-24
Number of pages12
DOIs
Publication statusPublished - 2010
Externally publishedYes

Cite this

Disser, Y., Mihalák, M., & Widmayer, P. (2010). Reconstructing a Simple Polygon from Its Angles. In Proceedings of the 12th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT) (pp. 13-24) https://doi.org/10.1007/978-3-642-13731-0_2