### 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 language | English |
---|---|

Title of host publication | Proceedings of the 12th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT) |

Pages | 13-24 |

Number of pages | 12 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

## 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