### Abstract

The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained point sets to polygonal environments. In this paper we use this extension to generalize the concept of the order type of a set of points in the Euclidean plane to geodesic order types. In particular, we show that, for any set S of points and an ordered subset B ⊆ S of at least four points, one can always construct a polygon P such that the points of B define the geodesic hull of S w.r.t. P, in the specified order. Moreover, we show that an abstract order type derived from the dual of the Pappus arrangement can be realized as a geodesic order type.

Original language | English |
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Pages (from-to) | 216-227 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 7434 LNCS |

DOIs | |

Publication status | Published - 2012 Sep 6 |

Externally published | Yes |

Event | 18th Annual International Computing and Combinatorics Conference, COCOON 2012 - Sydney, NSW, Australia Duration: 2012 Aug 20 → 2012 Aug 22 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*7434 LNCS*, 216-227. https://doi.org/10.1007/978-3-642-32241-9_19