TY - JOUR

T1 - Geodesic order types

AU - Aichholzer, Oswin

AU - Korman, Matias

AU - Pilz, Alexander

AU - Vogtenhuber, Birgit

N1 - Funding Information:
Research supported by the ESF EUROCORES programme EuroGIGA - ComPoSe, Austrian Science Fund (FWF): I 648-N18 and grant EUI-EURC-2011-4306. M. K. received support of the Secretary for Universities and Research of the Ministry of Economy and Knowledge of the Government of Catalonia and the European Union. A.P. is recipient of a DOC-fellowship of the Austrian Academy of Sciences at the Institute for Software Technology, Graz University of Technology, Austria.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-642-32241-9_19

DO - 10.1007/978-3-642-32241-9_19

M3 - Conference article

AN - SCOPUS:84865630120

VL - 7434 LNCS

SP - 216

EP - 227

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

T2 - 18th Annual International Computing and Combinatorics Conference, COCOON 2012

Y2 - 20 August 2012 through 22 August 2012

ER -