Path of a triangulation

Oswin Aichholzer

doi:10.1145/304893.304896

Path of a triangulation

Oswin Aichholzer^*

^*Corresponding author for this work

Graz University of Technology (90000)

Research output: Contribution to conference › Paper › peer-review

Abstract

For a planar point set S let T be a triangulation of S and l a line properly intersecting T. We show that there always exists a unique path in T with certain properties with respect to l. This path is then generalized to (non triangulated) point sets restricted to the interior of simple polygons. This so-called triangulation path enables us to treat several triangulation problems on planar point sets in a divide & conquer-like manner. For example, we give the first algorithm for counting triangulations of a planar point set which is observed to run in time sublinear in the number of triangulations. Moreover, the triangulation path proves to be useful for the computation of optimal triangulations.

Original language	English
Pages	14-23
Number of pages	10
DOIs	https://doi.org/10.1145/304893.304896
Publication status	Published - 1999
Event	Proceedings of the 1999 15th Annual Symposium on Computational Geometry - Miami Beach, FL, USA Duration: 13 Jun 1999 → 16 Jun 1999

Conference

Conference	Proceedings of the 1999 15th Annual Symposium on Computational Geometry
City	Miami Beach, FL, USA
Period	13/06/99 → 16/06/99

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Mathematics

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10.1145/304893.304896

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abstract = "For a planar point set S let T be a triangulation of S and l a line properly intersecting T. We show that there always exists a unique path in T with certain properties with respect to l. This path is then generalized to (non triangulated) point sets restricted to the interior of simple polygons. This so-called triangulation path enables us to treat several triangulation problems on planar point sets in a divide & conquer-like manner. For example, we give the first algorithm for counting triangulations of a planar point set which is observed to run in time sublinear in the number of triangulations. Moreover, the triangulation path proves to be useful for the computation of optimal triangulations.",

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author = "Oswin Aichholzer",

year = "1999",

doi = "10.1145/304893.304896",

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AB - For a planar point set S let T be a triangulation of S and l a line properly intersecting T. We show that there always exists a unique path in T with certain properties with respect to l. This path is then generalized to (non triangulated) point sets restricted to the interior of simple polygons. This so-called triangulation path enables us to treat several triangulation problems on planar point sets in a divide & conquer-like manner. For example, we give the first algorithm for counting triangulations of a planar point set which is observed to run in time sublinear in the number of triangulations. Moreover, the triangulation path proves to be useful for the computation of optimal triangulations.

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T2 - Proceedings of the 1999 15th Annual Symposium on Computational Geometry

Y2 - 13 June 1999 through 16 June 1999

ER -

Path of a triangulation

Abstract

Conference

ASJC Scopus subject areas

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