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Optimal Area Triangulation

of Planar Point Sets

Language EnglishEnglish
Book Paperback
Book Optimal Area Triangulation Tzvetalin S. Vassilev
Libristo code: 06822650
Publishers VDM Verlag, April 2009
Triangulations of point sets play an important role §in Computational Geometry and have been studied... Full description
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Triangulations of point sets play an important role §in Computational Geometry and have been studied §extensively in the last decades. The results on §optimizing angles and edge lengths are classical in §the field. Here we present a study on optimizing the §area in two ways: minimizing the maximum area of a §triangle, and maximizing the minimum area of a §triangle. In the case of a point set in convex §position we present nearly quadratic algorithms for §both problems. The geometric properties of these two §optimal triangulations are derived and extensively §discussed. We strongly believe that both problems §admit no worse than quadratic solution. Such will be §based on a refinement of the geometric properties. §Furthermore, the properties and the methods §described here can serve as a starting point to §obtaining efficient optimal triangulation algorithms §for other quality measures such as maximizing §inradius or aspect ratio of a triangle. In the case §of a point set in general position, we present a §polynomial time approximation algorithm. The §algorithm is based on the matching properties of §triangulations and further geometric considerations.

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About the book

Full name Optimal Area Triangulation
Language English
Binding Book - Paperback
Date of issue 2009
Number of pages 136
EAN 9783639140101
ISBN 3639140109
Libristo code 06822650
Publishers VDM Verlag
Weight 209
Dimensions 152 x 229 x 8
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