Optimal Area Triangulation

Name: Optimal Area Triangulation
Brand: VDM Verlag
SKU: 9783639140101
Price: 304.48 RON
Availability: InStock

of Planar Point Sets

Autor: Tzvetalin S. Vassilev

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Editura: VDM Verlag

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Triangulations of point sets play an important role §in Computational Geometry and have been studied...

Informații despre carte

Autor

Tzvetalin S. Vassilev

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2009

Pagini

136

EAN

9783639140101

ISBN

3639140109

Enbook ID

06822650

Editura

VDM Verlag

Greutate

209

Dimensiuni

152 x 229 x 8

Descriere completă

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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Optimal Area Triangulation

of Planar Point Sets

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