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SIAM J. on Computing / Volume 32 / Issue 6

SIAM J. Comput. 32, pp. 1621-1653 (33 pages)

Pseudotriangulations from Surfaces and a Novel Type of Edge Flip

Oswin Aichholzer, Franz Aurenhammer, Hannes Krasser, and Peter Brass

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We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.

© 2003 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

68U05, 68W40, 52C45, 52C25, 52B55, 52B05

PUBLICATION DATA

ISSN:

0097-5397 (print)  
1095-7111 (online)

Publisher:

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

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http://dx.doi.org/10.1137/S0097539702411368

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