Pseudotriangulations from Surfaces and a Novel Type of Edge Flip

Authors:
Oswin Aichholzer;Franz Aurenhammer;Hannes Krasser;Peter Brass
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Computing
Year:
2003

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Abstract

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.