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Adapting (Pseudo)Triangulations with a NearLinear Number of Edge Flips

Summary: Adapting (Pseudo)­Triangulations with
a Near­Linear Number of Edge Flips
Oswin Aichholzer 1 , Franz Aurenhammer, Hannes Krasser 2
1 Introduction
In geometric data processing, structures that partition the geometric input, as well as
connectivity structures for geometric objects, play an important role. A versatile tool
in this context are triangular meshes, often called triangulations; see e.g., the survey
articles [6, 12, 5]. A triangulation of a finite set S of points in the plane is a maximal
planar straight­line graph that uses all and only the points in S as its vertices. Each
face in a triangulation is a triangle spanned by S.
In the last few years, a relaxation of triangulations, called pseudo­triangulations
(or geodesic triangulations), has received considerable attention. Here, faces bounded
by three concave chains, rather than by three line segments, are allowed. The scope
of applications of pseudo­triangulations as a geometric data stucture ranges from ray
shooting [10, 14] and visibility [25, 26] to kinetic collision detection [1, 21, 22], rigid­
ity [32, 29, 15], and guarding [31]. Still, only very recently, results on the combina­
torial properties of pseudo­triangulations have been obtained. These include bounds
on the minimal vertex and face degree [20] and on the number of possible pseudo­
triangulations [27, 3].
The usefulness of (pseudo­)triangulations partially stems from the fact that these


Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz
Krasser, Hannes - Institute for Theoretical Computer Science, Technische Universität Graz
Technische Universität Graz, Institute for Software Technology


Collections: Computer Technologies and Information Sciences