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Convexity Minimizes PseudoTriangulations Oswin Aichholzer #+ Franz Aurenhammer # Hannes Krasser ## Bettina Speckmann
 

Summary: Convexity Minimizes Pseudo­Triangulations
Oswin Aichholzer #+ Franz Aurenhammer # Hannes Krasser ## Bettina Speckmann §
Abstract
The number of minimum pseudo­triangulations is minimized for point sets in convex position.
1 Introduction
A pseudo­triangle is a planar polygon with exactly
three convex vertices, called corners. Three reflex
chains of edges join the corners. Let S be a set of
n points in general position in the plane. A pseudo­
triangulation for S is a partition of the convex hull
of S into pseudo­triangles whose vertex set is S. A
pseudo­triangulation is called minimum if it consists of
exactly n - 2 pseudo­triangles (and 2n - 3 edges), the
minimum possible. Each vertex of a minimum pseudo­
triangulation is pointed, that is, its incident edges span
a convex angle. In fact, minimum pseudo­triangulations
can be characterized as maximal planar straight­line
graphs where each vertex is pointed [15].
Pseudo­triangulations, also called geodesic triangula­
tions, have received considerable attention in the last

  

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
Wismath, Stephen - Department of Mathematics and Computer Science, University of Lethbridge

 

Collections: Computer Technologies and Information Sciences; Mathematics