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1 date: July 23, 2007 file: aurexu2 OPTIMAL TRIANGULATIONS

Summary: 1 date: July 23, 2007 file: aurexu2
Introduction. A triangulation of a given set S
of n points in the Euclidean plane is a maxi­
mal set of non­crossing straight line segments
(called edges) which have both endpoints in S.
As an equivalent definition, a triangulation of S
is a partition of the convex hull of S into tri­
angular faces whose vertex set is exactly S. Tri­
angulations are a versatile means for partition­
ing and/or connecting geometric objects. They
are used in many areas of engineering and sci­
entific applications such as finite element meth­
ods, approximation theory, numerical computa­
tion, computer­aided geometric design, compu­
tational geometry, etc. Many of their applica­
tions are surveyed in [8], [11], [20], [61].
A triangulation of S can be viewed as a pla­
nar graph whose vertex set is S and whose edge
set is a subset of S × S. The Eulerian relation


Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz


Collections: Computer Technologies and Information Sciences