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Summary: 1 date: November 15, 1999 le: optriang
OPTIMAL TRIANGULATIONS
Introduction. A triangulation of a given set S
of n points in the Euclidean plane is a maximal
set of non-crossing line segments (called edges)
which have both endpoints in S. Any triangu-
lation of S partitions the interior of the con-
vex hull of S into triangles. Triangulations are
used in many areas of engineering and scien-
ti c applications such as nite element meth-
ods, approximation theory, numerical computa-
tion, computer-aided geometric design, compu-
tational geometry, etc. Many applications are
surveyed in [5], [8], [17], [56].
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
for planar graphs implies that the number e(S)
of edges, and the number t(S) of triangles, do
not depend on the way of triangulating S. In
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