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Summary: On Compatible Triangulations of Point Sets
Oswin Aichholzer
Franz Aurenhammer
Hannes Krasser y
Institute for Theoretical Computer Science
Graz University of Technology, Graz, Austria
e-mail: foaich,auren,hkrasserg@igi.tu-graz.ac.at
Abstract
Two conjectures on compatible triangulations for planar point sets are
stated and proved for small sets and for special sets of arbitrary size.
1 Introduction
Let S 1
and S 2
be two nite sets of points in the Euclidean plane. Two tri-
angulations T 1 of S 1 and T 2 of S 2 are called compatible if the face lattices
formed by their triangles, edges, and vertices (points) are isomorphic. The
problem of triangulating two given point sets compatibly comes in two
a-
vors, namely where the correspondence between the points of S 1
and S 2
is
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