Computing Triangulations Using Oriented Matroids

Julian Pfeifle and Jörg Rambau
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Julian Pfeifle: TU Berlin, Dept. of Mathematics, MA 6-2
Jörg Rambau: Zuse-Institute Berlin

A chapter in Algebra, Geometry and Software Systems, 2003, pp 49-75 from Springer

Abstract: Abstract Oriented matroids are combinatorial structures that encode the combinatorics of point configurations. The set of all triangulations of a point configuration depends only on its oriented matroid. We survey the most important ingredients necessary to exploit oriented matroids as a data structure for computing all triangulations of a point configuration, and report on experience with an implementation of these concepts in the software package TOPCOM. Next, we briefly overview the construction and an application of the secondary polytope of a point configuration, and calculate some examples illustrating how our tools were integrated into the polymake framework.

Keywords: Convex Hull; Symmetry Class; Point Configuration; Oriented Matroid; Initial Ideal (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-3-662-05148-1_3

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