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Computing Triangulations Using Oriented Matroids

Please always quote using this URN: urn:nbn:de:0297-zib-6692
  • 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 {\sc polymake} framework.

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Metadaten
Author:Julian Pfeifle, Jörg Rambau
Document Type:ZIB-Report
Tag:chirotope; circuit; cocircuit; hypergeometric function; oriented matroid; regular; secondary polytope; software; symmetry; triangulation
MSC-Classification:52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C22 Tilings in n dimensions [See also 05B45, 51M20]
52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C35 Arrangements of points, flats, hyperplanes [See also 32S22]
52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C40 Oriented matroids
52-XX CONVEX AND DISCRETE GEOMETRY / 52Cxx Discrete geometry / 52C45 Combinatorial complexity of geometric structures [See also 68U05]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area) / 68Rxx Discrete mathematics in relation to computer science / 68R05 Combinatorics
Date of first Publication:2002/01/15
Series (Serial Number):ZIB-Report (02-02)
ZIB-Reportnumber:02-02
Published in:Appeared in: Algebra, Geometry and Software Systems (Joswig, Michael and Takayama, Nobuki, eds.) Springer (2003) 49-76
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