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Computing Triangulations Using Oriented Matroids

In: Algebra, Geometry and Software Systems

Author

Listed:
  • Julian Pfeifle

    (TU Berlin, Dept. of Mathematics, MA 6-2)

  • Jörg Rambau

    (Zuse-Institute Berlin)

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.

Suggested Citation

  • Julian Pfeifle & Jörg Rambau, 2003. "Computing Triangulations Using Oriented Matroids," Springer Books, in: Michael Joswig & Nobuki Takayama (ed.), Algebra, Geometry and Software Systems, pages 49-75, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-05148-1_3
    DOI: 10.1007/978-3-662-05148-1_3
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