On flips in polyhedral surfaces

Oswin Aichholzer, Lyuba Alboul, Ferran Hurtado

    Research output: Contribution to journalArticleAcademicpeer-review

    8 Citations (Scopus)

    Abstract

    Let V be a finite point set in 3-space, and let S(V) be the set of triangulated polyhedral surfaces homeomorphic to a sphere and with vertex set V. Let abc and cbd be two adjacent triangles belonging to a surface SεS(V); the flip of the edge bc would replace these two triangles by the triangles abd and adc. The flip operation is only considered when it does not produce a self-intersecting surface. In this paper we show that given two surfaces S1,S2εS(V), it is possible that there is no sequence of flips transforming S1 into S2, even in the case that V consists of points in convex position.
    Original languageEnglish
    Pages (from-to)303-311
    JournalInternational journal of foundations of computer science
    Volume13
    Issue number2
    DOIs
    Publication statusPublished - 2002

    Keywords

    • METIS-206014
    • flip
    • IR-85951
    • Triangulation
    • Schönhardt's polyhedron
    • Triangulated polyhedral surface

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