On Flips in Polyhedral Surfaces: a new development

Lyuba Alboul, Ruud van Damme

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    Abstract

    Let V be a finite point set in 3D and let ST(V ) be the set of closed triangulated polyhedral surfaces with a vertex set V. Those surfaces can be dened as 2:5D (closed) triangulations of the given discrete data set V. We generalise the
    operation of diagonal flip for 2:5D triangulations by omitting the usual restriction that the flip operation should not
    produce a self-intersecting triangulation. We denote this flip operation by EDF (extended diagonal flip). Among all
    possible 2:5D triangulations with the vertex set V we first single out those that are topologically equivalent to the 2D
    sphere. We show that any two such 2:5D triangulations (if V is situated in general position), are equivalent under
    EDF, i.e., they can be transformed into each other via a finite sequence of EDF.
    Original languageEnglish
    Number of pages4
    Publication statusPublished - 11 Apr 2002
    Event18th European Workshop on Computational Geometry 2002 - Warsaw University, Warschaw, Poland
    Duration: 10 Apr 200212 Apr 2002
    Conference number: 18
    http://ewcg2002.mimuw.edu.pl/

    Conference

    Conference18th European Workshop on Computational Geometry 2002
    Abbreviated titleEWCG 2002
    CountryPoland
    CityWarschaw
    Period10/04/0212/04/02
    Internet address

    Keywords

    • Triangulations
    • diagonal flips
    • polyhedral surfaces

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