On compatible triangulations of simple polygons

Boris Aronov, Raimund Seidel, Diane Souvaine

    Research output: Contribution to journalArticle

    Abstract

    It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices inside the polygon are allowed? We give a positive answer and construct a pair of such triangulations with O(n2) new triangulation vertices. Moreover, we show that there exists a 'universal' way of triangulating an n-sided polygon with O(n2) extra triangulation vertices. Finally, we also show that creating compatible triangulations requires a quadratic number of extra vertices in the worst case.

    Original languageEnglish (US)
    Pages (from-to)27-35
    Number of pages9
    JournalComputational Geometry: Theory and Applications
    Volume3
    Issue number1
    DOIs
    StatePublished - 1993

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    Simple Polygon
    Triangulation
    Polygon
    Triangulate

    ASJC Scopus subject areas

    • Computational Theory and Mathematics
    • Discrete Mathematics and Combinatorics
    • Geometry and Topology

    Cite this

    On compatible triangulations of simple polygons. / Aronov, Boris; Seidel, Raimund; Souvaine, Diane.

    In: Computational Geometry: Theory and Applications, Vol. 3, No. 1, 1993, p. 27-35.

    Research output: Contribution to journalArticle

    Aronov, Boris ; Seidel, Raimund ; Souvaine, Diane. / On compatible triangulations of simple polygons. In: Computational Geometry: Theory and Applications. 1993 ; Vol. 3, No. 1. pp. 27-35.
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