Experimental results on quadrangulations of sets of fixed points

Prosenjit Bose, Suneeta Ramaswami, Godfried Toussaint, Alain Turki

    Research output: Contribution to journalArticle

    Abstract

    We consider the problem of obtaining "nice" quadrangulations of planar sets of points. For many applications "nice" means that the quadrilaterals obtained are convex if possible and as "fat" or squarish as possible. For a given set of points a quadrangulation, if it exists, may not admit all its quadrilaterals to be convex. In such cases we desire that the quadrangulations have as many convex quadrangles as possible. Solving this problem optimally is not practical. Therefore we propose and experimentally investigate a heuristic approach to solve this problem by converting "nice" triangulations to the desired quadrangulations with the aid of maximum matchings computed on the dual graph of the triangulations. We report experiments on several versions of this approach and provide theoretical justification for the good results obtained with one of these methods. The results of our experiments are particularly relevant for those applications in scattered data interpolation which require quadrangulations that should stay faithful to the original data.

    Original languageEnglish (US)
    Pages (from-to)533-552
    Number of pages20
    JournalComputer Aided Geometric Design
    Volume19
    Issue number7
    DOIs
    StatePublished - Jul 1 2002

    Fingerprint

    Quadrangulation
    Triangulation
    Fixed point
    Experimental Results
    Oils and fats
    Interpolation
    Experiments
    Set of points
    Scattered Data Interpolation
    Dual Graph
    Maximum Matching
    Faithful
    Justification
    Experiment
    Heuristics

    Keywords

    • Matchings
    • Mesh generation
    • Quadrangulations
    • Triangulations

    ASJC Scopus subject areas

    • Modeling and Simulation
    • Automotive Engineering
    • Aerospace Engineering
    • Computer Graphics and Computer-Aided Design

    Cite this

    Experimental results on quadrangulations of sets of fixed points. / Bose, Prosenjit; Ramaswami, Suneeta; Toussaint, Godfried; Turki, Alain.

    In: Computer Aided Geometric Design, Vol. 19, No. 7, 01.07.2002, p. 533-552.

    Research output: Contribution to journalArticle

    Bose, Prosenjit ; Ramaswami, Suneeta ; Toussaint, Godfried ; Turki, Alain. / Experimental results on quadrangulations of sets of fixed points. In: Computer Aided Geometric Design. 2002 ; Vol. 19, No. 7. pp. 533-552.
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