Recursive geometry of the flow complex and topology of the flow complex filtration

K. Buchin, T.K. Dey, J. Giesen, M. John

    Research output: Contribution to journalArticleAcademicpeer-review

    9 Citations (Scopus)

    Abstract

    The flow complex is a geometric structure, similar to the Delaunay tessellation, to organize a set of (weighted) points in . Flow shapes are topological spaces corresponding to substructures of the flow complex. The flow complex and flow shapes have found applications in surface reconstruction, shape matching, and molecular modeling. In this article we give an algorithm for computing the flow complex of weighted points in any dimension. The algorithm reflects the recursive structure of the flow complex. On the basis of the algorithm we establish a topological similarity between flow shapes and the nerve of a corresponding ball set, namely homotopy equivalence.
    Original languageEnglish
    Pages (from-to)115-137
    JournalComputational Geometry
    Volume40
    Issue number2
    DOIs
    Publication statusPublished - 2008

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