Computing the Width of a Set

Michael E. Houle, Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    Given a set of points P = { p1, p2, · · ·, pn} in three dimensions, the width of P, W(P), is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in 0(n log n + I) time and O(n) space, where I is the number of antipodal pairs of edges of the convex hull of P, and in the worst case I = Ω(n2). For convex polyhedra, the time complexity becomes 0(n + I). If P is a set of points in the plane, the complexity can be reduced to 0(n log n). Finally, for simple polygons linear time suffices.

    Original languageEnglish (US)
    Pages (from-to)761-765
    Number of pages5
    JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
    Volume10
    Issue number5
    DOIs
    StatePublished - Jan 1 1988

    Fingerprint

    Set of points
    Simple Polygon
    Convex polyhedron
    Computing
    Minimum Distance
    Convex Hull
    Time Complexity
    Three-dimension
    Linear Time

    Keywords

    • Algorithms
    • antipodal pairs
    • artificial intelligence
    • computational geometry
    • convex hull
    • geometric complexity
    • geometric transforms
    • image processing
    • minimax approximating line
    • minimax approximating plane
    • pattern recognition
    • rotating calipers
    • width

    ASJC Scopus subject areas

    • Software
    • Computer Vision and Pattern Recognition
    • Computational Theory and Mathematics
    • Artificial Intelligence
    • Applied Mathematics

    Cite this

    Computing the Width of a Set. / Houle, Michael E.; Toussaint, Godfried.

    In: IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 10, No. 5, 01.01.1988, p. 761-765.

    Research output: Contribution to journalArticle

    Houle, Michael E. ; Toussaint, Godfried. / Computing the Width of a Set. In: IEEE Transactions on Pattern Analysis and Machine Intelligence. 1988 ; Vol. 10, No. 5. pp. 761-765.
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