SOME COLLISION AVOIDANCE PROBLEMS BETWEEN SPHERES.

Godfried Toussaint

    Research output: Contribution to conferencePaper

    Abstract

    It is shown that a set of n spheres in 3-space, unlike convex polyhedra, exhibits the translation ordering property. Furthermore, such an ordering can be obtained in O(n log n) time. It is also proven that there always exist at least H spheres that can be translated to infinity without disturbing the others, where H is the number of spheres whose centers lie on the convex hull of the centers of the entire collection of spheres. In the worst case H equals minn, 4 and thus this strengthens the result of R. Dawson (1984). It also implies that at least H spheres can be identified with this property in O(n log n) time. Finally, for the two-dimensional problem, it is shown that for a given circle C//i in a collection of circles, all directions of allowable translations for C//i can be computed in O(n log n) time and, therefore, all circles that can be so translated individually without disturbing the others can be identified in O(n**2 log n) time. Some open problems are also discussed.

    Original languageEnglish (US)
    Pages291-295
    Number of pages5
    StatePublished - Dec 1 1985

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    Collision avoidance

    ASJC Scopus subject areas

    • Engineering(all)

    Cite this

    SOME COLLISION AVOIDANCE PROBLEMS BETWEEN SPHERES. / Toussaint, Godfried.

    1985. 291-295.

    Research output: Contribution to conferencePaper

    Toussaint, G 1985, 'SOME COLLISION AVOIDANCE PROBLEMS BETWEEN SPHERES.' pp. 291-295.
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