"An O(n^2) Shortest Path Algorithm for a Non-Rotating Convex Body."
    John Hershberger and Leonidas J. Guibas.
    November 27, 1986.  33 pages.

Authors' Abstract

    We investigate the problem of moving a convex body in the plane
    from one location to another while avoiding a given collection
    of polygonal obstacles. The method we propose is applicable when
    the convex body is not allowed to rotate. If  n  denotes the total
    size of all polygonal obstacles, the method yields an O(n^2)
    algorithm for finding a shortest path from the initial to the
    final location. In solving this problem, we develop some new tools
    in computational geometry that may be of independent interest.