# Joseph O'Rourke

• 1986
1, Introduetlon EIGindy and Avis [EA] considered the problem of determining the visibility polygon from a point inside a polygon. Their algorithm runs in optimal O(n) time and space, where n is the number of the vertices of the given polygon. Later their result was generalized to visibility polygons from an edge by EIGindy [Eli, and Lee and Lin ILL I. Both(More)
• 6
• 1983
An optimal algorithm is presented for constructing an arrangement of hyperplanes in arbitrary dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to improve known worst-case time complexities for five problems: computing all order-k Voronoi diagrams, computing the &#x03BB;-matrix, estimating halfspace(More)
• 3
• 1985
We consider the problem of finding a polygon nested between two given convex polygons that has a minimal number of vertices. Our main result is an <italic>&Ogr;</italic>(<italic>n</italic>log<italic>&kgr;</italic>) algorithm for solving the problem, where <italic>n</italic> is the total number of vertices of the given polygons, and <italic>&kgr;</italic> is(More)
• 1980
A system capable of analyzing image sequences of human motion is described. The system is structured as a feedback loop between high and low levels: predictions are made at the semantic level and verifications are sought at the image level. The domain of human motion lends itself to a model-driven analysis, and the system includes a detailed model of the(More)
• 2
• 1997
We introduce the notion of a star unfolding of the surface P of a three-dimensional convex polytope with n vertices, and use it to solve several problems related to shortest paths on P. The first algorithm computes the edge sequences traversed by shortest paths on P in time O(n 6 β(n) log n), where β(n) is an extremely slowly growing function. A much(More)
• 1991
The star unfolding of a convex polytope with respect to a point x is obtained by cutting the surface along the shortest paths from z to every vertex, and flattening the surface on the plane. Reestablish twomaiu properties of the star unfolding: (1) It does not self-overlap: its boundary is a simple polygon. (2) The ridge tree in the unfolding, which is the(More)
• 2
• 1982
An algorithm is presented that computes the intersection of two convex polygons in linear time. The algorithm is fundamentally different from the only known linear algorithms for this problem, due to Shames and Hoey. These algorithms depend on a division of the plane into either angular sectors (Shamos) or parallel slabs (Hoey), and are mildly complex. Our(More)