Joseph O'Rourke

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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 independently(More)
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 λ-matrix, estimating halfspace(More)
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)
The problem of finding minimal volume boxes circumscribing a given set of three-dimensional points is investigated. It is shown that it is not necessary for a minimum volume box to have any sides flush with a face of the convex hull of the set of points, which makes a naive search problematic. Nevertheless, it is proven that at least two adjacent box sides(More)
The inherent computational complexity of polygon decomposition problems is of theoretical interest to researchers in the field of computational geometry and of practical interest to those working in syntactic pattern recognition. Three polygon decomposit ion problems are shown to be NP-hard and thus unlikely to admit efficient algorithms. The problems are(More)
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(n6β(n) logn), where β(n) is an extremely slowly growing function. A much simpler(More)
Algorithms are presented for converting between different three-dimensional object representations: from a collection of cross section outlines to surface points, and from surface points to a collection of overlapping spheres. The algorithms effect a conversion from surface representations (outlines or surface points) to a volume representation (spheres).(More)