Steven Fortune

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A model of computation based on random access machines operating in parallel and sharing a common memory is presented. The computational power of this model is related to that of traditional models. In particular, deterministic parallel RAM's can accept in polynomial time exactly the sets accepted by polynomial tape bounded Turing machines; nondeterministic(More)
We present a transformation that can be used to compute Voronoi diagrams with a sweepline technique. The transformation is used to obtain simple algorithms for computing the Voronoi diagram of point sites, of line segment sites, and of weighted point sites. All algorithms have <italic>&Ogr;</italic>(<italic>n</italic> log <italic>n</italic>) worst case(More)
The Voronoi diagram of a set of sites partitions space into regions one per site the region for a site s consists of all points closer to s than to any other site The dual of the Voronoi diagram the Delaunay triangulation is the unique triangulation so that the circumsphere of every triangle contains no sites in its interior Voronoi diagrams and Delaunay(More)
We consider the motion planning problem for a point constrained to move along a path with radius of curvature at least one. The point moves in a two-dimensional universe with polygonal obstacles. We show the decidability of the reachability question: “Given a source placement (position and direction pair) and a target placement, is there a(More)
We experiment with exact integer arithmetic to implement primitives for geometric algorithms. Naive use of exact arithmetic&#8212;either modular or multiprecision integer&#8212;increases execution time dramatically over the use of floating-point arithmetic. By combining tuned multiprecision integer arithmetic and a floating-point filter based on interval(More)
A common goal of much recent research in computational geometaT has been to extend algorithms that have been developed for the Euclidean metric to the more complicated geodesic metric inside a simple polygon. The geodesic distance between two points in a simple polygon is the length of the shortest path connecting the points that remains inside the polygon.(More)
Geometric algorithms are usually described assuming that arithmetic operations are performed exactly on real numbers. A program implemented using a naive substitution of floating-point arithmetic for real arithmetic can fail, since geometric primitives depend upon sign-evaluation and may not be reliable if evaluated approximately. Geometric primitives are(More)