Joseph S. B. Mitchell

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We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n) and requires O(n2) space, where n is the number of edges of(More)
Model-based recognition is concerned with comparing a shape A, which is stored as a model for some particular object, with a shape B, which is found to exist in an image. If A and B are close to being the same shape, then a vision system should report a match and return a measure of how good that match is. To be useful this measure should satisfy a number(More)
Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur(More)
The problem of determining shortest paths through a weighted planar polygonal subdivision with <italic>n</italic> vertices is considered. Distances are measured according to a weighted Euclidean metric: The length of a path is defined to be the weighted sum of (Euclidean) lengths of the subpaths within each region. An algorithm that constructs a(More)
We show that any polygonal subdivision in the plane can be converted into an “mguillotine” subdivision whose length is at most (1 + c m ) times that of the original subdivision, for a small constant c. “m-Guillotine” subdivisions have a simple recursive structure that allows one to search for the shortest of such subdivisions in polynomial time, using(More)
In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of <i>n</i> regions (<i>neighborhoods</i>) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NP-hard. In this paper, we present new approximation results for the TSPN, including (1) a constant-factor approximation(More)
Wireless sensor networks are tightly associated with the underlying environment in which the sensors are deployed. The global topology of the network is of great importance to both sensor network applications and the implementation of networking functionalities. In this paper we study the problem of topology discovery, in particular, identifying boundaries(More)
Red-Blue Separation Problem (RBSP): Consider the problem of finding a minimum-perimeter Jordan curve (necessarily, a simple polygon) that separates a set of “red” points, R, from a set of “blue” points, B. This problem is seen to be NP-hard, using a reduction from the Euclidean traveling salesman problem [3, 12]. (Replace each city in the TSP instance by a(More)