An Efficient Algorithm for Shortest Path in Three Dimensions With Polyhedral Obstacles

[+] Author and Article Information
J. Khouri, K. A. Stelson

Productivity Center, Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455

J. Dyn. Sys., Meas., Control 111(3), 433-436 (Sep 01, 1989) (4 pages) doi:10.1115/1.3153072 History: Received May 01, 1987; Revised September 01, 1988; Online July 21, 2009


An algorithm to find the shortest path between two specified points in three-dimensional space in the presence of polyhedral obstacles is described. The proposed method iterates for the precise location of the minimum length path on a given sequence of edges on the obstacles. The iteration procedure requires solving a tri-diagonal matrix at each step. Both the computer storage and the number of computations are proportional to n, the number of edges in the sequence. The algorithm is stable and converges for the general case of any set of lines, intersecting, parallel or skew.

Copyright © 1989 by ASME
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