Computation of Shortest Paths on Free-Form Parametric Surfaces

[+] Author and Article Information
T. Maekawa

Department of Ocean Engineering, Massachusetts Institute of Technology, Design Laboratory, Cambridge, MA 02139-4307

J. Mech. Des 118(4), 499-508 (Dec 01, 1996) (10 pages) doi:10.1115/1.2826919 History: Received October 01, 1995; Revised March 01, 1996; Online December 11, 2007


Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path between a point and a curve on a free-form parametric surface. These problems can be reduced to solving a two point boundary value problem. Our approach for solving the two point boundary value problem is based on a relaxation method relying on finite difference discretization. Examples illustrate our method.

Copyright © 1996 by The American Society of Mechanical Engineers
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