Spherical Maps: Their Construction, Properties, and Approximation

[+] Author and Article Information
J. G. Gan

Nanyang Technological University, Singapore

T. C. Woo, K. Tang

University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117

J. Mech. Des 116(2), 357-363 (Jun 01, 1994) (7 pages) doi:10.1115/1.2919386 History: Received April 01, 1991; Online June 02, 2008


The Gaussian map and its allied visibility map on a unit sphere find wide applications for orientating the workpiece for machining by numerical control machines and for probing by coordinate measurement machines. They also provide useful aids in computerized scene analysis, computation of surface-surface intersection, component design for manufacturing and fabrication procedures. Spherical convex hulls and spherical circles are two geometric constructs used to approximate the Gaussian maps and the visibility maps. The duality and the complementarity of these spherical maps are examined so as to derive efficient algorithms.

Copyright © 1994 by The American Society of Mechanical Engineers
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