Cyclides in Geometric Modeling: Computational Tools for an Algorithmic Infrastructure

[+] Author and Article Information
Y. L. Srinivas, Debashish Dutta

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109

J. Mech. Des 117(3), 363-373 (Sep 01, 1995) (11 pages) doi:10.1115/1.2826689 History: Received January 01, 1994; Revised December 01, 1994; Online December 11, 2007


The Dupin cyclide is a quartic surface with useful properties such as circular lines of curvature, rational parametric representations and closure under offsetting. All natural quadrics (cone, cylinder, sphere) and the torus are special cases of the cyclide. Applications of cyclides include variable radius blending, piping design and design of tubular geometry, such as mold gates and wire harnesses. While the mathematical treatment of cyclides is well developed, the tools required to incorporate this surface into conventional modeling applications have not received sufficient attention. In this paper, we detail various methods for manipulating and computing with the cyclide. Issues such as auxiliary representations, inverse parameter mapping, point classification, normal projection of a point onto the surface, distance computation, bounding volumes and surface intersection detection are discussed in detail. We also provide implemented examples of design applications that utilize these computational tools.

Copyright © 1995 by The American Society of Mechanical Engineers
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