Computation of Self-Intersections of Offsets of Bézier Surface Patches

[+] Author and Article Information
Takashi Maekawa, Wonjoon Cho, Nicholas M. Patrikalakis

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

J. Mech. Des 119(2), 275-283 (Jun 01, 1997) (9 pages) doi:10.1115/1.2826247 History: Received June 01, 1995; Revised October 01, 1996; Online December 11, 2007


Self-intersection of offsets of regular Bézier surface patches due to local differential geometry and global distance function properties is investigated. The problem of computing starting points for tracing self-intersection curves of offsets is formulated in terms of a system of nonlinear polynomial equations and solved robustly by the interval projected polyhedron algorithm. Trivial solutions are excluded by evaluating the normal bounding pyramids of the surface subpatches mapped from the parameter boxes computed by the polynomial solver with a coarse tolerance. A technique to detect and trace self-intersection curve loops in the parameter domain is also discussed. The method has been successfully tested in tracing complex self-intersection curves of offsets of Bézier surface patches. Examples illustrate the principal features and robustness characteristics of the method.

Copyright © 1997 by The American Society of Mechanical Engineers
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