Computation of self-intersections of offsets of bézier surface patches

Takashi Maekawa, Wonjoon Cho, Nicholas M. Patrikalakis

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


Self-intersection of offsets of regular Bezier 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 Bezier surface patches. Examples illustrate the principal features and robustness characteristics of the method.

Original languageEnglish
Pages (from-to)275-283
Number of pages9
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number2
Publication statusPublished - 1997 Jun
Externally publishedYes

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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