Umbilics and lines of curvature for shape interrogation

T. Maekawa, F. E. Wolter, N. M. Patrikalakis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)


This paper describes a method to extract the generic features of free-form parametric surfaces for shape interrogation. The umbilical points, which are the singular points of the orthogonal net of lines of curvature, have generic features and may act like fingerprints for shape recognition. We investigate the generic features of the umbilics and behavior of lines of curvature which pass through an umbilic on a parametric free-form surface. Our method is based on a coordinate transformation to set the parametric surface in Monge form and on a Taylor expansion to compute the angles of the tangent lines to the lines of curvatures at an umbilic. We also develop a novel and practical criterion which assures the existence of local extrema of principal curvature functions at umbilical points. Finally, numerical experiments illustrate how the generic features of the umbilics can be applied for surface recognition.

Original languageEnglish
Pages (from-to)133-161
Number of pages29
JournalComputer Aided Geometric Design
Issue number2
Publication statusPublished - 1996 Mar
Externally publishedYes


  • CAD
  • CAGD
  • Lines of curvature
  • Monge form
  • Perturbation
  • Shape recognition
  • Umbilics
  • Vision

ASJC Scopus subject areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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