Umbilics and lines of curvature for shape interrogation

Takashi Maekawa, F. E. Wolter, N. M. Patrikalakis

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

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
Volume13
Issue number2
DOIs
Publication statusPublished - 1996 Jan 1
Externally publishedYes

Fingerprint

Parametric Surfaces
Curvature
Free-form Surface
Line
Shape Recognition
Principal curvature
Taylor Expansion
Coordinate Transformation
Extremum
Fingerprint
Singular Point
Tangent line
Numerical Experiment
Angle
Experiments

Keywords

  • 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

Cite this

Umbilics and lines of curvature for shape interrogation. / Maekawa, Takashi; Wolter, F. E.; Patrikalakis, N. M.

In: Computer Aided Geometric Design, Vol. 13, No. 2, 01.01.1996, p. 133-161.

Research output: Contribution to journalArticle

Maekawa, Takashi ; Wolter, F. E. ; Patrikalakis, N. M. / Umbilics and lines of curvature for shape interrogation. In: Computer Aided Geometric Design. 1996 ; Vol. 13, No. 2. pp. 133-161.
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