Principal curvatures from the integral invariant viewpoint

Helmut Pottmann*, Johannes Wallner, Yong Liang Yang, Yu Kun Lai, Shi Min Hu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

61 Scopus citations

Abstract

The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighborhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asymptotic analysis of the moments of inertia and the principal directions which are used in this approach. We also address implementation and, briefly, robustness issues and applications.

Original languageEnglish (US)
Pages (from-to)428-442
Number of pages15
JournalComputer Aided Geometric Design
Volume24
Issue number8-9
DOIs
StatePublished - Nov 1 2007

Keywords

  • Integral invariants
  • Principal curvatures
  • Robustness

ASJC Scopus subject areas

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

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