2008, English, Article edition: Ridges and Umbilics of Polynomial Parametric Surfaces Cazals, Frédéric; Faugère, Jean-Charles; Pouget, Marc; ...

User activity

Share to:
 
Bookmark: http://trove.nla.gov.au/version/203188
Physical Description
  • text
Published
  • HAL - CCSD
  • 2008
Language
  • English

Edition details

Title
  • Ridges and Umbilics of Polynomial Parametric Surfaces
Author
  • Cazals, Frédéric
  • Faugère, Jean-Charles
  • Pouget, Marc
  • Rouillier, Fabrice
Published
  • HAL - CCSD
  • 2008
Physical Description
  • text
Subjects
Notes
  • Given a smooth surface, a blue (red) ridge is a curve along which the maximum (minimum) principal curvature has an extremum along its curvature line. Ridges are curves of extremal curvature and therefore encode important informations used in segmentation, registration, matching and surface analysis. State of the art methods for ridge extraction either report red and blue ridges simultaneously or separately —in which case a local orientation procedure of principal directions is needed, but no method developed so far topologically certifies the curves reported. In this context, we make two contributions. First, for any smooth parametric surface, we exhibit the implicit equation P =​ 0 of the singular curve P encoding all ridges of the surface (blue and red), we analyze its singularities and we explain how colors can be recovered. Second, we instantiate to the algebraic setting the implicit equation P =​ 0. For a polynomial surface, this equation defines an algebraic curve, and we develop the first certified algorithm to produce a topologically certified approximation of it. The algorithm exploits the singular structure of P —umbilics and purple points, and reduces the problem to solving zero dimensional systems using Rational Univariate Representations and isolate roots of univariate rational polynomials. An experimental section illustrates the efficiency of the algorithm on a Bezier patch.
  • HAL:inria-00329762, version 1
  • HAL:http:/​/​hal.inria.fr/​inria-00329762/​en/​
  • DOI:10.1007/​978-3-540-72185-7_8
Language
  • English
Contributed by
OAIster

Get this edition

  • Set up My libraries

    How do I set up "My libraries"?

    In order to set up a list of libraries that you have access to, you must first login or sign up. Then set up a personal list of libraries from your profile page by clicking on your user name at the top right of any screen.

  • All (1)
  • Unknown (1)
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.

User activity


e.g. test cricket, Perth (WA), "Parkes, Henry"

Separate different tags with a comma. To include a comma in your tag, surround the tag with double quotes.

Be the first to add a tag for this edition

Be the first to add this to a list

Comments and reviews

What are comments? Add a comment

No user comments or reviews for this version

Add a comment