Umbilics and lines of curvature for shape interrogation

verfasst von: T. Maekawa, F. E. Wolter, N. M. Patrikalakis
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.
Organisationseinheit(en): Institut für Angewandte Mathematik
Externe Organisation(en): Massachusetts Institute of Technology (MIT)
Typ: Artikel
Journal: Computer aided geometric design
Band: 13
Seiten: 133-161
Anzahl der Seiten: 29
ISSN: 0167-8396
Publikationsdatum: 03.1996
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Modellierung und Simulation, Fahrzeugbau, Luft- und Raumfahrttechnik, Computergrafik und computergestütztes Design
Elektronische Version(en): https://doi.org/10.1016/0167-8396(95)00018-6 (Zugang: Geschlossen)

BibTeX

@article{510d822fa8f941de8efbff01db63c4de,
title = "Umbilics and lines of curvature for shape interrogation",
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.",
keywords = "CAD, CAGD, Lines of curvature, Monge form, Perturbation, Shape recognition, Umbilics, Vision",
author = "T. Maekawa and Wolter, {F. E.} and Patrikalakis, {N. M.}",
year = "1996",
month = mar,
doi = "10.1016/0167-8396(95)00018-6",
language = "English",
volume = "13",
pages = "133--161",
journal = "Computer aided geometric design",
issn = "0167-8396",
publisher = "Elsevier",
number = "2",
}