Families of surfaces: focal sets, ridges and umbilics

J.W. Bruce, P.J. Giblin, F. Tari

    Research output: Contribution to journalArticle

    15 Citations (Scopus)

    Abstract

    The contact between a surface in Euclidean space and the family of spheres carries a good deal of useful geometrical information about the surface. The centres of those spheres having degenerate tangency with the surface (in Arnold's notation of type A2) form the focal set, and the set of points on the surface where there is a contact of type A3, the so-called ridge curve, is of some interest in the field of computer vision, as a robust feature of the surface. These ridges come together at umbilics, where the contact between the surface and the unique sphere of curvature is of type D. A dual notion, that of a subparabolic curve is also of some interest. In this paper we describe the way in which the ridge and subparabolic curves can evolve in a generic 1-parameter family of surfaces.
    Original languageEnglish
    Pages (from-to)243-268
    JournalMathematical Proceedings of the Cambridge Philosophical Society
    Volume125
    Issue number2
    Publication statusPublished - 1999

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