Families of surfaces: focal sets, ridges and umbilics

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

Research output: Contribution to journalArticle

14 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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Ridge
Contact
Curve
Family
Computer Vision
Set of points
Notation
Euclidean space
Curvature

Cite this

Bruce, J.W. ; Giblin, P.J. ; Tari, F. / Families of surfaces: focal sets, ridges and umbilics. In: Mathematical Proceedings of the Cambridge Philosophical Society. 1999 ; Vol. 125, No. 2. pp. 243-268.
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Families of surfaces: focal sets, ridges and umbilics. / Bruce, J.W.; Giblin, P.J.; Tari, F.

In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 125, No. 2, 1999, p. 243-268.

Research output: Contribution to journalArticle

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T1 - Families of surfaces: focal sets, ridges and umbilics

AU - Bruce, J.W.

AU - Giblin, P.J.

AU - Tari, F.

PY - 1999

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M3 - Article

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SP - 243

EP - 268

JO - Mathematical Proceedings of the Cambridge Philosophical Society

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