Generic isotopies of space curves

Bill Bruce, P.J Giblin

    Research output: Contribution to journalArticle

    Abstract

    For a single space curve (that is, a smooth curve embedded in 3) much geometrical information is contained in the dual and the focal set of the curve. These are both (singular) surfaces in 3, the dual being a model of the set of all tangent planes to the curve, and the focal set being the locus of centres of spheres having at least 3-point contact with the curve. The local structures of the dual and the focal set are (for a generic curve) determined by viewing them as (respectively) the discriminant of a family derived from the height functions on the curve, and the bifurcation set of the family of distance-squared functions on the curve. For details of this see for example [6, pp. 123–8].
    Original languageEnglish
    Pages (from-to)41-63
    JournalGlasgow Mathematical Journal
    Volume29
    Issue number1
    DOIs
    Publication statusPublished - 1987

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