Generic isotopies of space curves

Bruce, Bill and Giblin, P.J (1987) Generic isotopies of space curves. Glasgow Mathematical Journal, 29 (1). pp. 41-63. ISSN 0017-0895 DOI https://doi.org/10.1017/S0017089500006650

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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].

Item Type: Article
Subjects: Q Science > QA Mathematics
Date Deposited: 12 Jan 2011 10:24
URI: http://repository.edgehill.ac.uk/id/eprint/2191

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