Geodesic
Generic isotopies of space curves
Glasgow mathematical journal, Tome 29 (1987) no. 1, pp. 41-63

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For a single space curve (that is, a smooth curve embedded in R3) much geometrical information is contained in the dual and the focal set of the curve. These are both (singular) surfaces in R3, 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]. 
Bruce, J. W.; Giblin, P. J. Generic isotopies of space curves. Glasgow mathematical journal, Tome 29 (1987) no. 1, pp. 41-63. doi: 10.1017/S0017089500006650
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