Geodesic
Singularities of the affine chord envelope for two surfaces in four-space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 230-242.

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We study local singularities of the envelope of the set of straight lines (chords) joining those points of two surfaces embedded in $\mathbb R^4$ which are not in general position to each other. 
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Graham M. Reeve; Vladimir M. Zakalyukin. Singularities of the affine chord envelope for two surfaces in four-space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 230-242. http://geodesic.mathdoc.fr/item/TM_2012_277_a15/

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