Anyone know how to compute the bitangent locus of a space curve, e.g. a torus knot (pick whatever parametrization you like)? Specifically, what is the set of normal vectors (in the two-sphere) of planes tangent to the curve in more than one place?
This 2013, long (47-page) PhD-thesis paper by Niels Lubbes may give some sense of how nontrivial is this task:
"Families of bitangent planes of space curves and minimal non-fibration families," (arXiv link)
He says, "In this paper we concentrate on cone curves, but many of our methods can be used to find bitangent families of arbitrary space curves." Algorithms are described starting on p.37.
p.42: An aﬃne chart of the cone curve $C$ lying on a quadric cone $Q$ and its tangent developable $Z$.