I have a data set that essentially looks like the picture below, i.e., it's given by sets of points in $\mathbb{R}^3$ that sample the cross-sections of a certain surface that in principle I do not know. In fact, I would like to recover this surface or, more precisely, a triangulation/mesh of it.

In this particular example, it is not difficult to see that we have a section of a cone. In this sense, I do not want to compute the convex hull of these points, but instead I just want to find its boundary (if this makes any sense; I actually don't know whether it does), i.e., I want to find the surface that one could obtain by simply joining the "corresponding" points in both "slices". (I've put "corresponding [points]" in quotes because I believe it's not straightforward to perform this matching exercise, i.e., find the point on the adjacent slice that isn't necessarily the closest one in the $\mathbb{R}^3$ metric, but would correspond to the closest one if we projected one slice into another and considered only the $\mathbb{R}^2$ distance between them, as seen below.)

samesample. – Aaron Golden Feb 23 '13 at 0:15