Given two simplicial complexes, and start and end vertices in each
complex, we show how to compute curves (in each complex) between
these vertices, such that the Frechet distance between these
curves is minimized. As a polygonal curve is a complex, this
generalizes the regular notion of Frechet distance between
curves. We also generalize the algorithm to handle an input of
k simplicial complexes.
Using this new algorithm we can solve a slew of new problems, from
computing a median curve for a given collection of curves, to
various motion planning problems.
Last modified: Mon Jul 27 22:42:40 CDT 2015