Generating discrete Morse functions from point data

If K is a finite simplicial complex and h is an injective map from the vertices of K to R, we show how to extend h to a discrete Morse function in the sense of Forman [Forman 02] in a reasonably efficient manner so that the resulting discrete Morse function mirrors the large-scale behavior of h. A concrete algorithm is given for the case where K is a subcomplex of R-3.