  Motivated by applications in geomorphology, the aim of this paper is to
extend Morse-Smale theory from smooth functions to the radial distance function
(measured from an internal point), defining a convex polyhedron in
3-dimensional Euclidean space. The resulting polyhedral Morse-Smale complex may
be regarded, on one hand, as a generalization of the Morse-Smale complex of the
smooth radial distance function defining a smooth, convex body, on the other
hand, it could be also regarded as a generalization of the Morse-Smale complex
of the piecewise linear parallel distance function (measured from a plane),
defining a polyhedral surface. Beyond similarities, our paper also highlights
the marked differences between these three problems and it also relates our
theory to other methods. Our work includes the design, implementation and
testing of an explicit algorithm computing the Morse-Smale complex on a convex
polyhedron.
