Shortest monotone descent path problem in polyhedral terrain

Given a polyhedral terrain with n vertices, the shortest monotone descent path problem deals with finding the shortest path between a pair of points, called source (s) and destination (t) such that the path is constrained to lie on the surface of the terrain, and for every pair of points p=(x(p),y(p),z(p)) and q=(x(q),y(q),z(q)) on the path, if dist(s,p)