Flow-related structures on terrains are defined in terms of paths of steepest descent (or ascent). A steepest descent path on a polyhedral terrain T with n vertices can have T(n2) complexity, since at worst case the path can cross T(n) triangles for T(n) times each. We present a technique for tracing a path of steepest descent on T in O(n log n) time implicitly, without computing all the intersection points of the path with the terrain triangles
