A path from $s$ to $t$ on a polyhedral terrain is descending if the height of a point $p$ never increases while we move p along the path from $s$ to $t$. No efficient algorithm is known to find a shortest descending path (SDP) from $s$ to $t$ in a polyhedral terrain. We will discuss the pros and cons for finding the optimum path on general terrains and finally discuss an approximation algorithm that solve the SDP problem on general terrains. Our algorithm is simple, robust and easy to implement.
