  We present a method for determining optimal walking paths in steep terrain
using the level set method and an optimal control formulation. By viewing the
walking direction as a control variable, we can determine the optimal control
by solving a Hamilton-Jacobi-Bellman equation. We then calculate the optimal
walking path by solving an ordinary differential equation. We demonstrate the
effectiveness of our method by computing optimal paths which travel throughout
mountainous regions of Yosemite National Park. We include details regarding the
numerical implementation of our model and address a specific application of a
law enforcement agency patrolling a nationally protected area.
