Abstract: Hamilton-Jacobi type (HJ) PDEs arise in optimal control, dynamic implicit surfaces for fluid animation and simulation, image processing, and many other fields. There are two broad classes of equations: time-dependent and stationary. Level set methods are a group of finite difference algorithms for the former class of equations, and I will describe a publicly released toolbox of Matlab routines for approximating a wide variety of common HJ forms in any
dimension. I will then describe and analyze a new algorithm for solving the stationary form of HJ equations. Finally, I will discuss applications of each of the two forms: reachable sets for the verification of continuous systems, and optimal path planning with multiple objectives.

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