We present a fast, general computational technique for computing the phase-space solution of static Hamilton-Jacobi equations. Start- ing with the Liouville formulation of the characteristic equations, we derive "Escape Equations" which are static, time-independent Eule- rian PDEs. They represent all arrivals to the given boundary from all possible starting configurations. The solution is numerically con- structed through a "one-pass" formulation, building on ideas from semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods.
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