  We propose an algorithm using method of evolving junctions to solve the
optimal path planning problems with piece-wise constant flow fields. In such
flow fields with a convex Lagrangian in the objective function, we can prove
that the optimal trajectories must be formed by constant velocity motions.
Taking advantage of this property, we transform the infinite dimensional
optimal control problem into a finite dimensional optimization and use
intermittent diffusion to solve the problems. The algorithm is proven to be
complete. At last, we demonstrate the performance of the algorithm with various
simulation examples.
