In this talk, we present our ideas for the search of a path in R^2 or R^3 that maximizes certain optimality conditions involving visibility. The visiblity is defined as the solution of a watered down high frequency wave propagation problem in the presence of occluders with complicated geometry.
Related applications include certain types of path-planning and pursuer-evader problems.
This framework uses a function that encodes visibility information in a continuous way. This continuity allows for powerful techniques to be
used in the discrete setting for interpolation, integration, differentiation, and set operations. Using these tools, we are able to limit the scope of search and produce locally optimized solutions.
This is joint work with Li-Tien Cheng
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