Visibility-based pursuit-evasion: the case of curved environments

We consider the problem of visually searching for an unpredictable target that can move arbitrarily fast in a simply-connected, curved, two-dimensional environment. A complete algorithm is presented that is guaranteed to find the elusive target if it is possible for a single pursuer. The key to the algorithm is a cell decomposition based on critical visibility events that occur because of inflections and bitangents of the environment boundary. We have implemented the cell decomposition algorithm, and show several computed examples. The technique is an extension and simplification of a previous technique for searching a polygonal environment. Our solution can also be considered as a step towards a unified approach to pursuit-evasion strategies that have little dependency on the representation of the environment.