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 two-dimensional curved environment. A complete algorithm is presented and is based on critical visibility events that occur because of inflections and bitangents on the environment boundary. By generalizing the notion of inflections and bitangents to polygonal and piecewise-smooth environments, the approach is considered as a step toward developing pursuit-evasion strategies that have little dependency on the representation of the environment