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.

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.