Scattering by a boundary with complex structure.

The distribution of escape times is usually studied in open billiards theory. In this work, we will concentrate on another important question: The distribution of outgoing rays by exit directions, which we refer to as billiard's indicatrix. It can be obtained analytically and consists of two parts: the symmetric diffuse part and the asymmetric directed part. The criterion for the separation of the indicatrix into these two parts is established. The asymmetry of the directed part of the indicatrix and the influence of the billiard's borders on it is investigated. We also propose a method of the creation of a matte surface model using open billiards with a fully diffuse indicatrix.