An algorithm to find the number of the digitizations of discs with a fixed radius

For digitizations a grid is given, usually it is considered as Z2. The digital image of a real object depends on the respective position of the object and the grid. In this paper we consider the simplest objects of the plane: the Euclidean circles (real and open discs) are given by a fixed radius. We present an algorithm which results all possible digital images of these real discs. Moreover discrete data-sets of these digital images are presented.