Algorithms for polyominoes based on the discrete Green theorem

The use of Green's theorem and bivariate difference calculus provides a general and unifying framework for the description and generation of incremental algorithms. The method is applied in order to provide algorithms computing various statistics about polyominoes coded by 4-letter words describing their contour. These statistics include area, coordinates of the center of gravity, moment of inertia, size of projections, hook lengths, number of pixels in common with a given set of pixels, in particular the intersection of two polyominoes and also q-statistics for projections.