Algorithms for polyominoes based on the discrete Green theorem

Authors:
S. Brlek;G. Labelle;A. Lacasse
Affiliations:
LaCIM, Université du Québec à Montréal, C.P. 8888 Succursale "Centre-Ville", Montréal(QC), Canada H3C 3P8;LaCIM, Université du Québec à Montréal, C.P. 8888 Succursale "Centre-Ville", Montréal(QC), Canada H3C 3P8;LaCIM, Université du Québec à Montréal, C.P. 8888 Succursale "Centre-Ville", Montréal(QC), Canada H3C 3P8
Venue:
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Year:
2005

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Abstract

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.