Journal
THEORETICAL COMPUTER SCIENCE
Volume 346, Issue 2-3, Pages 200-225Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.tcs.2005.08.019
Keywords
discrete Green Theorem; discrete geometry; polyominoes
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The discrete version of Green's Theorem and bivariate difference calculus provide a general and unifying framework for the description and generation of incremental algorithms. It may be used to compute various statistics about regions bounded by a finite and closed polygonal path. More specifically, we illustrate its use for designing algorithms computing many statistics about polyominoes, regions whose boundary is encoded by four letter words: area, coordinates of the center of gravity, moment of inertia, set characteristic function, the intersection with a given set of pixels, hook-lengths, higher order moments and also q-statistics for projections. (c) 2005 Published by Elsevier B.V.
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