An algorithm for polygon placement using a bottom-left strategy

This paper describes a fast and efficient implementation of a bottom-left (BL) placement algorithm for polygon packing. The algorithm allows pieces to be nested within the partial layout produced by previously placed pieces, and produces an optimal BL layout in the sense that the positions considered are guaranteed to contain the bottom-left position of the infinite set of possibilities. Full details of the way in which these positions are calculated are given. Computational experiments comparing the results of different orderings on a variety of datasets from the literature are reported, and these illustrate that problems having in excess of 100 pieces of several piece types can be solved within one minute on a modern desktop PC. The procedure can easily be incorporated into algorithms that apply more sophisticated piece selection procedures.