Abstract
Given a simple polygon in the plane we devise a quadratic algorithm for determining the existence of, and constructing, a tiling of the polygon with parallelograms. We also show that any two parallelogram tilings can be obtained from one another by a sequence of “rotations,” and give a condition for the uniqueness of such a tiling. Three generalizations of this problem, that of tiling by a fixed set of triangles, a fixed set of trapezoids, or parallelogram tiling for polygonal regions with holes, are shown to be NP-complete.
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Communicated by Jean-Daniel Bolssonnat.
Parts of this paper originally appeared in a technical report for the conference “Journées de Géometrie Algorithmique” at Sophia-Antipolis, France, under the same title. The author was supported by a Chateaubriand Fellowship and this work was partially completed while the author was at Princeton University, supported by an IBM graduate fellowship.
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Kenyon, R. Tiling a polygon with parallelograms. Algorithmica 9, 382–397 (1993). https://doi.org/10.1007/BF01228510
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DOI: https://doi.org/10.1007/BF01228510