Abstract
Let S be a simply connected orthogonal polygon in the plane. Assume that S is starshaped via staircase paths with corresponding staircase kernel K, where K ≠ S. For every point x in \({S \backslash K}\), define W x = {s : s lies on some staircase path in S from x to a point of K}. Then there is a minimal collection \({\mathcal{W}}\) of W x sets whose union is S. Moreover, \({\mathcal{W}}\) is unique and finite. Finally \({\mathcal{W}}\) is exactly the collection of maximal W x sets in S.
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Breen, M. Generating a staircase starshaped set from a minimal collection of its subsets. Beitr Algebra Geom 52, 113–123 (2011). https://doi.org/10.1007/s13366-011-0009-y
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DOI: https://doi.org/10.1007/s13366-011-0009-y