Maximal visibility and unions of orthogonally starshaped sets


Let S be an orthogonal polygon in the plane. For each point x in S,let V<sub>x</sub> denote the set of points which x sees via staircase paths and let(Error rendering LaTeX formula). For S simply connected, S is starshaped via staircase paths (i.e., orthogonally starshaped) if and only if S contains exactly one such closed set M<sub>x</sub>, and when this occurs M<sub>x</sub> is the staircase kernel of S. In general, if S contains exactly k such distinct closed set M_{x<sub>1</sub>},...M_{x<sub>k</sub>}, then S is a union of k (or possibly fewer) orthogonally starshaped sets chosen from V_{x<sub>1</sub>},...,V_{x<sub>k</sub>}.

DOI Code: 10.1285/i15900932v24n1p1

Keywords: Orthogonal polygons; Starshaped via staircase paths

Classification: 52A30

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