Maximal visibility and unions of orthogonally starshaped sets
Marilyn Breen · Università del Salento · 2009
Let S be an orthogonal polygon in the plane. For each point x in S,let $Vx$ denote the set of points which x sees via staircase paths and let $Mx = {y : Vy = Vx}$. 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 $Mx$, and when this occurs $Mx$ is the staircase kernel of S. In general, if S contains exactly k such distinct closed set $M_{x1},...M_{xk}$, then S is a union of k (or possibly fewer) orthogonally starshaped sets chosen from $V_{x1},...,V_{xk}$.