Maximal visibility and unions of orthogonally starshaped sets
Abstract
Let S be an orthogonal polygon in the plane. For each point x in S,let
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
, and when this occurs
is the staircase kernel of S. In general, if S contains exactly k such distinct closed set
, then S is a union of k (or possibly fewer) orthogonally starshaped sets chosen from
.
![V<sub>x</sub>](http://212.189.136.205/plugins/generic/latexRender/cache/e6a8a101c9a381fff64e11e3f2a20f48.png)
![M<sub>x</sub>](http://212.189.136.205/plugins/generic/latexRender/cache/e64478f604ac1cc364b8846d1ae3ccec.png)
![M<sub>x</sub>](http://212.189.136.205/plugins/generic/latexRender/cache/e64478f604ac1cc364b8846d1ae3ccec.png)
![M_{x<sub>1</sub>},...M_{x<sub>k</sub>}](http://212.189.136.205/plugins/generic/latexRender/cache/99dfd9f3debc3845429d7fd070fe6696.png)
![V_{x<sub>1</sub>},...,V_{x<sub>k</sub>}](http://212.189.136.205/plugins/generic/latexRender/cache/d73a1f1104bcad0db0502e46380897a6.png)
DOI Code:
10.1285/i15900932v24n1p1
Keywords:
Orthogonal polygons; Starshaped via staircase paths
Classification:
52A30
Full Text: PDF