New Results on Visibility in Simple Polygons

We show that (A), 14 points on the boundary of a Jordan curve, and (B), 16 points in convex position encircled by a Jordan curve, cannot be shattered by interior visibility domains. This means that there always exists a subset of the given points, for which no point of the curve’s interior domain sees all points of the subset and no point of its complement. As a consequence, we obtain a new result on guarding art galleries. If each point of the art gallery sees at least an r-th part of the gallery’s boundary, then the art gallery can be covered by 13 · C · r log r guards placed on the boundary. Here, C is the constant from the -net theorem.

• Type: Conference
• Year: 2009
• Where: WADS
• Authors: Alexander Gilbers, Rolf Klein
• Keywords: Curve’s Interior Domain, Interior Visibility Domains, Jordan Curve, WADS 2009