33 Visibility

In a geometric context, two objects are “visible” to each other if there is a line segment connecting them that does not cross any obstacles. Over 500 papers have been published on aspects of visibility in computational geometry in the last 40 years. The research can be broadly classified as primarily focused on combinatorial issues, or primarily focused on algorithms. We partition the combinatorial work into “art gallery theorems” (Section 33.1) and illumination of convex sets (33.2), and research on visibility graphs (33.3) and the algorithmic work into that concerned with polygons (33.4), more general planar environments (33.5) paths (33.6), and mirror reflections (33.7). All of this work concerns visibility in two dimensions. Investigations in three dimensions, both combinatorial and algorithmic, are discussed in Section 33.8, and the final section (33.9) touches on visibility in R.