Review of visibility algorithms in the plane by Subir Kumar Ghosh (Cambridge University Press, 2007)

Abstract

Computational Geometry is a young field, tracing its beginnings to the PhD thesis of Michael Shamos [6] in 1978. Its many applications include, to name a few, computer graphics and imaging, robotics and computer vision, and geometric information systems. Topics studied within computational geometry include arrangements, convex hulls, partitions, triangulation of polygons, Voronoi diagrams, and visibility. One of the most famous theorems in computational geometry is the Art Gallery Theorem, and this theorem also serves as an example of the focus of the book under review. Posed by Victor Klee in 1973, it asks how many stationary guards are required to see all points in an art gallery represented by a simple, n-sided polygon. The answer, given first by Chvatal [3] and later by Fisk [5], using an elegant graph-theoretic proof, is that bn/3c guards are always sufficient and may be necessary. Questions such as this one, of visibility within a polygon, are the subject of Visibility Algorithms in the Plane, by S. Ghosh.