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Art Gallery Visibility Theorems: An Introduction

© Joseph O'Rourke 2026, 2027

Cambridge University Press

158 pages, 121 figures, 52 exercises. Publication: Mar 2027. ISBN 9781047769693.

Cover
Fig.3.2 One point guard in the kernel covers the whole polygon. Halfplane boundaries bound the kernel.
See also original 1987 book: Art Gallery Theorems and Algorithms (freely downloadable).
Illuminating orthogonal polygon. n=34, [n/4] = 8.
Fig.9.11(b) Tokarsky polygon: x cannot see/illuminate y
Fig.9.18. Pach's mirror forest.
100 disjoint trees, 100 lightrays from a single light source,
after about half have escaped.
[Calculations by student Octavia Petrovici.]

Templates

Articles of Interest

Art Gallery Visibility Theorems

Fig, 3.3

Star-shaped polygon

Fig. 4.8

Contiguous lower bound

Fig. 5.1

Orthogonal polygon

Fig. 5.2

Orthogonal spiral

Fig. 7.8b

Brocard point

Fig. 8.3

Find 2-kernel

Fig. 8.9

Orthogonal spiral

Fig. 9.10

Find lightray x to y

Fig. 9.14

Orthogonal Tokarsky polygon

Articles of Interest