Art Gallery Theorems and Algorithms by Joseph O'Rourke
Art Gallery Theorems and Algorithms - Table of Contents
1. Polygon Partitions
2. Orthogonal Polygons
3. Mobile Guards
4. Miscellaneous Shapes
5. Holes
6. Exterior Visibility
7. Visibility Graphs
8. Visibility Algorithms
9. Minimal Guard Covers
10. Three Dimensions and Miscellany
What You Will Learn in Art Gallery Theorems and Algorithms
"Art Gallery Theorems and Algorithms" by "Joseph O’Rourke" is a foundational book in "computational geometry" that studies visibility problems in polygonal spaces. The book is centered on the famous "art gallery problem", which asks how many guards are needed to observe every point inside a polygonal gallery. O’Rourke presents the problem in a clear, structured way, combining mathematical theory with practical algorithmic thinking.
The book develops key "geometric theorems" and algorithmic techniques used to analyze visibility, including polygon triangulation, partitioning methods, and guard placement strategies. It explores different gallery models such as simple polygons, orthogonal polygons, and galleries with holes. The text also introduces efficient "visibility algorithms" and discusses their computational complexity, making it valuable for understanding both theory and implementation.
Written for advanced undergraduates, graduate students, and researchers, the book remains a classic reference in "algorithm design" and discrete geometry. Although later research has expanded the field, O’Rourke’s work is still widely cited for its clarity, rigorous proofs, and strong connection between geometric insight and algorithmic solutions.
Book Details & Specifications
Title:
Art Gallery Theorems and Algorithms by Joseph O'Rourke
Publisher:
Oxford University Press
Year:
1987
Pages:
296
Type:
PDF
Language:
English
ISBN-10 #:
0195039653
ISBN-13 #:
978-0195039658
License:
External Educational Resource
Amazon:
Amazon
About the Author: Joseph O'Rourke
The author
Joseph O'Rourke
is a well-known "American computer scientist" and mathematician recognized for his work in "computational geometry". He served as a professor at "Smith College", where he researched geometric algorithms, polygon theory, and visibility problems in mathematics and computer science. O’Rourke is especially famous for "Art Gallery Theorems and Algorithms", a landmark book on the "art gallery problem" and "geometric algorithms". His clear writing and rigorous approach have made complex geometric concepts accessible to students and researchers worldwide.
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