Handbook of Discrete and Computational Geometry

The Handbook of Discrete and Computational Geometry serves as a comprehensive reference text covering fundamental concepts and recent developments in geometric computing. This volume brings together contributions from experts across computational geometry, discrete geometry, and related mathematical disciplines. The book contains sections on core topics like convex hulls, Voronoi diagrams, triangulations, and geometric data structures. Additional chapters explore applications in robotics, computer graphics, geometric modeling, and computational topology. Each chapter provides theoretical foundations, key algorithms, implementation considerations, and open research problems. The text includes hundreds of illustrations, pseudocode, and references to support both theoretical understanding and practical implementation. This handbook bridges pure mathematics and computer science, demonstrating how geometric theory translates into computational methods that solve real-world problems. The work stands as a key resource for researchers, practitioners and students working at the intersection of geometry and computing.

Readers cite this as a comprehensive reference text for computational geometry researchers and graduate students. Reviews note its detailed coverage of both foundational topics and advanced concepts. Likes: - Clear organization makes it useful as a reference - Thorough citations and bibliography - Problems and exercises help with learning - Each chapter written by subject matter experts Dislikes: - Dense mathematical notation can be challenging for beginners - Some chapters are more technical than others - Price point is high for individual purchase - Limited coverage of implementation details Ratings: Goodreads: 4.25/5 (12 ratings) Amazon: 4.3/5 (6 ratings) One reviewer on Amazon noted it serves better as a reference than a textbook: "Not ideal for self-study, but invaluable on my shelf when I need to look up specific geometric algorithms and proofs." A Goodreads review praised the comprehensive scope but cautioned: "Requires strong math background to get full value."

Discrete and Combinatorial Mathematics by Ralph P. Grimaldi Presents geometric concepts through combinatorial methods while connecting discrete mathematics to computational applications.

Computational Geometry: Algorithms and Applications by Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars Covers fundamental geometric algorithms with implementation details and practical applications in computer graphics and robotics.

Introduction to Graph Theory by Richard J. Trudeau Bridges geometric visualization with graph theory principles through mathematical proofs and geometric representations.

Geometric Algorithms and Combinatorial Optimization by Martin Grötschel, László Lovász, and Alexander Schrijver Integrates geometric methods with optimization theory for solving computational problems in discrete mathematics.

Computational Geometry: An Introduction by Franco P. Preparata, Michael Ian Shamos Establishes core theoretical foundations of computational geometry with emphasis on algorithm design and analysis.

🔷 The book, first published in 1997 and now in its third edition (2017), has become a cornerstone reference in computational geometry, cited over 4,000 times in academic works. 🔷 Joseph O'Rourke pioneered the field of "folding and unfolding" in geometry, which has applications in robotics, protein folding, and deployable structures in space technology. 🔷 Computational geometry, the subject of the handbook, helps solve real-world problems like collision detection in video games, computer-aided design (CAD), and geographic information systems (GIS). 🔷 The author maintains an open problem collection called "The Open Problems Project" (TOPP) that has influenced research directions in computational geometry for decades. 🔷 While serving as a professor at Smith College, O'Rourke not only contributed to mathematics and computer science but also published works in art theory, exploring the intersection of geometry and artistic expression.