This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.
Arvustused
"D-Z Du and F Hwang have put to rest an optimization problem known as the Steiner ratio conjecture. Their solution closes the book on a problem that had frustrated a generation of geometers, but it also writes the first chapter of a new volume. The key to Du and Hwang's successful attack on the conjecture is a new method that has potential for solving a raft of other optimization problems." Barry A Cipra SIAM News, USA "... the eight surveys are well organized. Each survey is preceded by a good introductory section with a rich bibliography. Both beginners and experts will benefit from this book." Jie Tian Mathematical Reviews "The papers are not just summaries; the authors present new material or fresh points of view ... I recommend the book to anyone who works in one of the areas surveyed or who is interested in the interaction of Euclidean geometry and computers." Carol Hazlewood IEEE Parallel & Distributed Technology
Mesh generation and optimal triangulation, M. Bern and D. Eppstein;
machine proofs of geometry theorems, S.C. Chou and M. Rethi; randomized
geometric algorithms, K. Clarkson; Voronoi diagrams and Delanney
triangulations, S. Fortune; the state of art on Steiner ratio problems, D-Z.
Du and F. Hwang; on the development of quantitative geometry from Pythagoras
to Grassmann, W-Y. Hsiang; computational geometry and topological network
designs, J. Smith and P. Winter; polar forms and triangular B-spline
surfaces, H-P. Seidel; algebraic foundations of computational geometry, Chee
Yap.
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