Lecture Notes Series on Computing - Vol. 1
COMPUTING IN EUCLIDEAN GEOMETRY
edited by Ding-Zhu Du (University of Minnesota) & Frank Hwang (AT&T Bell Laboratories)
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.
Contents:
- Mesh Generation and Optimal Triangulation (M Bern & D
Eppstein)
- Machine Proofs of Geometry Theorems (S-C Chou & M Rathi)
- Randomized Geometric Algorithms (K L Clarkson)
- Voronoi Diagrams and Delauney Triangulations (S Fortune)
- The State of Art on Steiner Ratio Problems (D-Z Du & F Hwang)
- On the Development of Quantitative Geometry from Pythagoras to Grassmann (W-Y Hsiang)
- Computational Geometry and Topological Network Design (J M Smith & P Winter)
- Polar Forms and Triangular B-Spline Surfaces (H-P Seidel)
Readership: Computer scientists and mathematicians.
"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 |
| 400pp |
Pub. date: Sept 1992 |
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