Overview

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 specialist in the field and together they are intended to provide a clear picture of what computational Euclidean geometry is and the direction in which research is going.

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9789810209667

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""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

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

"""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"

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