Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization) - Hardcover

Hardcover

ISBN 10: 3540332588 ISBN 13: 9783540332589

Publisher: Springer, 2006

Synopsis

Computational geometry emerged as a discipline in the seventies and has had considerable success in improving the asymptotic complexity of the solutions tobasicgeometricproblemsincludingconstructionsofdatastructures,convex hulls, triangulations, Voronoi diagrams and geometric arrangements as well as geometric optimisation. However, in the mid-nineties, it was recognized that the computational geometry techniques were far from satisfactory in practice and a vigorous e?ort has been undertaken to make computational geometry more practical. This e?ort led to major advances in robustness, geometric software engineering and experimental studies, and to the development of a large library of computational geometry algorithms, Cgal. The goal of this book is to take into consideration the multidisciplinary nature of the problem and to provide solid mathematical and algorithmic foundationsfore?ectivecomputationalgeometryforcurvesandsurfaces. This book covers two main approaches. In a ?rst part, we discuss exact geometric algorithms for curves and s- faces. We revisit two prominent data structures of computational geometry, namely arrangements (Chap. 1) and Voronoi diagrams (Chap. 2) in order to understand how these structures, which are well-known for linear objects, behave when de?ned on curved objects. The mathematical properties of these structures are presented together with algorithms for their construction. To ensure the e?ectiveness of our algorithms, the basic numerical computations that need to be performed are precisely speci?ed, and tradeo?s are considered between the complexity of the algorithms (i. e. the number of primitive calls), and the complexity of the primitives and their numerical stability. Chap.

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Review

From the reviews:

"Boissonat and Teillaud have collected in this book the foundations of a computational geometry that no longer deals exclusively with linear objects but also with curved objects that arise in applications. The book is composed of eight chapters written by teams of experts in each theme, and is the result of an European Union project named ECG. The book can serve as an advanced graduate course on computational geometry and as a reference for researchers interested in geometric algorithms for curved objects." (Luiz Henrique de Figueiredo, MathDL, March, 2007)

Synopsis

The intent of this book is to settle the foundations of non-linear computational geometry. It covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter provides a state of the art, as well as a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. References to open source software and discussion of potential applications of the presented techniques are also included. This book can serve as a textbook on non-linear computational geometry. It will also be useful to engineers and researchers working in computational geometry or other fields, like structural biology, 3-dimensional medical imaging, CAD/CAM, robotics, and graphics.

Edition details

• Publisher: Springer
• Publication date: 2006
• Language: English
• ISBN 10: 3540332588
• ISBN 13: 9783540332589
• Binding: Hardcover
• Number of pages: 356
• Editor: Boissonnat Jean-Daniel, Teillaud Monique