| Effective Computational Geometry for Curves and Surfaces 2006 Edition Contributor(s): Boissonnat, Jean-Daniel (Editor), Teillaud, Monique (Editor) |
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ISBN: 3540332588 ISBN-13: 9783540332589 Publisher: Springer OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: October 2006 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Applied - Mathematics | Number Systems - Computers | Computer Vision & Pattern Recognition |
| Dewey: 004 |
| LCCN: 2006931844 |
| Series: Mathematics and Visualization |
| Physical Information: 1.02" H x 6.41" W x 9.44" (1.48 lbs) 344 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 |