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 | | Geometric Methods and Applications: For Computer Science and Engineering by Jean Gallier ISBN-10: 0387950443 ISBN-10: 0-387-95044-3 ISBN-13: 9780387950440 ISBN-13: 978-0-387-95044-0 Hardcover 2000-11-03 Springer Find Lowest Price |
Editorials | ||
Product Description As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics, which sometimes do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine geometry, projective geometry, Euclidean geometry, basics of differential geometry and Lie groups, and a glimpse of computational geometry (convex sets, Voronoi diagrams and Delaunay triangulations) and explores many of the practical applications of geometry. Some of these applications include computer vision (camera calibration) efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers. | ||
Reviews | ||
Fantastic! One of a kind. This is a beautiful and unique book. The style is lively and the explanations are remarkably clear. The author makes a significant effort to demistify concepts before defining them rigorously and proving facts about them. It is impressive to see the variety of the topics covered in the book. For example, there is a nice and easy introduction to Lie groups and Lie algebras, and an exquisite treatment of the elementary differential geometry of curves and surfaces. As the author states, this material is a write-up of lectures given by the famous geometer Eugene Calabi (of the Calabi-Yau manifolds!), and this is quite a treat. Gallier's presentation definitely rivals do Carmo, one of the best. It is also refreshing and illuminating to see topics such as QR-decomposition and decomposition in terms of Householder matrices, treated from a geometric point of view. For that matter, the treatment of polar forms and SVD is superior, although perhaps a bit abstract for my taste. There are lots of problems, including programming projects. At first glance, the problems are on the hard side. This could turn off some students. In conclusion, this is a great book. Even though it is very well written, this is not an "easy book". However, perseverant readers will find its reading very rewarding. It is a great preparation for more advanced books on Lie groups, differential geometry, and projective and algebraic geometry. The sections on applications are very nice, but there should be more and they should be more extensive. Oh, I was forgetting, the internet supplement is great. For example, there is a wonderful treatment of rational curves and surfaces. Every geometry lover should have this book! | ||