Geometric Methods and Applications
Published on 1. November 2000
Book
Paperback/Softback
586 pages
978-1-4612-6509-2 (ISBN)
Description
As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, 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 / Votes
From the reviews: SIAM REVIEW "The treatment of each topic is in depth and to the point. It is a rigorous theorem-proof approach on the one hand, but there are plenty of comments and remarks that make for easier reading. The level of the book, if intended for engineers and computer scientists, is advance graduate...The style of the book is often refreshingly informal but never lacks rigor and precision. Each chapter has a copious section of problems. These are not just simple questions such as 'prove theorem xy,' but are thorough investigations of subtopics, in a way that will certainly motivate a student's desire to explore that topic further...I am a mathematician embedded in a computer science environment, and I will certainly study some of the chapters in this book in more depth." MATHEMATICAL REVIEWS "The presentation of the material is mathematically rigorous, including precise definitions and proofs for almost all results...Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications."More details
Series
Edition
Softcover reprint of the original 1st ed. 2001
Language
English
Place of publication
New York, NY
United States
Target group
Professional and scholarly
Illustrations
1 black & white illustrations
Dimensions
Height: 235 mm
Width: 155 mm
Weight
896 gr
ISBN-13
978-1-4612-6509-2 (9781461265092)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Book
04/2013
2nd Edition
Springer
€85.59
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Book
06/2011
2nd Edition
Springer
€117.69
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Additional editions
E-Book
12/2012
1st Edition
Springer
€82.38
Available for download
Content
Preface.- Introduction.- Basics of Affine Geometry.- Properties of Convex Sets, A Glimpse.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- The Cartan-Dieudonne Theorem.- Quaternions and Rotations.- Dirichlet-Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.- Applications of Euclidean Geometry.- Basics of Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- Bibliography.- Index.