Geometric Methods and Applications
For Computer Science and Engineering
1st Edition
Published on 1. December 2000
Book
Hardback
XXI, 565 pages
978-0-387-95044-0 (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
Language
English
Place of publication
New York, NY
United States
Target group
College/higher education
Professional and scholarly
Research
Edition type
New edition
Product notice
Laminated cover
Illustrations
77 s/w Abbildungen
1, black & white illustrations
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 34 mm
Weight
2210 gr
ISBN-13
978-0-387-95044-0 (9780387950440)
Schweitzer Classification
Other editions
New editions
Book
06/2011
2nd Edition
Springer
€117.69
Shipment within 15-20 days
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-Dieudonné 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.