Texts in Applied Mathematics

Geometric Methods and Applications

For Computer Science and Engineering

Authors: Gallier, Jean

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About this Textbook

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

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."


Table of contents (17 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4613-0137-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Methods and Applications
Book Subtitle
For Computer Science and Engineering
Authors
Series Title
Texts in Applied Mathematics
Series Volume
38
Copyright
2001
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4613-0137-0
DOI
10.1007/978-1-4613-0137-0
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XXI, 566
Topics