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Geometric Methods and Applications

For Computer Science and Engineering

  • Textbook
  • © 2001

Overview

Authors:
  1. Jean Gallier

    1. Department of Computer and Information Science, University of Pennsylvania, Philadelphia, USA

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Part of the book series: Texts in Applied Mathematics (TAM, volume 38)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Introduction

    • Jean Gallier
    Pages 1-5

  3. Basics of Affine Geometry

    • Jean Gallier
    Pages 6-61

  4. Properties of Convex Sets: A Glimpse

    • Jean Gallier
    Pages 62-69

  5. Embedding an Affine Space in a Vector Space

    • Jean Gallier
    Pages 70-86

  6. Basics of Projective Geometry

    • Jean Gallier
    Pages 87-161

  7. Basics of Euclidean Geometry

    • Jean Gallier
    Pages 162-196

  8. The Cartan-Dieudonné Theorem

    • Jean Gallier
    Pages 197-247

  9. The Quaternions and the Spaces S3, SU(2), SO(3), and ℝP3

    • Jean Gallier
    Pages 248-266

  10. Dirichlet-Voronoi Diagrams and Delaunay Triangulations

    • Jean Gallier
    Pages 267-286

  11. Basics of Hermitian Geometry

    • Jean Gallier
    Pages 287-308

  12. Spectral Theorems in Euclidean and Hermitian Spaces

    • Jean Gallier
    Pages 309-332

  13. Singular Value Decomposition (SVD) and Polar Form

    • Jean Gallier
    Pages 333-351

  14. Applications of Euclidean Geometry to Various Optimization Problems

    • Jean Gallier
    Pages 352-366

  15. Basics of Classical Lie Groups: The Exponential Map, Lie Groups, and Lie Algebras

    • Jean Gallier
    Pages 367-414

  16. Basics of the Differential Geometry of Curves

    • Jean Gallier
    Pages 415-464

  17. Basics of the Differential Geometry of Surfaces

    • Jean Gallier
    Pages 465-529

  18. Appendix

    • Jean Gallier
    Pages 530-534

  19. Back Matter

    Pages 535-566
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Keywords

About this book

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."

Authors and Affiliations

  • Department of Computer and Information Science, University of Pennsylvania, Philadelphia, USA

    Jean Gallier

Bibliographic Information

  • Book Title: Geometric Methods and Applications

  • Book Subtitle: For Computer Science and Engineering

  • Authors: Jean Gallier

  • Series Title: Texts in Applied Mathematics

  • DOI: https://doi.org/10.1007/978-1-4613-0137-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2001

  • eBook ISBN: 978-1-4613-0137-0Published: 06 December 2012

  • Series ISSN: 0939-2475

  • Series E-ISSN: 2196-9949

  • Edition Number: 1

  • Number of Pages: XXI, 566

  • Topics: Geometry

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