Geometric Methods and Applications

For Computer Science and Engineering

  • Jean Gallier

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

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Jean Gallier
    Pages 1-5
  3. Jean Gallier
    Pages 7-63
  4. Jean Gallier
    Pages 65-83
  5. Jean Gallier
    Pages 103-175
  6. Jean Gallier
    Pages 177-212
  7. Jean Gallier
    Pages 213-229
  8. Jean Gallier
    Pages 231-280
  9. Jean Gallier
    Pages 321-342
  10. Jean Gallier
    Pages 387-410
  11. Jean Gallier
    Pages 411-430
  12. Jean Gallier
    Pages 431-437
  13. Jean Gallier
    Pages 439-457
  14. Jean Gallier
    Pages 655-658
  15. Back Matter
    Pages 659-680

About this book


This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning.

 This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics.

  In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA.

 The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

 Reviews of first edition:

"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." (Mathematical Reviews, 2001)

" will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001)



Affine Geometry Convex Optimization Euclidean Geometry Projective geometry

Authors and affiliations

  • Jean Gallier
    • 1
  1. 1., Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-9960-3
  • Online ISBN 978-1-4419-9961-0
  • Series Print ISSN 0939-2475
  • Buy this book on publisher's site