© 2001

Geometric Methods and Applications

For Computer Science and Engineering


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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Jean Gallier
    Pages 1-5
  3. Jean Gallier
    Pages 6-61
  4. Jean Gallier
    Pages 62-69
  5. Jean Gallier
    Pages 87-161
  6. Jean Gallier
    Pages 162-196
  7. Jean Gallier
    Pages 197-247
  8. Jean Gallier
    Pages 287-308
  9. Jean Gallier
    Pages 530-534
  10. Back Matter
    Pages 535-566

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.


Triangulation communication computational geometry computer graphics computer vision cryptography differential geometry differential geometry of surfaces geometry modeling robotics sets

Authors and affiliations

  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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
  • Copyright Information Springer-Verlag New York, Inc. 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-95044-0
  • Softcover ISBN 978-1-4612-6509-2
  • eBook ISBN 978-1-4613-0137-0
  • Series ISSN 0939-2475
  • Edition Number 1
  • Number of Pages XXI, 566
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site


From the reviews:


"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."


"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."