Geometric Methods and Applications: For Computer Science and Engineering [Hardcover]

Jean Gallier (Author)

Book Description

ISBN-10: 0387950443 | ISBN-13: 978-0387950440 | Publication Date: November 3, 2000 | Edition: 1

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.

Editorial Reviews

Review

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."

From the Back Cover

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) "...it 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)   --This text refers to an alternate Hardcover edition.

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Product Details

• Hardcover: 565 pages
• Publisher: Springer; 1 edition (November 3, 2000)
• Language: English
• ISBN-10: 0387950443
• ISBN-13: 978-0387950440
• Product Dimensions: 9.3 x 6.3 x 1.5 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,089,111 in Books (See Top 100 in Books)

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21 of 21 people found the following review helpful:

5.0 out of 5 stars Fantastic! One of a kind., January 12, 2001

By A Customer

This review is from: Geometric Methods and Applications: For Computer Science and Engineering (Hardcover)

This is a beautiful and unique book. The style is lively and the explanations are remarkably clear. The author makes a significant effort to demistify concepts before defining them rigorously and proving facts about them. It is impressive to see the variety of the topics covered in the book. For example, there is a nice and easy introduction to Lie groups and Lie algebras, and an exquisite treatment of the elementary differential geometry of curves and surfaces. As the author states, this material is a write-up of lectures given by the famous geometer Eugene Calabi (of the Calabi-Yau manifolds!), and this is quite a treat. Gallier's presentation definitely rivals do Carmo, one of the best. It is also refreshing and illuminating to see topics such as QR-decomposition and decomposition in terms of Householder matrices, treated from a geometric point of view. For that matter, the treatment of polar forms and SVD is superior, although perhaps a bit abstract for my taste. There are lots of problems, including programming projects. At first glance, the problems are on the hard side. This could turn off some students. In conclusion, this is a great book. Even though it is very well written, this is not an "easy book". However, perseverant readers will find its reading very rewarding. It is a great preparation for more advanced books on Lie groups, differential geometry, and projective and algebraic geometry. The sections on applications are very nice, but there should be more and they should be more extensive. Oh, I was forgetting, the internet supplement is great. For example, there is a wonderful treatment of rational curves and surfaces. Every geometry lover should have this book!