Jean Gallier

Geometric Methods and Applications

For Computer Science and Engineering

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Texts in Applied Mathematics 38
• Verlag: Springer, Berlin
• 2000.
• Seitenzahl: 565
• Englisch
• Abmessung: 240mm
• Gewicht: 996g
• ISBN-13: 9780387950440
• ISBN-10: 0387950443
• Artikelnr.: 09175004

Inhaltsangabe

Preface.- Introduction.- Basics of Affine Geometry.- Properties of Convex Sets, A Glimpse.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- The Cartan-Dieudonné Theorem.- Quaternions and Rotations.- Dirichlet-Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.- Applications of Euclidean Geometry.- Basics of Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- Bibliography.- Index.

Rezensionen

From the reviews:

"This is a worthwhile book to have in the library of any univeristy which is involved with these areas of computer science." (The Mathematical Gazette, 2002)

"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." (SIAM Review, 2002)

From the reviews of the second edition:

"The book contains a valuable collection of modern geometric methods and algorithms readily prepared for solving problems occurring in computer science and engineering. ... The second edition is even more comprehensive and puts more emphasis on the links between different fields. It can be recommended to anybody who is interested in modern geometry and its applications." (Anton Gfrerrer, Zentralblatt MATH, Vol. 1247, 2012)

"Anyone who likes to read about geometry, differential geometry, linear algebra, or Lie theory should find something of interest in this book. ... this is, of course, a text in geometry, and many aspects of it are covered. ... this book is filled with interesting mathematics, superbly presented. Aside from its potential use as a text, the book should be looked at by anyone who uses or is interested in the topics covered. It is highly recommended." (Mark Hunacek, The Mathematical Association of America, September, 2011)