Geometric Methods and Applications : For Computer Science and Engineering
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
1 online resource (xxi, 565 pages 77 illustrations)
9781461301370, 9780387950440, 1461301378, 0387950443
852788805
Print version:
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
English