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
CONTENT
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-Dieudonnรฉ 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
