Ebook: 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.

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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:
Front Matter....Pages i-xxi
Introduction....Pages 1-5
Basics of Affine Geometry....Pages 6-61
Properties of Convex Sets: A Glimpse....Pages 62-69
Embedding an Affine Space in a Vector Space....Pages 70-86
Basics of Projective Geometry....Pages 87-161
Basics of Euclidean Geometry....Pages 162-196
The Cartan-Dieudonn? Theorem....Pages 197-247
The Quaternions and the Spaces S 3, SU(2), SO(3), and ?P 3 ....Pages 248-266
Dirichlet-Voronoi Diagrams and Delaunay Triangulations....Pages 267-286
Basics of Hermitian Geometry....Pages 287-308
Spectral Theorems in Euclidean and Hermitian Spaces....Pages 309-332
Singular Value Decomposition (SVD) and Polar Form....Pages 333-351
Applications of Euclidean Geometry to Various Optimization Problems....Pages 352-366
Basics of Classical Lie Groups: The Exponential Map, Lie Groups, and Lie Algebras....Pages 367-414
Basics of the Differential Geometry of Curves....Pages 415-464
Basics of the Differential Geometry of Surfaces....Pages 465-529
Appendix....Pages 530-534
Back Matter....Pages 535-566

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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:
Front Matter....Pages i-xxi
Introduction....Pages 1-5
Basics of Affine Geometry....Pages 6-61
Properties of Convex Sets: A Glimpse....Pages 62-69
Embedding an Affine Space in a Vector Space....Pages 70-86
Basics of Projective Geometry....Pages 87-161
Basics of Euclidean Geometry....Pages 162-196
The Cartan-Dieudonn? Theorem....Pages 197-247
The Quaternions and the Spaces S 3, SU(2), SO(3), and ?P 3 ....Pages 248-266
Dirichlet-Voronoi Diagrams and Delaunay Triangulations....Pages 267-286
Basics of Hermitian Geometry....Pages 287-308
Spectral Theorems in Euclidean and Hermitian Spaces....Pages 309-332
Singular Value Decomposition (SVD) and Polar Form....Pages 333-351
Applications of Euclidean Geometry to Various Optimization Problems....Pages 352-366
Basics of Classical Lie Groups: The Exponential Map, Lie Groups, and Lie Algebras....Pages 367-414
Basics of the Differential Geometry of Curves....Pages 415-464
Basics of the Differential Geometry of Surfaces....Pages 465-529
Appendix....Pages 530-534
Back Matter....Pages 535-566
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