Geometric Methods and Applications For Computer Science and Engineering /

• Main Author: Gallier, Jean (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2011.
• Series: Texts in Applied Mathematics, 38
• Subjects: Mathematics.; Computer graphics.; Geometry.; Mathematical optimization.; Control engineering.; Robotics.; Mechatronics.; Computer Imaging, Vision, Pattern Recognition and Graphics.; Control, Robotics, Mechatronics.; Optimization.

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 m...

Table of Contents:

• Introduction
• Basics of Affine Geometry
•  Basic Properties of Convex Sets
• Embedding an Affine Space in a Vector Space
• Basics of Projective Geometry
• Basics of Euclidean Geometry
• Separating and Supporting Hyperplanes; Polar Duality
• Polytopes and Polyhedra
• The Cartan–Dieudonn´e Theorem
• The Quaternions and the Spaces S3, SU(2), SO(3), and RP3
•  Dirichlet–Voronoi Diagrams
• Basics of Hermitian Geometry
• Spectral Theorems
•  Singular Value Decomposition (SVD) and Polar Form
• Applications of SVD and Pseudo-Inverses
• Quadratic Optimization Problems
• Schur Complements and Applications
• Quadratic Optimization and Contour Grouping
• Basics of Manifolds and Classical Lie Groups
• Basics of the Differential Geometry of Curves
• Basics of the Differential Geometry of Surfaces
• Appendix
• References
• Symbol Index
• IndexAppendix
• References
• Symbol Index
• Index.