Geometric Methods and Applications : For Computer Science and Engineering

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...

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Main Author: Gallier, Jean
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: New York, NY Springer New York 2011, 2011
Edition:2nd ed. 2011
Series:Texts in Applied Mathematics
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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