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    Полное описание

    Gallier, J. Geometric Methods and Applications : for Computer Science and Engineering / by Jean Gallier. - New York, NY : Springer, 2011. - on-line. - (Texts in Applied Mathematics, ISSN 0939-2475 ; vol. 38). - URL: http://dx.doi.org/10.1007/978-1-4419-9961-0. - Загл. с экрана. - ISBN 978-1-4419-9961-0. - Текст : электронный.
    Содержание:
    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.

    ГРНТИ УДК
    27.21514
    50004
    81.1362

    Рубрики:
    mathematics
    computer graphics
    geometry
    mathematical optimization
    control engineering
    robotics
    mechatronics
    mathematics
    geometry
    computer Imaging, Vision, Pattern Recognition and Graphics
    control, Robotics, Mechatronics
    optimization

    Аннотация: 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 machine learning.  This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics.   In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA.  The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers.  Reviews of first edition: "Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001) "...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001)  .

    http://dx.doi.org/10.1007/978-1-4419-9961-0


    Держатели документа:
    Государственная публичная научно-техническая библиотека России : 123298, г. Москва, ул. 3-я Хорошевская, д. 17 (Шифр в БД-источнике (KATBW): -649742435)

    Шифр в сводном ЭК: 9f5ecd4698b9b319a80a5ae64e7053a1



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