PirateBay Download | dorst l geometric algebra computer science 2007

dorst l geometric algebra computer science 2007

Type:: E-books
Files:: 1
Size:: 5.8 MB
Uploaded On:: Nov. 28, 2022, 2:18 p.m.
Added By:: andryold1
Seeders:: 1
Leechers:: 0
Info Hash:: 6D61D0A7A9B52F5A8FDCED3F5B61E67B71A05BDC

Textbook in PDF format Geometric algebra is a powerful and practical framework for the representation and solution of geometrical problems. We believe it to be eminently suitable to those subfields of computer science in which such issues occur: computer graphics, robotics, and computer vision. We wrote this book to explain the basic structure of geometric algebra, and to help the reader become a practical user. We employ various tools to get there: Explanations that are not more mathematical than we deem necessary, connecting algebra and geometry at every step. A large number of interactive illustrations to get the object-oriented feeling of constructions that are dependent only on the geometric elements in them (rather than on coordinates) Drills and structural exercises for almost every chapter Detailed programming examples on elements of practical applications An extensive section on the implementational aspects of geometric algebra (Part III of this book) This is the first book on geometric algebra that has been written especially for the computer science audience. When reading it, you should remember that geometric algebra is fundamentally simple, and fundamentally simplifying. That simplicity will not always be clear; precisely because it is so fundamental, it does basic things in a slightly different way and in a different notation. This requires your full attention, notably in the beginning, when we only seem to go over familiar things in a perhaps irritatingly different manner. The patterns we uncover, and the coordinate-free way in which we encode them, will all pay off in the end in generally applicable quantitative geometrical operators and constructions. We emphasize that this is not primarily a book on programming, and that the subtitle An Object-oriented Approach to Geometry should not be interpreted too literally. It is intended to convey that we finally achieve clean computational objects (in the sense of object-oriented programming) to correspond to the oriented elements and operators of geometry by identifying them with oriented objects of the algebra. Why Geometric Algebra? Geometric Algebra Spanning Oriented Subspaces Metric Products of Subspaces Linear Transformations of Intersection and Union of Subspaces The Fundamental Product of Geometric Algebra Orthogonal Transformations as Versors Geometric Differentiation Models of Geometries Modeling Geometries The Vector Space Model: the Algebra of Directions The Homogeneous Model Applications of the Homogeneous Model The Conformal Model: Operational Euclidean Geometry New Primitives for Euclidean Geometry Constructions in Euclidean Geometry Conformal Operators Operational Models for Geometries Implementing Geometric Algebra Implementation Issues Basis Blades and Operations The Linear Products and Operations Fundamental Algorithms for Nonlinear Products Specializing the Structure for Efficiency Using the Geometry in a Ray-Tracing Application Appendices Metrics and Null Vectors Contractions and Other Inner Products Subspace Products Retrieved Common Equations

Get This Torrent

Dorst L. Geometric Algebra for Computer Science...2007.pdf 5.8 MB

Details for: Dorst L. Geometric Algebra for Computer Science...2007

dorst l geometric algebra computer science 2007