Description
Book SynopsisUnderstanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics introduces geometric algebra with an emphasis on the background mathematics of Hamilton, Grassmann, and Clifford. It shows how to describe and compute geometry for 3D modeling applications in computer graphics and computer vision.
Unlike similar texts, this book first gives separate descriptions of the various algebras and then explains how they are combined to define the field of geometric algebra. It starts with 3D Euclidean geometry along with discussions as to how the descriptions of geometry could be altered if using a non-orthogonal (oblique) coordinate system. The text focuses on Hamiltonâs quaternion algebra, Grassmannâs outer product algebra, and Clifford algebra that underlies the mathematical structure of geometric algebra. It also presents points and lines in 3D as objects in 4D in the projective geometry framework; explores conformal geometry
Trade Review
"Several software tools are available for executing geometric algebra, but the purpose of the book is to bring about a deeper insight and interest in the theory on which these tools are based."
—Zentralblatt MATH 1319
Table of ContentsIntroduction. 3D Euclidean Geometry. Oblique Coordinate Systems. Hamilton's Quaternion Algebra. Grassmann's Outer Product Algebra. Geometric Product and Clifford Algebra. Homogeneous Space and Grassmann-Cayley Algebra. Conformal Space and Conformal Geometry: Geometric Algebra. Camera Imaging and Conformal Transformations. Answers. Bibliography. Index.
