# New book – K. Kanatani: Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics

Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics, by Kenichi Kanatani, April 6, 2015 by A K Peters/CRC Press, 208 Pages – 74 B/W Illustrations, ISBN 9781482259506 – CAT# K24188, Price: £49.99. URL: http:www.crcpress.com/product/isbn/9781482259506

Features

• Describes the basis of 3D geometry at a level suitable for undergraduate students in science or engineering

• Covers the geometry of lines and planes as well as camera imaging geometry involving circles and spheres, including fisheye lens and omnidirectional cameras for computer vision and robotics applications
• Emphasizes the fundamental principle of algebra without referring to linear algebra
• Includes a column throughout that highlights important aspects of twentieth-century mathematics, such as topology, projective geometry, and group representations
• Provides notes on historical developments, recommended references, and exercises at the end of each chapter, with answers to the exercises at the back of the book

Summary
Understanding 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 Hamilton’s quaternion algebra, Grassmann’s 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 in 5D, which is the main ingredient of geometric algebra; and delves into the mathematical analysis of camera imaging geometry involving circles and spheres.

With useful historical notes and exercises, this book gives readers insight into the mathematical theories behind complicated geometric computations. It helps readers understand the foundation of today’s geometric algebra.

Source: Email from K. Kanatani, kanatani2013_AT_yahoo.co.jp, 13 Apr. 2015, http:www.crcpress.com/product/isbn/9781482259506

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