Get Free Ebook Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics
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Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics
Get Free Ebook Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics
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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.
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Product details
Hardcover: 208 pages
Publisher: A K Peters/CRC Press; 1 edition (April 6, 2015)
Language: English
ISBN-10: 1482259508
ISBN-13: 978-1482259506
Product Dimensions:
7.2 x 0.7 x 10.1 inches
Shipping Weight: 15.2 ounces (View shipping rates and policies)
Average Customer Review:
5.0 out of 5 stars
2 customer reviews
Amazon Best Sellers Rank:
#1,573,703 in Books (See Top 100 in Books)
This book is very clearly written and organized well. I especially appreciated the introduction to oblique coordinate systems chapter which introduces the metric tensor and reciprocal bases in the simplest, most approachable fashion I have ever read on this topic. The book leads the reader through increasingly comprehensive algebras and geometries each building on previous chapters in a very logical and straightforward manner. I loved this book!
I come from a differential geometry background (as an engineer) and the subject of Clifford algebra was not easy for me. I never get Porteous to work for me. Then I tried Lounesto, easier this time, but not everything is clearly defined (e.g. contraction, general terms for conjugation), and nor is conformal geometric algebra discussed. Besides, I think it is really meant to be a intro book for physicists.Then I found this book written by Kenichi Kanatani. I can't complain about this book in any way (even the typos in the book are easily corrected). It establishes the modern notion of geometric algebra layer by layer, from Euclidean geometry, to Grassmann algebra, to Clifford algebra, to Grassmann-Cayley algebra (though the exact definition of shuffle product is missing), to conformal geometric algebra. With all due respects, Jon Selig's Geometric Fundamentals of Robotics cannot have achieved such a level of clarity.The book is so well and smoothly written that the first reading of this book costs me only four days, mobilizing only the basic euclidean, projective geometry and tensor analysis I picked up when learning baby differential geometry (from say Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry). I could feel that the book is not written in a hurry, but instead is tested through some time. And therefore the quality of the book is superb.Five stars for a Five-star book. Job well done, Kenichi Sensei.
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