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Books > Science & Mathematics > Mathematics > Algebra
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Understanding Geometric Algebra - Hamilton, Grassmann, and Clifford for Computer Vision and Graphics (Paperback)
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Understanding Geometric Algebra - Hamilton, Grassmann, and Clifford for Computer Vision and Graphics (Paperback)
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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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