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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 arithmetic of Hamilton, Grassmann, and Clifford. It reveals the proper method to describe and compute geometry for 3D modeling functions in laptop graphics and laptop imaginative and prescient.
In distinction to comparable texts, this book first offers separate descriptions of the numerous algebras and then explains how they’re combined to stipulate the sector of geometric algebra. It begins with 3D Euclidean geometry along with discussions as to how the descriptions of geometry might probably be altered if using a non-orthogonal (oblique) coordinate system. The textual content material focuses on Hamilton’s quaternion algebra, Grassmann’s outer product algebra, and Clifford algebra that underlies the mathematical development of geometric algebra. It moreover presents elements and strains in 3D as objects in 4D inside the projective geometry framework; explores conformal geometry in 5D, which is the first ingredient of geometric algebra; and delves into the mathematical analysis of camera imaging geometry involving circles and spheres.
With useful historic notes and exercises, this book offers readers notion into the mathematical theories behind troublesome geometric computations. It helps readers understand the inspiration of at this time’s geometric algebra.
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