Geometric Algebra for Computer Science

by Dorst; Fontijne; Mann

• ISBN13: 9780123694652
• ISBN10: 0123694655
• Format: Hardcover
• Copyright: 2007-04-19
• Publisher: Elsevier Science

Summary

Stephen Mann is Associate Professor in the David R. Cheriton School of Computer Science at the University of Waterloo.

Table of Contents

Why geometric algebra?	p. 1
Geometric algebra
Spanning oriented subspaces	p. 23
Metric products of subspaces	p. 65
Linear transformations of subspaces	p. 99
Intersection and union of subspaces	p. 125
The fundamental product of geometric algebra	p. 141
Orthogonal transformations as versors	p. 167
Geometric differentiation	p. 213
Models of geometries
Modeling geometries	p. 245
The vector space model : the algebra of directions	p. 247
The homogeneous model	p. 271
Applications of the homogeneous model	p. 327
The conformal model : operational Euclidean geometry	p. 355
New primitives for Euclidean geometry	p. 397
Constructions in Euclidean geometry	p. 437
Conformal operators	p. 465
Operational models for geometries	p. 497
Implementing geometric algebra
Implementation issues	p. 503
Basis blades and operations	p. 511
The linear products and operations	p. 521
Fundamental algorithms for nonlinear products	p. 529
Specializing the structure for efficiency	p. 541
Using the geometry in a ray-tracing application	p. 557
Appendices
Metrics and null vectors	p. 585
Contractions and other inner products	p. 589
Subspace products retrieved	p. 597
Common equations	p. 603
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