The book Geometric Algebra For Computer Science, by Dorst, Fontijne, and Mann has one of the best introductions to the subject that I have seen.
It contains particularly good introductions to the dot and wedge products and how they can be applied and what they can be used to model. After one gets comfortable with these ideas they introduce the subject axiomatically. Much of the pre-axiomatic introductory material is based on the use of the scalar product, defined as a determinant. You'll have to be patient to see where and why that comes from, but this choice allows the authors to defer some of the mathematical learning overhead until one is ready for the ideas a bit better.
Having started study of the subject with papers of Hestenes, Cambridge, and Baylis papers, I found the alternate notation for the generalized dot product (L and backwards L for contraction) distracting at first but adjusting to it does not end up being that hard.
This book has three sections, the first covering the basics, the second covering the conformal applications for graphics, and the last covering implementation. As one reads geometric algebra books it is natural to wonder about this, and the pros, cons and efficiencies of various implementation techniques are discussed.
There are other web resources available associated with this book that are quite good. The best of these is GAViewer, a graphical geometric calculator that was the product of some of the research that generated this book. Performing the GAViewer tutorial exercises is a great way to build some intuition to go along with the math, putting the geometric back in the algebra.
There are specific GAViewer exercises that you can do independent of the book, and there is also an excellent interactive tutorial available. Browse the book website, or Search for '2003 Game Developer Lecture, Interactive GA tutorial. UvA GA Website: Tutorials'. Even if one decided not to learn GA, using this to play with the graphical cross product manipulation, with the ability to rotate viewpoints, is quite neat and worthwhile.
Author(s): Leo Dorst, Daniel Fontijne, Stephen Mann
Series: The Morgan Kaufmann Series in Computer Graphics
Edition: Revised
Publisher: Morgan Kaufmann
Year: 2007
Language: English
Pages: 622
Cover Page
......Page 1
Copyright
......Page 2
List of Figures......Page 3
List of Tables......Page 9
List of Programming
Examples......Page 11
Preface......Page 13
1 WHY GEOMETRIC
ALGEBRA?......Page 18
2 SPANNING ORIENTED
SUBSPACES......Page 37
3 METRIC PRODUCTS
OF SUBSPACES......Page 79
4 LINEAR TRANSFORMATIONS
OF SUBSPACES......Page 113
5 INTERSECTION AND
UNION OF SUBSPACES......Page 138
6 THE FUNDAMENTAL
PRODUCT OF GEOMETRIC
ALGEBRA......Page 154
7 ORTHOGONAL
TRANSFORMATIONS
AS VERSORS......Page 179
8 GEOMETRIC
DIFFERENTIATION......Page 225
9 MODELING GEOMETRIES......Page 254
10 THE VECTOR SPACE
MODEL: THE ALGEBRA
OF DIRECTIONS......Page 256
11 THE HOMOGENEOUS
MODEL......Page 280
12 APPLICATIONS OF THE
HOMOGENEOUS MODEL......Page 336
13 THE CONFORMAL MODEL:
OPERATIONAL EUCLIDEAN
GEOMETRY......Page 364
14 NEW PRIMITIVES FOR
EUCLIDEAN GEOMETRY......Page 406
15 CONSTRUCTIONS IN
EUCLIDEAN GEOMETRY......Page 446
16 CONFORMAL OPERATORS......Page 474
17 OPERATIONAL MODELS
FOR GEOMETRIES......Page 505
18 IMPLEMENTATION
ISSUES......Page 508
19 BASIS BLADES AND
OPERATIONS......Page 515
20 THE LINEAR PRODUCTS
AND OPERATIONS......Page 524
21 FUNDAMENTAL
ALGORITHMS FOR
NONLINEAR PRODUCTS......Page 531
22 SPECIALIZING THE
STRUCTURE FOR
EFFICIENCY......Page 543
23 USING THE GEOMETRY
IN A RAY-TRACING
APPLICATION......Page 559
A METRICS AND NULL
VECTORS......Page 584
B CONTRACTIONS AND
OTHER INNER PRODUCTS......Page 587
C SUBSPACE PRODUCTS
RETRIEVED......Page 595
D COMMON EQUATIONS......Page 600
Bibliography......Page 605
Index......Page 609
