文档介绍：List of Figures
Example of the use of geometric algebra 2
Code to generate Figure 5
Example of the use of geometric algebra 6
The outer product and its interpretations 11
Spanning homogeneous subspaces in a 3-D vector space 25
Imagining vector addition 27
Bivector representations 32
Imagining bivector addition in 2-D space 33
Bivector addition in 3-D space 34
The associativity of the outer product 35
Solving linear equations with bivectors 40
Intersecting lines in the plane 41
Code for drawing bivectors 58
Drawing bivectors screenshot (Example 1) 59
The orientation of front- and back-facing polygons 59
A wire-frame torus with and without backface culling 60
The code that renders a model from its 2-D vertices (Exercise 2) 61
Sampling a vector field and summing trivectors 62
Code to test for singularity (Example 3) 63
A helix-shaped singularity, as detected by Example 3 64
the scalar product of 2-blades 70
From scalar product to contraction 72
Thecontractionofavectorontoa2 76
Duality of vectors in 2-D 81
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LIST OF FIGURES xxi
Duality of vectors and bivectors in 3-D 82
Projection onto a subspace 84
Three uses of the cross product 87
Duality and the cross product 89
Orthonormalization code (Example 1) 93
Orthonormalization 94
Reciprocal frame code 96
Color space conversion code (Example 4) 97
Color space conversion screenshot 98
The defining properties of a linear transformation 100
Projection onto a line a in the b-direction 104
A rotation around the origin of unit vectors in the plane 105
Projectionofavectorontoabivector 121
Matrix representation of projection code 122
Transforming normals vector 123
The ambiguity of the magnitude of the intersection of two planes 126
The meet of two oriented planes 130
A line meeting a plane in the origin