April 2015
Beginner to intermediate
208 pages
7h 31m
English
Content preview from Understanding Geometric Algebra
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20 3D Euclidean Geometry
O
n
x
l
Π
m
x
H
O
n
m
v
x
l
Π
d
(a) (b)
FIGURE 2.11 (a) Line l is specified by the surface normal n to the supporting plane Π and th e
direction vector m of l. (b) The distance d of point x from line x × m = n.
which is equal to the firs t equation in Eq. (2.53) except for scale normalization. The equa-
tion on the right of Eq. (2.58) equals the second equation in Eq. (2.53) except for scale
normalization.
2.9 LINES
Given a line l in space, we call the plane Π passing through l and the origin O the supporting
plane of l. If the s upporting plane Π is given, the line l on it is specified by its direction and
distance fr om the origin O (Fig.
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