Homogeneous Coordinates
Homogeneous coordinates 
of
a finite point 
in the plane are any three numbers
for which
 |
(1)
|
 |
(2)
|
Coordinates (
for which
 |
(3)
|
describe the point at infinity in the direction of slope 
.
In homogeneous coordinates, the equation of a line
 |
(4)
|
is given by
 |
(5)
|
Two points expressed using homogeneous coordinates 
and
are identical iff
 |
(6)
|
Two lines expressed using homogeneous coordinates
 |
(7)
|
 |
(8)
|
are identical iff
 |
(9)
|
The intersection of the two lines above is given by
 |  |  |
(10)
|
 |  |  |
(11)
|
 |  |  |
(12)
|
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6-sphere coordinates
