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The projective plane
The projective plane is the projective space . A point of is represented by a 3vector
. A line is also represented by a 3vector. A point is located on a line if and only if

(B1) 
This equation can however also be interpreted as expressing that the line passes through the point . This symmetry in the equation shows that there is no formal difference between points and lines in the projective plane. This is known as the principle of duality.
A line passing through two points and is given by their vector product
. This can also be written as

(B2) 
The dual formulation gives the intersection of two lines.
All the lines passing through a specific point form a pencil of lines. If two lines and are distinct elements of the pencil, all the other lines can be obtained through the following equation:

(B3) 
for some scalars and . Note that only the ratio
is important.
Next: Projective 3space
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Marc Pollefeys
20021122