Homogeneous Notation Interlude

Notation for plane (i.e. 2D) projective geometry. NB ``='' means equality up to scale.

• point: a point is represented by the homogeneous 3-vector

  

  where and are the inhomogeneous plane coordinates. Only the ratio of the homogeneous coordinates is significant.

• line: a line is represented by the homogeneous 3-vector

  

  for the line . Again, only the ratio of the homogeneous line coordinates is significant.

• point on line: or or

• two points define a line:

• two lines define a point:

• matrix notation for vector product: The vector product can be represented as a matrix multiplication

  

  where

  

  is a skew-symmetric matrix of rank 2. is the one dimensional kernel of , since .