# Homogeneous Coordinates and the Projective Plane

Homogeneous Coordinates and the Projective Plane

The points of the projective plane have three homogeneous coordinates, so that and , are the same point, as long as ; these points can be represented as lines in three dimensions passing through the origin (the dotted lines), , , . These lines intersect any plane in points with the two coordinates of the Cartesian plane. This Demonstration shows the action of the transformation matrix on the lines and the points in the plane and another such plane.

(a,b,c)

(a,b,c)

(at,bt,ct)

t∈

t≠0

x=at

y=bt

z=ct

z=k,k≠0

z=1