Homogeneous coordinates

Every vertex in opengl is represented as a vector of 4 elements: [x y z w]. Whilst the purpose of x, y, and z is obvious, w isn't. This vector is actually a homogeneous coordinate, where the corresponding coordinate in 3space is (x/w, y/w, z/w). Homogeneous coordinates allows the points in 3space to be easily projected, with perspective, onto a 2D surface. This property of homogeneous co-ordinates is used in all areas of 3D graphics, including CAD and games.

For an in depth and technical look at the application of homogeneous coordinates, try Homogeneous Coordinates by Jules Bloomenthal and Jon Rokne.

Cheers,
Steve