Practical Algorithms for 3D Computer Graphics, 2nd Edition

16 2. Basic theory and mathematical results

homogeneous vectors. Thus, for our specific case where the vector (wx, wy, w)

represents the coor d in ates of a point on a 2D plane it is known as a homogeneous

coordinate.

In its simplest form we can think of the homogeneous coordinate of the 2D

point (x, y) as (x, y, 1). For a point in 3D (x, y, z) we can propose that the

equivalent homogeneous coordinate will be (wx, wy, wz, w), or in its simplest

form (x, y, z, 1). The last element, the 1, is essential becau s e if it was zero then

c in 2.1 would disappear and only lines that pass through the coordinate origin

could be specified.

Considering 2D vectors