OpenGL Programming Guide: The Official Guide to Learning OpenGL, Version 4.3, Eighth Edition

Homogeneous Coordinates

OpenGL commands usually deal with two- and three-dimensional vertices, but in fact all are treated internally as three-dimensional homogeneous vertices comprising four coordinates. Every column vector

(which we write as (x, y, z, w)^T) represents a homogeneous vertex if at least one of its elements is nonzero. If the real number a is nonzero, then (x, y, z, w)^T and (ax, ay, az, aw)^T represent the same homogeneous vertex. (This is just like fractions: x/y = (ax)/(ay).) A three-dimensional Euclidean space point (x, y, z)^T becomes the homogeneous vertex with coordinates (x, y, z, 1.0)^T, and the two-dimensional Euclidean point ...