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

Homogeneous Coordinates

The geometry we want to transform is innately three-dimensional. However, we will gain two key advantages by moving from three-component Cartesian coordinates to four-component homogeneous coordinates. These are 1) the ability to apply perspective and 2) the ability to translate (move) the model using only a linear transform. That is, we will be able to get all the rotations, translations, scaling, and projective transformations we need by doing matrix multiplication if we first move to a four-coordinate system. More accurately, the projective transformation is a key step in creating perspective, and it is the step we must perform in our shaders. (The final step is performed by the system when it eliminates this new fourth ...