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

Linear Transformations and Matrices

We start our task of mapping into device coordinates by adding a fourth component to our three-dimensional Cartesian coordinates, with a value of 1.0, to make homogeneous coordinates. These coordinates are then ready to be multiplied by one or more 4 × 4 matrices that rotate, scale, translate, and apply perspective. Examples of how to use each of these transforms are given below. The summary is that each of these transformations can be made through multiplication by a 4 × 4 matrix, and a series of such transformations can be composed into a single 4 × 4 matrix, once, that can then be used on multiple vertices.

Translation

Translating an object takes advantage of the fourth component we just added to our model ...