Mathematics is the core to all of computer graphics. In earlier versions, OpenGL provided support for managing coordinate transformations and projections using the standard matrix stacks (GL_MODELVIEW and GL_PROJECTION). In modern versions of core OpenGL however, all of the functionality supporting the matrix stacks has been removed. Therefore, it is up to us to provide our own support for the usual transformation and projection matrices, and then pass them into our shaders. Of course, we could write our own matrix and vector classes to manage this, but some might prefer to use a ready-made, robust library.

One such library is OpenGL Mathematics (GLM), written by Christophe Riccio. Its design is based on the GLSL specification, so the syntax will be familiar to anyone using GLSL. Additionally, it provides extensions that include functionality similar to some of the much-missed OpenGL utility functions, such as glOrtho, glRotate, or gluLookAt.