View matrix

The LookAt function is mainly used for 3D graphics. It is a convenient way to position a 3D camera. While graphics programming is outside the scope of this book, for our math library to be practical we need to implement some graphics-related functionality.

Getting a vertex (vector) to become a pixel primarily involves three matrix transformations. The world transform, view transform, and projection transform. All three of these transformations are expressed as a matrix multiplication.

• The world transform takes the vertex from model space to world space, we've already implemented this as the Transform function

• The view transform takes a vertex from world space and transforms it to eye space, sometimes called view space or camera space

• The projection transform takes vertices from eye space and puts them into normalized device coordinates

If we multiply a vertex by the view matrix, the vertex ends up in eye space. Eye space transforms the vertex in the world so it's relative to a camera...