Octahedron Encoding
Using a vec3 to store 3D unit vectors isn’t ideal because it can represent vectors of any length. Since normalized vectors make up only a small fraction of vec3, much of the floating-point numbers’ bit patterns are wasted.
There are many ways to store 3D unit vectors, like using the spherical coordinates. Although spherical coordinates reduce the vector representation from 3 floats to 2, they still face issues with floating-point precision being concentrated at the poles. Additionally, manipulating spherical coordinates involves costly trig functions.
While the octahedron encoding is not fit for computation, it is overall one of the best methods for in-memory storage of 3D unit vectors.
Mapping from a sphere to octahedron can be viewed as changing from L2 norm to L1 (Manhattan) norm. The process is illustrated by the following diagram:
