Pages in Math

Planets
Just as with the problem of map projection, creating planets shows a fundamental fact with voxels: As they are regular grids, shaping the actual grid into a planet, without distortions or discontinuities, is mathematically impossible. As such, we need to employ different methods depending on what we ultimately want to achieve.

3D Raycasting
The Digital Differential Analyzer (
DDA
) algorithm, adapted to 3D, is exactly the thing one needs to travel along a line (or a ray) through a grid of voxels. 
Noise
Fields of pseudorandom numbers.

Types of Noise
Types of noise commonly used for procedural generation.

Coordinate Systems
When dealing with voxels (and math in threedimensional space in general), it is extremely important to get your coordinate systems and the conversions between them right. Even slightly wrong conversions can (and will) lead to massive headaches and horrible debugging sessions.