## How to generate uniformly random points on n-spheres and in n-balls

For many Monte Carlo methods, such as those in graphical computing, it is critical to uniformly sample from $d$-dimensional spheres and balls. This post describes over twenty different methods to uniformly random sample from the (surface of) a $d$-dimensional sphere or the (interior of) a $d$-dimensional ball.

## Maximal Poisson disk sampling: an improved version of Bridson’s algorithm

Bridson’s Algorithm (2007) is a very popular method to produce maximal ‘blue noise’ sample point distributions such that no two points are closer than a specified distance apart. In this brief post we show how a minor modification to this algorithm can make it 20x faster and allows it to produce much higher density blue noise sample point distributions. Figure 1. Poisson disc sampling based on a modified version of Bridson’s algorithm. This modified algorithm runs in linear time and is up to 20x faster than the original algorithm

## Evenly distributing points on a sphere

How to distribute points on the surface of a sphere as evenly as possibly is an incredibly important problem in maths, science and computing, and mapping the Fibonacci lattice onto the surface of a sphere via equal-area projection is an extremely fast and effective approximate method to achieve this. I show that with only minor modifications it can be made even better. 