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.
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 up to 20x faster and allows it to produce much higher density blue noise sample point distributions.
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.