Uniform distribution on a sphere

randomThetaPhi.js

//Return random directions, spherical angle pairs theta [0,PI) and phi [0,TWO_PI), distributed uniformly over a sphere
//Pairs generated with theta=random(PI) and phi=random(TWO_PI) have a higher density around the poles.
//See spherical coordinates: https://en.wikipedia.org/wiki/Spherical_coordinate_system
//Optimalization by Dan Gries

//https://pastebin.com/7uPYaA8G

function randomThetaPhi () {
    "use strict";
    
    var eps = Math.random(),
        z = 1 - 2 * eps,
        t = Math.PI * 2 * Math.random();
    
    return [Math.acos(z), t];
}