Returns a random point on the surface of a sphere with radius 1.

Random.onUnitSphere.js

// Fastest
// Marsaglia (1972)
// https://stackoverflow.com/a/5408344
const randomOnUnitSphere = N => {
  const vectors = new Float32Array(N * 3);

  for (let i = 0; i < N; i++) {
    let x, y, z, norm;
    while (true) {
      x = 0.5 - Math.random();
      y = 0.5 - Math.random();
      z = 0.5 - Math.random();
      norm = (x ** 2 + y ** 2 + z ** 2) ** 0.5;
      if (norm < 1) break;
    }
    vectors[i * 3 + 0] = x / norm;
    vectors[i * 3 + 1] = y / norm;
    vectors[i * 3 + 2] = z / norm;
  }
  return vectors;
};

// Alternative
// https://mathworld.wolfram.com/SpherePointPicking.html
const randomOnUnitSphere = N => {
  const vectors = new Float32Array(N * 3);

  for (let i = 0; i < N; i++) {
    const u = Math.random();
    const v = Math.random();
    const theta = u * Math.PI * 2;
    const phi = Math.acos(2 * v - 1);
    const x = (1 - Math.cos(phi) ** 2) ** 0.5 * Math.cos(theta);
    const y = (1 - Math.cos(phi) ** 2) ** 0.5 * Math.sin(theta);
    const z = Math.cos(phi);
    const norm = (x ** 2 + y ** 2 + z ** 2) ** 0.5;
    vectors[i * 3 + 0] = x / norm;
    vectors[i * 3 + 1] = y / norm;
    vectors[i * 3 + 2] = z / norm;
  }
  return vectors;
};