A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2π. Picking random points on a circle is therefore a great deal more straightforward than sphere point picking. n random points can be picked on a unit circle in the Wolfram Language using the function RandomPoint[Circle[], n]. Random points on a circle can also be obtained by picking two numbers x_1, x_2 from a uniform distribution on (-1, 1), and rejecting pairs with x_1^2 + x_2^2>=1.

circle lattice points | circle line picking | disk point picking | sphere point picking