for (var finger_point = 0; finger_point <= params.finger_points; finger_point++) {
var angle = (finger_angle + twirl_angle * finger_point / params.finger_points) * 2 * Math.PI;
var x = ring_radius * Math.cos(angle);
for (var finger_point = 0; finger_point <= params.finger_points; finger_point++) {
var angle = (finger_angle + twirl_angle * finger_point / params.finger_points) * 2 * Math.PI;
var x = ring_radius * Math.cos(angle);