function R = rot_axis_angle(axis, angle)
	axis = axis / norm(axis);
	H = hat(axis);
	R = eye(3) + H * sin(angle) + H * H * (1-cos(angle));

function H = hat(v)
	H = [0 -v(3) v(2); v(3) 0 -v(1); -v(2) v(1) 0];