1. A computer-implemented method for generating point clouds on a surface, the surface being described as the zero set of a mathematical function, the method comprising: selecting a direction from a set of uniformly distributed random directions on a unit sphere in space; selecting a point from a set of uniformly distributed random points on a disc in a plane; and rotating the selected point on the disc to a plane perpendicular to the selected direction; and constructing a line in the selected direction through a resulting nearest point to an origin.