def arcball_map_to_sphere(point, center, radius):
    """Return unit sphere coordinates from window coordinates."""
    v0 = (point[0] - center[0]) / radius
    v1 = (center[1] - point[1]) / radius
    n = v0*v0 + v1*v1
    if n > 1.0:
        # position outside of sphere
        n = math.sqrt(n)
        return numpy.array([v0/n, v1/n, 0.0])
    else:
        return numpy.array([v0, v1, math.sqrt(1.0 - n)])
Return unit sphere coordinates from window coordinates.