We propose a simple and straightforward analytic solution for the Q-ball reconstruction of the diffusion orientation distribution function (ODF) of the underlying fiber population. First, the signal is modeled with a high order spherical harmonic series using a Laplace-Beltrami regularization method which leads to an elegant mathematical simplification of the Funk-Radon transform using the Funk-Hecke formula. In doing so, we obtain a fast and robust model-free ODF approximation. We validate the accuracy of the estimation quantitatively against synthetic data generated from the multi-tensor model and show that our estimated ODF can recover known multiple fiber regions in a biological phantom and in the human brain.