Implicit surface reconstruction from unorganized point sets has been recently approached with methods based on multi-level partition of unity. We improve this approach by addressing local approximation robustness and iso-surface extraction issues. Our method relies on the J ₁ ^A triangulation to perform both the spatial subdivision and the iso-surface extraction. We also make use of orthogonal polynomials to provide adaptive local approximations in which the degree of the polynomial can be adjusted to accurately reconstruct the surface locally. Finally, we compare our results with previous work to demonstrate the robustness of our method.