  Continuous representations are fundamental for modeling sampled data and
performing computations and numerical simulations directly on the model or its
elements. To effectively and efficiently address the approximation of point
clouds we propose the Weighted Quasi Interpolant Spline Approximation method
(wQISA). We provide global and local bounds of the method and discuss how it
still preserves the shape properties of the classical quasi-interpolation
scheme. This approach is particularly useful when the data noise can be
represented as a probabilistic distribution: from the point of view of
nonparametric regression, the wQISA estimator is robust to random
perturbations, such as noise and outliers. Finally, we show the effectiveness
of the method with several numerical simulations on real data, including curve
fitting on images, surface approximation and simulation of rainfall
precipitations.
