This paper presents a new fast and local method of 3D surface reconstruction for scattered data. The algorithm makes use of quasi-interpolants to compute the control points from a coarse to fine hierarchy to generate a sequence of bicubic B-spline functions whose sum approaches to the desired interpolation function. Quasi-interpolants gives a procedure for deriving local spline approximation methods where a B-spline coefficient only depends on data points taken from the neighborhood of the support corresponding B-spline. Experimental results demonstrate that high-fidelity reconstruction is possible from a selected set of irregular samples.