Abstract: We consider the fitting of tensor-product parametric spline surfaces to gridded data. The continuity of the surface is provided by the basis chosen. When tensor-product splines are used with gridded data, the surface-fitting problem decomposes into a sequence of curve-fitting processes, making the computations particularly efficient. The use of a hierarchical representation for the surface adds further efficiency by adaptively decomposing the fitting process into subproblems involving only a portion of the data. Hierarchy also provides a means of storing the resulting surface in a compressed format. Our approach is compared to multiresolution analysis and the use of wavelets,