A piecewise approach to piecewise approximation

Tensor-product B-spline surfaces offer a convenient means for representing a set of bivariate data, especially if many surface evaluations are required. This is because the compact support property of the tensor-product spline allows the spline value to be obtained in a time that is (almost) independent of the number of coefficients used to define the surface. The main calculation is the precomputation involved in fitting the data and this can be impractically large if there are many spline coefficients to be calculated. Since the surface produced may be evaluated locally and efficiently, it would be advantageous to exploit local properties in order to fit the data in a piecewise manner. An algorithm to do this is presented.