Rational Approximation of Scientific Data

Scientific datasets are becoming increasingly challenging to transfer, analyze, and store. There is a need for methods to transform these datasets into compact representations that facilitate their downstream management and analysis, and ideally model the underlying scientific phenomena with defined numerical fidelity. To address this need, we propose nonuniform rational B-splines (NURBS) for modeling discrete scientific datasets; not only to compress input data points, but also to enable further analysis directly on the continuous fitted model, without the need for decompression. First, we evaluate three different methods for NURBS fitting, and compare their performance relative to unweighted least squares approximation (B-splines). We then extend current state-of-the-art B-spline adaptive approximation to NURBS; that is, adaptively determining optimal rational basis functions and weighted control point locations that approximate given input data points to prespecified accuracy. Additionally, we present a novel local adaptive algorithm to iteratively approximate large data input domains. This method takes advantage of NURBS local support to refine regions of the approximated model, acting locally on both input and model subdomains, without affecting other regions of the global approximation. We evaluate our methods in terms of approximated model compactness, achieved accuracy, and computational cost on both synthetic smooth functions and real-world scientific data.