Optimized Evaluation of Box Splines via the Inverse FFT

Box splines are a multivariate extension of uniform univariate B-splines. Direct evaluation of a box spline basis function can be difficult , but they have a relatively simple Fourier transform and can therefore be evaluated with an inverse FFT. Symmetry, recursive evaluation of the coefficients, and parallelization can be used to optimize performance. A windowing function can also be used to reduce truncation artifacts. We explore all these options in the context of a high-performance parallel implementation. Our goal is the provision of an empirical touchstone for the inverse FFT evaluation of box spline basis fun ctions.