AbstractBox splines are a multivariate extension of uniform univariate B‐splines. Direct evaluation of a box spline basis function can he 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 improve absolute performance. A windowing function can also he 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 functions, for eventual application to forward projection (splat‐based) volume rend