Premium
Accelerated Evaluation of Box Splines via a Parallel Inverse FFT
Author(s) -
McCool Michael D.
Publication year - 1996
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.1510035
Subject(s) - computer science , fast fourier transform , inverse , algorithm , truncation (statistics) , box spline , univariate , rendering (computer graphics) , spline (mechanical) , basis function , mathematics , multivariate statistics , computer graphics (images) , mathematical analysis , geometry , spline interpolation , computer vision , machine learning , structural engineering , engineering , bilinear interpolation
Box 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 rendering.