CINAPACT-splines: A family of infinitely smooth, accurate and compactly supported splines

Abstract

We introduce CINAPACT-splines, a class of C∞ , accurate and compactly supported splines. The integer translates of a CINAPACT-spline form a reconstruction space that can be tuned to achieve any order of accuracy. CINAPACT-splines resemble traditional B-splines in that higher orders of accuracy are achieved by successive convolutions with a B-spline of degree zero. Unlike B-splines however, the starting point for CINAPACT-splines is an infinitely smooth and compactly supported bump function that has been properly normalized so that it fulfills the partition of unity criterion. We use our construction to design two CINAPACT-splines, and explore their properties in the context of rendering volumetric data sampled on Cartesian grids. Our results show that CINAPACT-splines, while being infinitely smooth, are capable of providing similar reconstruction accuracy compared to some well-established filters of similar cost.