BCC-Splines: Generalization of B-Splines for the Body-Centered Cubic Lattice

Recently, the B-spline family of reconstruction filters has been generalized for the hexagonal lattice, which is optimal for sampling 2D circularly band-limited signals. In this paper, we extend this generalization to the body-centered cubic (BCC) lattice, which is optimal for sampling spherically band-limited 3D signals. We call the obtained new reconstruction filters BCC-splines. Although the explicit analytical formulas are not defined yet, we evaluate the discrete approximation of these filters in the frequency domain in order to analyze their performance in a volume-rendering application. Our experimental results show that the BCC-splines can be superior over the box splines previously proposed for the BCC lattice.