Efficient volume rendering on the body centered cubic lattice using box splines

We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation methods such as de Boor's algorithm for splines in box splines basis. Further on, we offer a comparison of quintic box splines with the only other interactive rendering available on BCC lattices that is based on separable kernels for interleaved Cartesian cubic (CC) lattices. While quintic box splines result in superior quality, interleaved CC lattices are still faster, since they can take advantage of the highly optimized circuitry for CC lattices, as it is the case in graphics hardware nowadays. This result is valid with and without prefiltering. Experimental results are shown for both a synthetic phantom and data from optical projection tomography. We provide shader code to ease the adaptation of box splines for the practitioner.