Time and Space Optimal Data Parallel Volume Rendering Using Permutation Warping

In this paper we present a data parallel volume rendering algorithm with numerous advantages over prior published solutions. Volume rendering is a three-dimensional graphics rendering algorithm that computes views of sampled medical and simulation data, but has been much slower than other graphics algorithms because of the data set sizes and the computational complexity. Our algorithm uses permutation warping to achieve linear speedup (run time is O(S/P) for P processors when P=O(S/logS) for S=n*n*n samples), linear storage ( O(S) ) for large data sets, arbitrary view directions, and high quality filters. We derived a new processor permutation assignment of five passes (our prior known solution was eight passes), and a new parallel compositing technique that is essential for scaling linearly on machines that have more processors than view rays to process (P<n*n). We show a speedup of 15.7 for a 16k processor over a 1k processor MasPar MP-1 (16 is linear) and two frames/second with a 128*128*128 volume and trilinear view reconstruction. In addition we demonstrate volume sizes of 256*256*256, constant run time over angles 5 to 75 degrees, filter quality comparisons, and communication congestion of just 19% to 29%.