Volume Ray Casting on Sparse Grids

These days sparse grids are of increasing interest in numerical simulations. Based upon hierarchical tensor product bases, the sparse grid approach is a very efficient one improving the ratio of invested storage and computing time to the achieved accuracy for many problems in the area of numerical solution of partial dif-ferential equations. The volume visualization algorithms that are available so far cannot cope with sparse grids. Now we present an approach that directly works on sparse grids. As a second aspect in this paper, we suggest to use sparse grids as a data compression method in order to visualize huge data sets even on workstations with low main memory. Because the size of data sets used in nu-merical simulations is still growing, this feature makes it possible that workstations can continue to handle these data sets. Besides the standard sparse grid interpolation algorithm and the so called combination approach, we have developed a new sparse grid in-terpolation method, which harnesses the texture-mapping hardware of Silicon Graphics workstations for accelerating purposes. There-fore, hardware based volume rendering becomes possible on com-pressed data sets at interactive frame rates