Volume visualization on sparse grids

Abstract

Volume rendering is an important technique of displaying volumetric three-dimensional scalar data sets resulting from measurement or simulation. Additionally, 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 differential equations, for instance in numerical fluid mechanics. The volume visualization algorithms that are available so far cannot cope with sparse grids. We present an approach that directly works on these 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. Since the size of data sets used in numerical simulations is still growing, this feature makes it possible that workstations can continue to handle these data sets. In addition to the standard sparse grid interpolation algorithm and the so-called combination technique, we have developed a new sparse grid interpolation method, which harnesses the texture-mapping hardware of graphics workstations for acceleration purposes. Therefore, hardware based volume rendering becomes possible on compressed data sets at interactive frame rates. This is not possible if other compression methods like wavelet or fractal compression are used.