Figure 1: RBF reconstruction of unstructured CFD data. (a) Volume rendering of 1,943,383 tetrahedral shock data set using 2,932 RBF functions. (b) Volume rendering of a 156,642 tetrahedral oil reservoir data set using 222 RBF functions organized in a hierarchy of 49 cells. While interactive visualization of rectilinear gridded volume data sets can now be accomplished using texture mapping hardware on commodity PCs, interactive rendering and exploration of large scattered or unstructured data sets is still a challenging problem. We have developed a new approach that allows the interactive rendering and navigation of procedurally-encoded 3D scalar fields by reconstructing these fields on PC class graphics processing units. Since the radial basis functions (RBFs) we use for encoding can provide a compact representation of volumetric scalar fields, the large grid/mesh traditionally needed for rendering is no longer required and ceases to be a data transfer and computational bottleneck dur...