I/O optimal isosurface extraction

In this paper we give I/O-optimal techniques for the extraction of isosurfaces from volumetric data, by a novel application of the I/O-optimal interval tree of Arge and Vitter. The main idea is to preprocess the dataset once and for all to build an efficient search structure in disk, and then each time we want to extract an isosurface, we perform an output-sensitive query on the search structure to retrieve only those active cells that are intersected by the isosurface. During the query operation, only two blocks of main memory space are needed, and only those active cells are brought into the main memory, plus some negligible overhead of disk accesses. This implies that we can efficiently visualize very large datasets on workstations with just enough main memory to hold the isosurfaces themselves. The implementation is delicate but not complicated. We give the first implementation of the I/O-optimal interval tree, and also implement our methods as an I/O filter for Vtk's isosurface extraction for the case of unstructured grids. We show that, in practice, our algorithms improve the performance of isosurface extraction by speeding up the active-cell searching process so that it is no longer a bottleneck. Moreover, this search time is independent of the main memory available. The practical efficiency of our techniques reflects their theoretical optimality.