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We present in-core and out-of-core parallel techniques for implementing isosurface rendering based on the notion of span-space buckets. Our in-core technique makes conservative use of the RAM and is amenable to parallelization. The out-of-core variant keeps the amount of data read in the search process to a minimum, visiting only the cells that intersect the isosurface. The out-of-core technique additionally minimizes disk I/O time through in-order seeking, interleaving data records on the disk and by overlapping computational and I/O threads. The overall isosurface rendering time achieved using our out-of-core span space buckets is comparable to that of well-optimized in-core techniques that have enough RAM at their disposal to avoid thrashing. When the RAM size is limited, our out-of-core span-space buckets maintains its performance level while in-core algorithms either start to thrash or must sacrifice performance for a smaller memory footprint.