For over two decades, topologically correct isosurface extraction algorithms have been studied. In particular, Marching Cubes has received special attention from the scientific community. Chernyaev's Marching Cubes 33 is one of the first algorithms intended to preserve the topology of the trilinear interpolant. In this work, we address three issues with the Marching Cubes 33 algorithm, two of which are related to its original description and one that is related to its variant. In particular, we solve a problem with the core disambiguation procedure of Marching Cubes 33 that prevents the extraction of topologically correct isosurfaces for the ambiguous configuration 13.5. This is an important step towards closing an existing gap in the topological correctness Marching Cubes 33. Furthermore, we make our results reproducible, meaning that examples provided in this work can be easily explored and studied. Finally, as part of the philosophy of reproducibility, we provide a corrected version of the Marching Cubes 33 open-source implementation and access to datasets that can be used to verify the correctness of any available topologically correct isosurface extraction implementation that preserves the topology of the trilinear interpolant.
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[Paper figure 8] [Paper figure 9] [Paper figure 12] [Paper algorithm 2] [Additional page]
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[Marching Cubes cases] [Randomly generated grids] [Paper examples] [ C-MC33 code]
Lewiner et al. work