Practical considerations on Marching Cubes 33 topological correctness

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 work closes an existing gap in the topological correctness of 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.