MCPro: A Procedural Method for Topologically Correct Isosurface Extraction based on Marching Cubes [1]
We present an innovative procedural algorithm designed for extracting isosurfaces from scalar data within hexahedral grids. The geometry and the topological features of the intersection of a level set of the trilinear interpolant with the faces and the interior of a reference unit cell are analyzed. Ambiguities are solved without the help of lookup tables, generating a topologically correct triangulation of the level set within the cell that is consistent across cell boundaries. The algorithm is based on constructing and triangulating a polygonal halfedge data structure that includes contours and critical points of the trilinear interpolant. Our algorithm is capable of handling some singular cases that were not solved by previous methods.
The algorithm is contained in the file mc.py.
main.py is used to test specific configurations.
By running paper_images.py the figures from the paper can be reproduced.
For the validation of the algorithm based on Etiene et al. [2] the test files in "Marching Cubes cases" and "Randomly generated grids" have to be downloaded from here and placed into src/data/.
The verifier.py file can then be run to check for topological correctness.
[1]: J. Stahl and R. Grosso, "MCPro: A Procedural Method for Topologically Correct Isosurface Extraction based on Marching Cubes"
[2]: T. Etiene et al., "Topology Verification for Isosurface Extraction," in IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 6, pp. 952-965, June 2012, doi: 10.1109/TVCG.2011.109.