Marching cubes

Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline,[1] for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels).

The applications of this algorithm are mainly concerned with medical visualizations such as CT and MRI scan data images, and special effects or 3-D modelling with what is usually called metaballs or other metasurfaces.

The first published version of the algorithm exploited rotational and reflective symmetry and also sign changes to build the table with 15 unique cases.

The popularity of the Marching Cubes and its widespread adoption resulted in several improvements in the algorithm to deal with the ambiguities and to correctly track the behavior of the interpolant.

At this point, even with all the improvements proposed to the algorithm and its triangulation table, the meshes generated by the Marching Cubes still had topological incoherencies.

The Marching Cubes 33, proposed by Chernyaev[8] in 1995, is one of the first isosurface extraction algorithms intended to preserve the topology of the trilinear interpolant.

Later, in 2003, Nielson[9] proved that Chernyaev's lookup table is complete and can represent all the possible behaviors of the trilinear interpolant, and Lewiner et al.[10] proposed an implementation to the algorithm.