Comparison With Marching Cubes
Marching tetrahedrons computes up to nineteen edge intersections per cube, where marching cubes only requires twelve. Only one of these intersections cannot be shared with an adjacent cube (the one on the main diagonal), but sharing on all faces of the cube complicates the algorithm and increases memory requirements considerably. On the other hand, the additional intersections provide for a slightly better sampling resolution.
The number of configurations, determining the size of the commonly used lookup tables, is much smaller, since only four rather than eight separate vertices are involved per tetrahedron. There are six tetrahedrons to process instead of one single cube. The process is unambiguous, so no additional ambiguity handling is necessary.
The downside is that the tessellation of a cube with tetrahedrons requires a choice regarding the orientation of the tetrahedrons, which may produce artificial "bumps" in the isosurface because of interpolation along the face diagonals.
Read more about this topic: Marching Tetrahedrons
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