I am reading Eric Lengel’s paper about the Transvoxel algorithm.
In an early part describing the classical Marching Cubes (3.1.1), he talks about ambiguous cases. From what I understand, these can result from grouping the cases into “equivalence classes”.
However, in the Marching Cubes paper I read (is this the one he is referring to ?), there does not seem to be any grouping done, and each of the 256 cases produces its own triangulation. For example, taking the case of Lengyel’s figure 3.2 (on page 12 of the first document), the left cube has index 189 (vertices 0 2 3 4 5 7) and the right cube index 24 (vertices 3 and 4), which gives non “equivalent” triangulations: 4 triangles for the left cube, and 2 for the right cube.
To phrase this as a question: are there different versions of Marching Cubes, and could Lengyel be referring to a different one than Paul Bourke's ?