# What version of Marching Cubes bring “ambiguities”

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 ?

• Isn't this exact purpose for dual contouring? to explain and fix these "edge cases" ... to give an example the paper on DC talks about where the surface comes in to then out of a given space portion something that MC / transvoxel on their own would miss. – War Sep 16 '14 at 9:39
• I don't know, I haven't looked into DC yet. I'm not complaining about MC ambiguities here, just saying I don't see such ambiguities, and trying to understand. – Gnurfos Sep 16 '14 at 12:14
• Yeh i was saying if you read up on DC it might explain those ambiguities (unless I misunderstood the problem) since DC was created to address certain shortcomings in MC. – War Sep 16 '14 at 14:17
• A very simple way to see how ambiguity can arise is to go down a dimension and look at 'Marching Squares'. In that case, a square with two positive vertices (diagonally opposite) and two negative vertices (also diagonally opposite) can clearly be contoured in two ways: we can either connect the edges such that the two negative nodes are part of the same region, or such that the two positive nodes are. A priori (i.e., without analytical or topological information), there's no reason to prefer one over the other. – Steven Stadnicki Sep 17 '14 at 23:37