Marching Hexahedra

Iso Surfaces | | Tetrahedra Decomposition

The Marching Hexahedra Algorithm is the extension of the marching quads algorithm from 2D to 3D.

Since each egde of the hexahedron can have an intersection point there are $2^8$ cases to consider. A well established method is the original algorithm published by Lorensen & Cline in 1987.

A couple of cases have shown not to match the original scalar function, so that the method has to be considered to be inconsistent because of ambiguous cases in 3D. It is working very well in practice, though.

For this reason, we consider the Marching Tetrahedra algorithm in the following, which does not exhibit ambiguities.

Iso Surfaces | | Tetrahedra Decomposition