Marching tetrahedra (or cubes) on a non-orthogonal 3D grid I have data for points of a 3D grid. The points of the grid are generated from three nonorthogonal vectors: each grid point has coordinates $\mathbf{q}_{ijk} = i \mathbf{a} + j \mathbf{b} + k \mathbf{c}$, where $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$ are nonorthogonal, noncoplanar vectors. (In cristallography, it's called a triclinic system) So, my question is: how would you adapt the marching tetrahedra (or marching cubes, if easier) to this case? Has this been treated already somewhere, is there software for that (I haven't found any).

Nothing in Marching Cubes (or Marching Tetrahedra, AFAIK) actually requires that the grid be cubical or even orthogonal; the algorithms are inherently topological (or arguably, combinatorial) in nature. The heart of Marching Cubes is really just a table matching the $2^8$ combinations of positive/negative function values at the cube corners to a set of topological triangulations that are consistent with the 'simplest' isosurface of a function taking on those values (e.g., when only one vertex is positive we have a single triangle, with vertices along the three edges connecting the positive vertex to its neighbors), and those triangulations are invariant under linear transformations - which is all your skewed grid represents.