This is easy with a cubic grid because the cube subdivides into cubes, and so {1.1, 2.2345, 3.4} has a well understood grid translation and visualization. Not sure what the equivalent would be in a FCC grid. All the formulations I’ve seen, for example, using integer coordinates for the cell grid positions would not seem to accommodate this, of course. Still searching der google, but was wondering if anyone had any pointers here. Seen a lot of voxel stuff, which is cool, but I’m looking for traditional analytical tools that seem to require more from coordinates than what I’ve been able to find so far.
Adding question:
For a cubic grid, I can use non integer coordinates and the meaning is understood. I cannot find the equivalent for the face centered cubic grid coordinates. My need is to address the subdivisions within a cell and it’s unclear how to express this with FCC coordinates.
This paper, A Continuous Coordinate System for the Plane by Triangular Symmetry appears to point to the path I was looking for. I believe I’d could then use the dual, cuboctahedron, and leverage its shell progression in sphere packing as an analog to the cube subdivision. That means this would be using the hexagonal close packing lattice, rather than the FCC.