For unstructured meshes of points, pandas.MultiIndex is not the right abstraction.

Suppose you have a (very long) list of sorted points (x, y, z) in a multi-index. You can efficiently query within fixed bounds along x by doing binary search. But for queries in y and z, you cannot do any better than looking through the entire list. Moreover, pandas.MultiIndex factorizes each level into unique values, which is a complete waste on an unstructured grid where few coordinate overlap.

For unstructured meshes, you need something like a KDTree (see discussion in https://github.com/pydata/xarray/issues/475), with ideally with nearby points in space stored in contiguous array chunks.

I would start with trying to get an in-memory KDTree working, and then switch to something out of core only when/if necessary. For example, SciPy's cKDTree can load 1e7 points in 3-dimensions in only a few seconds:

``` x = np.random.rand(int(1e7), 3) %time tree = scipy.spatial.cKDTree(x, leafsize=100)

CPU times: user 2.58 s, sys: 0 ns, total: 2.58 s

Wall time: 2.55 s

```

The might be good enough.