Identify Grid Data Required during Intepolation

I'm trying to figure out a way to identify which grid points are queried when doing a n-D interpolation. The general problem is:

I have a large n-Dimensional hypercube bounding the data I need. Since it is very expensive to fill in a fine grid across that whole hypercube, I wish to initially generate a very coarse grid over the hypercube and get data points. I will then use that data to run through the simulations for which the interpolation is needed. From that, I want to identify what points on a finer grid would be required by the simulation. Ideally, I could generate something like a heat map, where I can count the number of times each data point gets called, so I could determine to what fidelity I need to obtain data. In addition, this will let me identify which points in the cube can be ignored, which I expect to be 90-95% of the total.

My first thought is to dig into the interpn function and find where it queries the grid and modify it for my purposes, but I'm open to an existing or more elegant approach.