Let me know if this is more on-topic for physics.se (or more generally, off-topic for mathematics.se).
Okay, imagine you have a volume of space with instruments measuring air pressure (and for simplicity, this volume has an average pressure of $1$). But in this volume, portals can appear. These portals connect to an infinitely big volume of space with a pressure of $0$. So, they act as a kind of $3$D leak of air (as opposed to air leaks that are limited to the surface of a pressurized volume).
For simplicity, we assume the instruments are immovable points dispersed evenly across the volume, and the portals are immovable balls all with the same volume $V$ and open-duration $T$, and they can appear anywhere in the volume.
When portals appear, since they always have the same $V$ and $T$, they should create the same-ish negative pressure differential each time (with noise causing difference), the events mainly differing by their locations. It seems intuitive that these locations would be determinable, to some resolution, by the instruments. I guess that resolution would depend on the density of the instrument throughout the volume, the amount of noise, and the precision of the instruments.
Anyways, I wonder how (if at all) these instruments' data could be used to determine the space of possible locations for the portal. I guess you'd look at the instrument that read the highest pressure differential, and then look the neighbors with the highest readings, and then suddenly you have a polygon bound by these instruments.
Now, you give this polygon a weight based on the pressure differential of its vertices, and then the center of gravity of this polygon is roughly where you expect the portal to be... yes? That's just my speculation, and I don't even know how you would determine the "weight" of this polygon, because it's not like you could linearly interpolate between the vertices, right? Or maybe you could?
My question is this: how could you use the data from these instruments to determine the locations of the portals, and what degree of resolution could you achieve given the parameters like instrument density, instrument precision and noise?
