Intersection of two sets in openstreetmap to find parent of any area

Question

I am trying to determine what the parent administrative area of any given area. The idea is that the closest parent is the administrative area with the highest/deepest admin_level that is shared as a parent by all points of the area boundary. Her the pseudo-algorithm I would like to be able to reproduce with the OSM API.

For a given area: For n in all nodes of its boundaries:

• parents are the administrative area the node n lies in

potential_parent = intersect(list of parents)

unique_parent = parent in potential_parent where admin_level == min(admin_level)

Unfortunately I wasn't able to define the intersection of the different sets of parents for each node composing the boundary of the area of interest

Hehre is the solution I came up with:

rel(426391772) -> .obj;
.obj>;
is_in;
area._[boundary=administrative] -> .parents;
foreach .parents -> .shared(
  (.shared; - (.shared; - ._;););
);
out tags;

The for loop was my attempt to create the intersection set. But it doesn't return anything, while the .parents set is not empty. I suspect the difference is not working as I thing it would.

The rest of the request to filter the good area is as follow and seems to work:

area.shared[boundary=administrative](if:t["admin_level"] == max(t["admin_level"]));

If you have a better approach to this problem, I am happy to hear it.

Here is an example of my request with the turbo-overpass.

Answer 1

You could use the following approach, which assumes to have at least one node with tags inside your relation. It restricts the output to adminsitrative boundaries.

rel(1681994) -> .r;
.r map_to_area;
(node[~"."~"."](area); - (.r;way(r);node(w);););
is_in;
area._[boundary=administrative];
area._(if:number(t["admin_level"]) < number (r.set(t["admin_level"])));
area._(if:number(t["admin_level"]) == max(number(t["admin_level"])));
rel(pivot);
out;

NOTICE: This sort of query is very expensive. Don't use it in any app unless you're happy to hammer your own Overpass API instance!

In general, I highly recommend to do this sort of query with a GIS database, like Postgresql with Postgis instead.