Restricting Overpass queries to yielding objects whose *centers* are inside a particular area

Question

In OSM, some buildings stand on administrative borders; for example, the base of the building https://www.openstreetmap.org/way/333896751 intersects the neighboring municipalities Riedering, Rohrdorf and Stephanskirchen, even though these seem to share no common area.

In Overpass, area-based filtering apparently allows restricting result sets to features where some part of the geometry is in contact with an area, which likely explains that certain queries yield a nonempty intersection of "straddling" buildings, even when the underlying areas appear "geometrically disjunctive".

For instance:

// buildings in Riedering: 
[out:json]; wr[building](area:3602186935); out geom; 

// buildings in Stephanskirchen: 
[out:json]; wr[building](area:3602186942); out geom; 

// some buildings appear to belong to both administrative areas: 
[out:json]; wr[building](area:3602186935)(area:3602186942); out geom; 

For a certain statistical analysis that should be stratified by municipalities, I would like to modify the above queries so that each building should belong unambiguously to a single municipality. Since building centers have no expansion, I assume that these should mostly be unequivocal w.r.t. identifying a single underlying municipality. For example, according to its center, the mentioned building would be interpreted as belonging to Rohrdorf:

[out:json]; // computed via [out:json]; way(333896751); out center; 
is_in(47.8373143, 12.1714380); 
wr(pivot)[admin_level=8][boundary=administrative];
out geom; 

This suggests that unequivocal building sets could be computed from sequences of Overpass queries that (initially) calculate building centers and that (in a second step) identify underlying municipalities. When reading about features such as the more recent center()-function, I was wondering whether such a maneuver could be integrated into a single query, which for a given municipality (e.g., Stephanskirchen) yields a set of unambiguous buildings (i.e. whose centers lie on the area). Unfortunately, I could not come up with an executable syntax. Do you have any idea?

Answer 1

First of all, I'm starting with an example how to use the center() function to generate the center point for all ways in the current inputset, here for a single way 333896751.

way[building](333896751);
out geom;
convert way :: = ::,
            ::geom = center(geom()),
            ::id = id();
out geom ;
derived._(area:3602186942);   // << area filter on derived object not supported
out geom;

The "convert" statement processes all objects in your inputset and generates so called "derived objects". Derived objects are runtime-only objects that can take over some of the characteristics of the original objects, such as their object id, tags, or geometry.

Now regarding the filtering of those derived objects: unfortunately, the area filter only supports nodes, ways and relations, but not derived objects. This way, you cannot filter your derived objects by municipality areas.