ESRI software has a concept of a 'label point' for a (multi)polygon. It is like the centroid, except it is guaranteed to be within the (multi)polygon. Like for a U-shaped polygon, the label point is somewhere in the bottom of the U. See the ArcGIS REST API Reference on the subject.
I'd like to know a reference, English description, or pseudocode for how something like this is calculated for a polygon or multipolygon.
I get the vibe from results in ArcGIS that the label point is somewhere on the the medial axis transform (skeleton). But not just in its middle, because a big bulge at one end of a polygon will pull the label point into it. So it has a 'center of mass' aspect.
I haven't found an equivalent function in PostGIS (there is ST_PointOnSurface, but that is not quite the same thing). Nor have I found something in QGIS, but maybe I'm not looking for the right non-ESRI terminology.
This duplicates this question, but that one didn't get any high-rated non-hacky answers so I thought I'd ask again. Forgive me if it isn't the done thing.