My real-world problem is that I want to combine state House and Senate legislative districts so that a user can pick a region (not a point) on a map that is included in both their House and Senate districts, to identify who their legislators are.
I have shapefiles for both House and Senate districts. I'm looking for a library that will, given the two sets of shapes, emit a minimal set of shapes for which, by selecting one, a user may identify both their House and Senate district. I can imagine how to do it myself by doing lots of intersection and difference operations, but also can imagine problems that others hopefully have solved.
My first problem is that I can't search for something to do this operation because I don't know what it's called.
Does it have a commonly-used name?