I like your example and perspective. I would just add on that it is not facile to do this for metric spaces, but leads directly to constructive solid geometry [

I like your example and perspective. I would just add on that it is not facile to do this for metric spaces, but leads directly to constructive solid geometry [0], where we render images of complex solid objects by exchanging the object for a signed distance function [1], a function which indicates how far the object is from any point in the space. [0] https://en.wikipedia.org/wiki/Constructive_solid_geometry https://en.wikipedia.org/wiki/Constructive_solid_geometry [1] https://en.wikipedia.org/wiki/Signed_distance_function https://en.wikipedia.org/wiki/Signed_distance_function