
Better geometry through graph theory - memexy
https://ideolalia.com/2018/08/28/artifex.html
======
memexy
The trick reminds me of transverse intersection assumption from topology:
[https://en.wikipedia.org/wiki/Transversality_(mathematics)#:...](https://en.wikipedia.org/wiki/Transversality_\(mathematics\)#:~:text=transversality%20is%20a,intersection).

The confusing part is the description of how the edges are added and removed
to make a "consistent" graph. Graphs don't have a metric associated with the
edges but he goes back and forth between the graph representation and
referencing a metric structure between the nodes and either adding or removing
the shortest path. It makes sense but it's not clear why. I couldn't think of
obvious counter-examples to the claim but maybe someone else can. The graphs
he draws don't make it obvious that the edges are "directed" (inside vs
outside requires choosing a direction/orientation). But after deciding the
direction of each edge why does removing the shortest one make sense for
computing the correct set of nodes for the union of some given geometric
elements?

