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I'm not familiar with coedges --- they sound like the darts in the dual map of a planar combinatorial map[1] to me. Do you know if they correspond like this?

In short, a combinatorial map is a graph along with a counterclockwise order of incident half-edges ("darts") at each vertex. This is exactly enough data to record the topological information about how a given connected planar graph is embedded in the plane. They also work for graphs in general oriented surfaces, with the proviso that the complement of the graph consists of a bunch of faces homeomorphic to disks. For example, no annulus faces.

When reading the article, it seemed like what the author was doing was to construct something like a combinatorial map from the purported intersections then use that to answer inside/outside questions. (A graph by itself is unable to answer these questions since it's merely abstract vertices and edges. While the code they use shows the use of graphs[2], the graphs contain the geometric information of the vertex locations, which sort of lets you work with it as if it were a combinatorial map.)

[1] https://en.wikipedia.org/wiki/Combinatorial_map

[2] https://github.com/lacuna/artifex/blob/master/src/io/lacuna/...

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