Selecting Shared Edges from a Mesh

Question

Consider the following mesh

mesh0 = VoronoiMesh[RandomReal[1, {50, 2}]]

I can select interior polygons with

mesh = MeshRegion[MeshCoordinates[mesh0], MeshCells[mesh0, {2, "Interior"}]]

My goal is to select only the edges that share a polygon. MeshPrimitives gets me close

Graphics[MeshPrimitives[mesh, 1]]

Now I would just need to select the edges from MeshPrimitives[mesh, 1] that share a polygon, in order to get something like

I know about "Frontier" as an option for MeshCells, but not entirely sure if I could use it. Any ideas?

I believe the first time I learned about them was on MarcoB's answer on my question: https://mathematica.stackexchange.com/a/212625/64001 — sam wolfe, Mar 18 '20 at 20:18
I believe I solved, see below. Any improvements are welcome. — sam wolfe, Mar 18 '20 at 20:25

score 1 · Accepted Answer · answered Mar 18 '20 at 20:23

1

In the meantime, I have figured out an answer. The code

Complement[MeshPrimitives[mesh, 1], MeshPrimitives[BoundaryMesh[mesh], 1]] // Graphics

yields

which is what I want. Any comments/improvements are welcome.

answered Mar 18 '20 at 20:23

sam wolfe

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score 1 · Answer 2 · answered Mar 18 '20 at 21:37

With the syntax that you brought up yourself:

edges = Complement[
   MeshCells[mesh, {1}, "Multicells" -> True][[1, 1]],
   MeshCells[mesh, {1, "Boundary"}, "Multicells" -> True][[1, 1]]
   ];
primitives = Partition[MeshCoordinates[mesh][[Flatten[edges]]], 2];

But also

edges= Union[
 MeshCells[mesh, {1, "Frontier"}, "Multicells" -> True][[1, 1]],
 MeshCells[mesh, {1, "Interior"}, "Multicells" -> True][[1, 1]]
 ]

looks good.

Selecting Shared Edges from a Mesh

2 Answers2