Bisector plane in a mesh for each line

Given a mesh, for each line which is the best method to obtain the bisector plan of the two adjacent faces?
Component “mesh closest point” and “Mesh Eval” can give the vector for example in the middle point of the line, but the vector doesn’t belong to the bisector plane.

Unify (if possible) the normals and compute the Mesh Face normals.

Loop into the clothed edges collection.

Get the edge.Direction: this could be your xAxis.

Get the 2 adjacent Faces (and obviously the normals since their indexing is the same).

Get the normal’s sum (note: normals are unitized anyway). This could be your yAxis. If the unification failed and the mesh is closed you can control the yAxis direction via some inclusion test (but mesh contains pt has issues some times).

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This uses the Sandbox plugin to determine the mesh topology Thank you to @PeterFotiadis for suggesting just adding the mesh normals, saving me a lot effort.
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mesh bisector planes.gh (10.6 KB)

Hmm … what means a bisector Plane for a naked edge?

Anyway … the attached does some checks more (but not all) related with good/bad meshes (and disjoined pieces).

Mesh_BisectorFacePlanes_EntryLevel_V1.gh (123.6 KB) .

Fair enough, but it might have some meaning to the OP since the planes are orthogonal to the faces.

mesh bisector planes-b.gh (13.0 KB)

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Fair enouph.

Added a quad-what-to-do option.

Mesh_BisectorFacePlanes_EntryLevel_V1A.gh (126.7 KB)

And the naked option (but what is a quad face normal? is it a bird?, is it a plane? is it the superman?):

Mesh_BisectorFacePlanes_EntryLevel_V1B.gh (126.8 KB)

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Thank you for the quick response.
I’ll try to check it as soon as possible