@Campbell Barton (campbellbarton) I've implemented those four functions, while doing some testing I thought it might be a useful to add a fifth function calc_tangent_edge_center_diagonal which would use the vector going from the farthest vert to the center of the edge (useful for tris and odd sided ngons) Thoughts?

Just for fun, here's the result from profiling the performance of calling each function on every face in a torus with 20,992 faces (all quads):

      83974 function calls in 0.093 seconds

Ordered by: standard name

ncalls  tottime  percall  cumtime  percall filename:lineno(function)
     1    0.005    0.005    0.093    0.093 <string>:1(<module>)
     1    0.024    0.024    0.088    0.088 Text:6(main)
     1    0.000    0.000    0.000    0.000 {built-in method bmesh.new}
     1    0.000    0.000    0.093    0.093 {built-in method builtins.exec}
 20992    0.005    0.000    0.005    0.000 {method 'calc_tangent_edge' of 'BMFace' objects}
 20992    0.012    0.000    0.012    0.000 {method 'calc_tangent_edge_diagonal' of 'BMFace' objects}
 20992    0.004    0.000    0.004    0.000 {method 'calc_tangent_edge_pair' of 'BMFace' objects}
 20992    0.009    0.000    0.009    0.000 {method 'calc_tangent_vert_diagonal' of 'BMFace' objects}
     1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
     1    0.034    0.034    0.034    0.034 {method 'from_mesh' of 'BMesh' objects}

I made the requested changes (plus a little cleanup)

I also changed BM_face_calc_tangent_edge_pair to normalize the edge directions for triangles. After some more testing, I think the result is a lot more useful this way.

I rewrote BM_face_calc_plane to call BM_face_calc_tangent_edge for ngons and BM_face_calc_tangent_edge_pair for quads. It still calculates the tangent for triangles the same way (uses the shortest edge), not sure if it makes more sense to use BM_face_calc_tangent_edge_pair for that too.

Also, I removed the note from the doc string about the result not being normalized.

• Fix ngon edge-pair bug, edge v1/v2 direction doesn't follow the face

Various tweaks to logic:

• rename BM_vert_tri_calc_plane -> BM_vert_tri_calc_tangent_edge
• add BM_vert_tri_calc_tangent_edge_pair which works similar to BM_vert_tri_calc_tangent_edge, however instead of using the unique edge, use the center-line between it and the adjacent vertex.
• both BM_vert_tri_calc_tangent_edge and BM_vert_tri_calc_tangent_edge_pair normalize their result (so callers don't need to remember which functions do/don't normalize the tangent). but normalizes both edges adjacent to the most unique edge (before adding).
• Add fallback for when the ngon has 2x edges that are the same length, pointing in the same direction (could give a zero length normal). Even with this change - this part is susceptible to float precision error causing jitter in the result.

BM_face_calc_tangent_edge_diagonal: Use real length between verts and edges

Instead of using the edges center point, calculate closest_to_line_segment_v3 from the vertex to the edge.

Make sure r_tangent is set, even when degenerate faces are passed in.

• Update py docs

BM_vert_tri_calc_tangent_edge_pair: Use a better method of calculating the center-line

Own update for this function was incorrect (should have normalized hothe edges before adding).
However this isn't needed if we use the center-point from the edge to the opposite vertex.

• Optimize BM_vert_tri_calc_tangent_* functions, avoid sqrt, use squared lengths instead.

• De-duplicate code to find the unique edge