# How can curves created from a cubic mesh have a consistent tangent direction in relation to the other 3 curves that share the original quad?

### Problem Description

After splitting edges and scaling elements, when the 4 edges of a face are converted to individual curves, it seems that almost always one curve will have a tangent in the opposite direction.

For example, looking at the factor value from 0 to 1 from point "4" on the top face, it can be seen that:

4-5: clockwise
5-6: clockwise
6-7: clockwise
7-4: counter-clockwise It can also be seen that when the tangent value is viewed, one curve is black while the others are white or vise versa. ### Application Goal

Ideally, in this proof of concept, each instance would have:

1. An axis pointing in the same direction as the curve (all uniform either clockwise or counter-clockwise)
2. An axis pointed towards the opposite edge
3. An axis pointing in the same direction as the original face's z-normal: If this is accomplished, then, should the instances have an additional line rotated 135° from the line pointing towards the opposite edge, they should be parallel and point in the same direction:  I have referenced many questions, but these two seemed to be the most relevant (the first of which provided a node group that is in the blend file below thanks to quellenform):

How to correct curve tilt, tangents and normals of a curve?

Geometry Nodes: Whether the curve rotates clockwise or counter-clockwise?

Any help would be very much appreciated. This group takes a different approach to yours. The strategy:

• Create a Curve Line for every face-corner on the mesh
• Set endpoint 0 of each spline on the sampled position of each corner of the mesh
• Set endpoint 1 of each spline on the sampled position of each corner, offset by 1, in its face
• Tilt each spline through the signed angle between its own Normal, and the underlying face normal The result is 1 spline for each edge of the mesh, with its Tangent (Z) down the edge (anticlockwise to face-normal), and its Normal (X) set to the normal of the underlying face-corner. ( Y is constrained )

Here, shown with arrows instanced on the curves, aligned to the curves' 'Ŕotations' In the case of rectilinear quads, -Y is the direction towards the opposite edge. • Wow. This setup even covers n-gons. What a brilliant idea to eschew trying to manipulate the original edges and just arrange new curves. As someone who is trying to learn more math for GN I really appreciate your explanations. Thank you very much. Jun 17 at 15:36
• @bobhasajetpack Cheers! Forgive me for not going a bit further, with your 135° thing, but I didn't fully understand that, and figured step 1 might be enough. Jun 17 at 15:46
• It absolutely was enough. The occurance of parallel 135° line alignment (assuming 90° corners) was just my hypothesis should the xyz of the curves have "correct" orientation. Sure enough, your answer was perfect imgur.com/a/MyuhoMB Jun 17 at 15:55