If something like this is extracted, it should probably be in the float3 class. I did an attempt at that here: D11773: BLI: Add "is_parallel" function for float3

Exposing the function in node_geometry_util.hh doesn't necessarily mean moving it to node_geometry_util.cc. I think the implementation can stay in the circle primitive file.

If you want to return a float3, there are a couple things to know:

• Pass the float3 by reference, (with &) then you can just assign it's value in the function and the caller will have the new value.
• Return arguments should generally be last.
• Return arguments should generally have an r_ prefix, like float3 &r_center

Looks like you don't have clang format set to run when you save the file. I strongly recommend doing that, it's a great time saver.

The reason I was questioning the abstraction of "circle centerpoint" earlier is that you have to repeat this work that was already done in it. Maybe there is a way to arrange things differently where that isn't possible, maybe not.

Hmm, it looks like most of this is dealing with reordering the points if necessary? Not sure. I think it's totally valid to assume that the first point is the beginning, the second the middle, and the last the end.

I wonder if these could get more descriptive names and they could also be returned from the circle calculation function. That way circle_centerpoint would be able to do most of the "hard thinking" for you.