Relative distances between high-symmetry points in the Brillouin Zone

One common situation when calculating the band structure of a material using Density Functional Theory (DFT) is deriving the relative distances between points in the Brillouin Zone (BZ). The DFT tool will use the number of points defined for each direction in the BZ to produce the eigenvalues.  Abinit calls this “circuit”, and luckily, can be set to calculate it automatically by defining the length (or points) of the smallest distance using the command “ndivsm”. This will produce something like the following in the output:

0.00000 0.00000 0.00000 ==> 0.33333 0.33333 0.00000 ( ndiv : 16 )
0.33333 0.33333 0.00000 ==> 0.50000 0.00000 0.00000 ( ndiv : 8 )
0.50000 0.00000 0.00000 ==> 0.00000 0.00000 0.00000 ( ndiv : 14 )

which is for the distance between four points, where the last is the same as the first (Γ->Κ->Μ->Γ).

Alternatively,  since I use Quantum Epsresso, and it requires to set the distances between points yourself, I use the ones that Wannier90 calculates, so that I can make a direct comparison between the two band structures.

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