Hex grids have six primary directions. Look at the max of |{{labels.s}}-{{labels.q}}|, |{{labels.r}}-{{labels.s}}|, |{{labels.q}}-{{labels.r}}|, and it will tell you which wedge you're in.
You can also construct six “diagonal” directions. Look at the max of |{{labels.q}}|, |{{labels.s}}|, |{{labels.r}}|:
In both cases, some hexes are on the boundary between two wedges. There will be a tie between two of the max() arguments.
Also see this stackoverflow answer[1], which includes an interactive demo.
Source code for the the diagrams on this page: directions.js
Angles#
If you want the angles, I the simplest thing is to convert to cartesian coordinates using hexToPixel, then use atan2(y,x) to calculate the angle. However, if you don't need the angle itself, but only a comparison key, you can use atan2(r,q) as a cheaper substitute. Compare the true angle to an angle-like sort key:
I wonder if there's a way to use spirals from cos/sin[2] with hexagonal grids[3] to construct hexagonal spirals on a grid.