(1) Determine distance from patch properly (also in general polygon cases)
(2) Move refine()
(3) Rewrite the logic of the patch (allow it to be a polygon)

The previous solution assumed that some sections consisted of a single
face on the coarse grid

Also changes the [Output]

The original coordinates are used and then rotated

This also reveals that the left angle is closer to 15.1 degrees than to
15; new calculations thus yield slightly different results

Note: the angle is not 15 but rather 15.1 degrees!