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This is rather easy by simply drawing all notes on the freeboard but then actually not drawing the note if it is not within the fret range.
You can even get more advanced by allowing non-box patterns. Basically 1 2 3 or 4 notes per string and just fill out the scale without duplicates.
e.g., for C major =
E 8 10 12 13
A 10 12 14 15
....
(that is 4 notes per string)
Essentially the algorithm just walks the frets and fills out the scale depending on the constraint. Sometimes it might produce non-usable results but generally works.
You can use more complex constraining conditions to get other scales, for example, a sort of "descending horizontal" C major scale:
E 8
A 5 7
D 3 5
G 2 4
B 1
This isn't a box, or could be seen as a skewed box.
Alternatively, if you really want to get far out, you could use kinematics to module a human hand and then use that to determine chords and scales that are playable. If it breaks the fingers of the model then it's and invalid chord.
Add an option to, instead of limiting to one note per string, find every valid note within the diagram (limited by reach).
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