Remember the old formula: y = m*x+b and m = tan(theta)
However, if you apply that naively then as you step x by integers, you will get non-integer y coordinates that you will need to make integral. You can floor() or ceil() or round() or fix() to make integral, but as you do so you may end up skipping some integral values (e.g., you might end up selecting y = [1 2 4 5 7 8...]) or you might end up re-using some integral y values. This is likely to throw off your computations.
I suggest you start with something simple like 30 degrees and placing the origin at the logical center of the bottom-left pixel, and computing the exact coordinates you want to be in a single line of length (say) 24. Then switch to 120 degrees and compute again. Now do the logical transpose to compute the lines running perpendicular to those two: is the result one-to-one or do you need to change how you want to define which pixels should be in the lines?
