How can I draw lines in this highly constrained way?

Please see the below image for examples of what I would like to do. On the left is the hand-drawn path and on the right is what I would like the result to be.

Essentially, I would like freehand drawings to be totally constrained to:

• A set grid (larger than the brush width)


• Straight lines of 0, 45 and 90 degrees only.


• Sections of curves that begin and terminate at 0, 45 and 90 degrees only and follow a perfectly round path (not oblong in any way).