I´d like to throw in the …provided the steppers are not moved during the tool change. Power must be kept on, step idle delay must be at 255 (fully on) and do not manhandle the spindle during tool change 
I always use g28.1 when I start a new project so the zero position is saved even after powering off (until you set a new one).
After a bit change I re-home, and then run g28 to return to the zero point.
That way if you snap a belt or wrestle the spindle about etc, you won’t lose your zero.
Word of warning though. G28 moves straight to the point you set using g28.1 (X, y, and z) so I often jog slightly before issuing it to avoid clamps
OK, you are right. Zero is the center of the bit. I cut my grid and the test pattern with a 1/16 bit. The first time, I set the bit just to the left and in front of an intersection on my grid. The circles are off to the side, and the square got cut off wrong, too. Second try, I set a different intersection on my grid as zero, and I set it as zero by actually jogging the bit down into the intersection to get it perfect. The circles cut right on intersections of the grid lines, and an entire square of the grid got cut away clean.
My first test was off because I was sloppy drawing the grid by hand with a straight edge and a pencil.
