After some thinking and a little random Googling I decided to go with the different mapping scheme that would lead to a more sparse mapping but would look better with animations.  Unfortunately this mapping yields almost 50% of the pixels not being mapped to the display.  But at least the circles are round.  Looks like I am going to have to investigate how to add a brush width to my drawing functions or just be cognizant that single pixel wide shapes may not map well.