Comment by danbruc

Your second one is somewhat in the right direction, I think. My guess would be that you split the circle into eights, that keeps the tangent slope between zero and one. Then you can go along one axis from 0 to sin(45°) times the radius and the value along the other axis will always either stay the same or change by one as the derivative is between zero and one. As you move along your primary axis, you generally keep the value along the secondary axis unchanged but you accumulate the error. When the error crosses 0.5, you move one pixel along the secondary axis and adjust the error accordingly. And of course you always draw eight mirrored and rotated pixels. In some way an adaptation of the Bresenham algorithm for drawing lines.