Anti-aliasing for circles is complex and the existing algorithms are not working satisfactory.To improve the efficiency and the anti-aliasing effect

an integral algorithm is presented for circle anti-aliasing based on midpoint generating algorithm.The new algorithm finds the grayscales of each pixel according to the distance between the center of the pixel and the circle.A circle with a 64 levels grayscale can be drawn.The algorithm abandons the two-order epsilon and corrects the error by simple calculations.We built a method to forecast the grayscale change between neighboring pixels using integer shift

addition

and comparing without using floating-point and divisions

making it easy to implement the algorithm on hardware.The results show that the anti-aliasing effect and its efficiency have been improved.