Double-Step Circle Drawing Algorithm with and without Grey Scale

In this paper, a double-step circle drawing algorithm is presented first. It chooses the best approximate pixels to the circle with only integer arithmetic. The results of comparison show that its speed is higher than the existing circle drawing algorithms. Furthermore, this algorithm can be used to draw anti-aliased circles, e.g. to draw filled circle edges with different intensity, without increase in calculations. It generates two more intermediate shades of grey scale than the double-step algorithm by Wu and Rokne and the greatest error of intensity is only half of that of the latter.