Abstract: In order to improve speed of circles drawing, some multi-step or run-length slice
algorithms are proposed. Based on careful analysis of the characteristics of raster-scan circles, a
simple and fast method to calculate lengths of slices is presented in this paper. In the new
algorithm, double-step control is mainly used for larger horizontal run-slices, and mixed
single-step and double-step control is adopted for complicated pattern and run-slices with 45°
angle, furthermore, each horizontal run-slice is output at once, only about 2.9 times basic
operations are needed for once stepping on average. Experiments and analysis shows that the new
algorithm is significantly faster than previously published ones, and its’ derivation can be gained
in a simple manner. Furthermore, it can be implemented with hardware since no complex
operations are involved, and can be developed to draw other conic curves.

Key words: circle drawing, integer operation, run-length algorithm, multi-point drawing;
scan-conversion