Midpoint Circle Algorithm Research Articles

An Efficient Ellipse-Drawing Algorithm

The midpoint algorithm for drawing ellipses on raster graphics displays is presented. The algorithm is highly accurate and requires only a few integer additions per pixel. It is also demonstrated that a simple extension of J.E. Bresenham's circle-drawing algorithm (1965) to the more general case of ellipses is not sufficient to guarantee accuracy. The accuracy of the midpoint algorithm is limited only by the resolution of the display device itself, yet is requires no more execution time than the extended Bresenham algorithm.

Freeman digitization of integer circles minimizes the radial error

It is proved that Freeman digitization of integer circles (i.e., circles with integer radius and center coordinates) minimizes the distance-to-the-center error of the digitization. It also proves the equivalence of Bresenham's circle digitization criteria to Freeman's scheme for integer circles, being therefore a contribution to the task of relating various proposed digitization schemata.