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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.