Algorithms for drawing bilevel (not antialiased) circles, prefiltered-antialiasing-along-straight-line edges, and antialiased circles and ellipses are described in literature cited in this paper. This work reports new algorithms for drawing antialiased circles and ellipses which do not require floating point, square root, or division operations in the inner loops. The basic scheme of the algorithms described in the paper is to employ polynomial prediction of a filter function, based on previous values of the function, and to use iteration to bring the prediction within tolerance. New algorithms are applied to rendering an octant of a filled circle using a square area integration filter. Some other techniques for drawing different types of circles and ellipses are also presented in the paper.