Fast Rendering of General Ellipses

Abstract

Even though GKS did not include circles and, in a more general form, ellipses and elliptical arcs in the list of elementary graphics primitives, CGM settled this omission with its standardization in 1987. According to CGM as well as to CGI, ellipses and elliptical arcs are defined in a very general way via endpoints of conjugate diameter pairs (CDP). Based on the algorithm of Maxwell & Baker [5] this paper presents a new algorithm for the rendering of general ellipses (i.e. not aligned to the coordinate axes) and elliptical arcs which is not only fast and very well suited for implementation in hardware but also deals with all degenerate cases of ellipses at no extra cost. Furthermore, the algorithm provides all the information which is necessary for the generation of anti-aliased elliptical curves.