Novel Algorithms for Scan-Conversion of Conic Sections

Novel algorithms for the generation of conic sections whose axes are aligned to the coordinate axes are proposed in this paper. The algorithms directly calculate difference between the expressions satisfied by two adjacent points lied on curves, and then, a kind of iteration relation including residuals is established. Furthermore, according to the criterion of nearest to curve, a residual in 1/2 is employed to obtain an integer decision variable. The analyses and experimental results show that in the case of the ellipse, our algorithm is faster than basic midpoint algorithm and Agathos algorithm because constant term accumulated in every loop is eliminated, but its idea and derivation are at least as simple as basic mid-point algorithm. Moreover, our algorithm does not set erroneous pixels at region boundaries, and anti-aliasing is easily incorporated.