Performance, and accuracy improvements in algorithms for centred, axes-aligned ellipses

Two new algorithms for nonparametric axes-aligned ellipses will be presented, addressing the question of accuracy and efficiency in the existing algorithms. Both algorithms are free of errors arising from slope approximation. However, the merit of the first algorithm is its accuracy as well as giving the best performance for the special class of ellipses under consideration. The second algorithm is as accurate as the first with added potential of generalization for arbitrary oriented ellipses and the general conics.