Algorithms for projecting points onto conics

We study the problem of projecting 2D points onto quadratic curves (ellipses, hyperbolas, parabolas). We investigate various projection algorithms focusing on those that are mathematically proven to produce (or converge to) correct results in all cases. Our tests demonstrate that those may be still unfit for practical use due to large computational errors. We present two new algorithms that are not only theoretically proven to converge, but achieve nearly perfect accuracy.