On modelling the Bezier cubic in algebraic form

Splines based on four-point Bezier cubic arcs show some disadvantages compared to general conic arcs. Efficient rendering and data fitting algorithms require that the cubic be expressed in algebraic form, but there are problems in the conversion from the parametric form because of a singularity associated with a special case, the parabola. In conversion from the general conic to the Bezier cubic format, on the other hand, the authors note that the arcs of an ellipse can be well approximated, but not sharply turning hyperbolic arcs.