On the derivatives of rational Bézier curves

We identify several theoretical shortcomings in the derivative formulas for rational Bézier curves and propose a new formula for the derivatives.

Dependence on control points gives a new recursive approach to the derivation of rational Bézier curves.

We present the new derivation formula for rational Bézier curves that overcomes this drawback and show that the kth degree derivative of a nth degree rational Bézier curve can be written in terms of a (2^kn)th degree rational Bézier curve.

This paper leads to a further complete understanding of the derivatives of rational Bézier curves.