Singularities of rational Bézier curves Original Research Article

We prove that if an nth degree rational Bézier curve has a singular point, then it belongs to the two (n−1)th degree rational Bézier curves defined in the (n−1)th step of the de Casteljau algorithm. Moreover, both curves are tangent at the singular point. A procedure to construct Bézier curves with singularities of any order is given.