Singularities of rational Bezier curves

摘要

We prove that if an nth degree rational Bezier curve has a singular point, then it belongs to the two (n -- 1)th degree rational Bezier 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 Bezier curves with singularities of any order is given.