Singularities of rational Bezier curves
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. (C) 2001 Elsevier Science B.V. All rights reserved.
singularity bezier curve discriminant order of singular points weights