Singularities of rational Bézier curves

@article{Monterde2001SingularitiesOR,
  title={Singularities of rational B{\'e}zier curves},
  author={Juan Monterde},
  journal={Computer Aided Geometric Design},
  year={2001},
  volume={18},
  pages={805-816}
}
We prove that if annth 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.  2001 Elsevier Science B.V. All rights reserved. 

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