The eccentricity of conic sections formulated as rational Bézier quadratics

Chendong Xu, Tae Wan Kim, Gerald Farin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The eccentricity of rational quadratic Bézier curves is formulated directly in terms of their control-points and weights. Based on this expression, we analyze the range and extreme values of the eccentricity of conic sections expressed in this form. We also provide an explicit expression for the eccentricity of the osculating conic of a rational Bézier curve of high degree.

Original languageEnglish (US)
Pages (from-to)458-460
Number of pages3
JournalComputer Aided Geometric Design
Issue number6
StatePublished - Aug 2010


  • CAGD
  • Conic sections
  • Eccentricity
  • Rational Bézier curves

ASJC Scopus subject areas

  • Modeling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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