The eccentricity of conic sections formulated as rational Bézier quadratics

Chendong Xu, Tae Wan Kim, Gerald Farin

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume27
Issue number6
DOIs
StatePublished - Aug 2010

Fingerprint

Eccentricity
Rational Curves
Extreme Values
Control Points
Curve
Range of data

Keywords

  • CAGD
  • Conic sections
  • Eccentricity
  • Rational Bézier curves

ASJC Scopus subject areas

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

Cite this

The eccentricity of conic sections formulated as rational Bézier quadratics. / Xu, Chendong; Kim, Tae Wan; Farin, Gerald.

In: Computer Aided Geometric Design, Vol. 27, No. 6, 08.2010, p. 458-460.

Research output: Contribution to journalArticle

Xu, Chendong ; Kim, Tae Wan ; Farin, Gerald. / The eccentricity of conic sections formulated as rational Bézier quadratics. In: Computer Aided Geometric Design. 2010 ; Vol. 27, No. 6. pp. 458-460.
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