Pythagorean-hodograph ovals of constant width

Rachid Ait-Haddou, Walter Herzog, Luc Biard*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A constructive geometric approach to rational ovals and rosettes of constant width formed by piecewise rational PH curves is presented. We propose two main constructions. The first construction, models with rational PH curves of algebraic class 3 (T-quartics) and is based on the fact that T-quartics are exactly the involutes of T-cubic curves. The second construction, models with rational PH curves of algebraic class m > 4 and is based on the dual control structure of offsets of rational PH curves.

Original languageEnglish (US)
Pages (from-to)258-273
Number of pages16
JournalComputer Aided Geometric Design
Issue number4-5
StatePublished - May 2008
Externally publishedYes


  • Constant width
  • Dual Bézier curve
  • Evolute and involute
  • Offset curve
  • Oval
  • PH curve
  • Rosette

ASJC Scopus subject areas

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


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