Curve design with rational Pythagorean-hodograph curves

Helmut Pottmann*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


The dual Bézier representation offers a simple and efficient constructive approach to rational curves with rational offsets (rational PH curves). Based on the dual form, we develop geometric algorithms for approximating a given curve with a G2 piecewise rational PH curve. The basic components of the algorithms are an appropriate geometric segmentation and G2 Hermite interpolation. The solution involves rational PH curves of algebraic class 4; these curves and important special cases are studied in detail.

Original languageEnglish (US)
Pages (from-to)147-170
Number of pages24
JournalAdvances in Computational Mathematics
Issue number1-2
StatePublished - Jan 1995
Externally publishedYes


  • Rational curve
  • curve approximation
  • dual Bézier representation
  • geometric Hermite interpolation
  • hodograph
  • offset curve

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Curve design with rational Pythagorean-hodograph curves'. Together they form a unique fingerprint.

Cite this