Sparse Pythagorean hodograph curves

Rachid Ait-Haddou, Marie Laurence Mazure*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We introduce cubic-like sparse Pythagorean hodograph curves which are possibly of high degrees though they can be handled as cubic curves. They offer more flexibility than the classical Pythagorean hodograph cubic curves with which they share many properties. We give an elegant geometric characterization of their control polygons. This characterization leads to many interesting computational algorithms for curve design. We show how to extend such algorithms to quintic-like sparse PH curves.

Original languageEnglish (US)
Pages (from-to)84-103
Number of pages20
JournalComputer Aided Geometric Design
StatePublished - Jul 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.


  • (Complete) Müntz spaces
  • (Sparse) Pythagorean hodograph curves
  • Blossoms
  • Control polygons
  • Extended Chebyshev spaces
  • Shape parameters

ASJC Scopus subject areas

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


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