Pythagorean hodograph spline spirals that match G3 Hermite data from circles

Zhong Li, Rachid Ait-Haddou, Luc Biard

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A construction is given for a G3 piecewise rational Pythagorean hodograph convex spiral which interpolates two G3 Hermite data associated with two non-concentric circles, one being inside the other. The spiral solution is of degree 7 and is the involute of a G2 convex curve, referred to as the evolute solution, with prescribed length, and composed of two PH quartic curves. Conditions for G3 continuous contact with circles are then studied and it turns out that an ordinary cusp at each end of the evolute solution is required. Thus, geometric properties of a family of PH polynomial quartics, allowing to generate such an ordinary cusp at one end, are studied. Finally, a constructive algorithm is described with illustrative examples.
Original languageEnglish (US)
Pages (from-to)162-180
Number of pages19
JournalJournal of Computational and Applied Mathematics
StatePublished - Apr 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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