A new selection scheme for spatial Pythagorean hodograph quintic Hermite interpolants

Chang Yong Han, Hwan Pyo Moon, Song Hwa Kwon

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

For given C1 Hermite data, there exists a two-parameter family of Pythagorean hodograph (PH) quintic curves which interpolate the data (two end-points and end-derivatives) as observed by Farouki et al. (2002b). As “good” candidate curves for a selection problem, we propose a special type of PH quintic interpolating curves called extremal interpolants and prove that the extremal interpolants preserve planarity, i.e., they are planar curves if the data are planar. Since there are only four distinct extremal interpolants, the selection problem, when only considering extremal interpolants as possible candidates, is reduced to picking one curve from finite candidates. Due to the preservation of planarity, extremal interpolants coincide with one of p0,0(t),p0,π(t),pπ,0(t),pπ,π(t) if the data are planar, where pϕ02 (t) denotes the parametrization proposed by Šír and Jüttler (2005). However, any of the four extremal interpolants is generically not identical to the interpolants for non-planar data, and empirical results suggest that being compared with the unique cubic interpolant, the best curve is one of extremal interpolants among all extremal interpolants and p0,0(t),p0,π(t),pπ,0(t),pπ,π(t).

Original languageEnglish
Article number101827
JournalComputer Aided Geometric Design
Volume78
DOIs
StatePublished - Mar 2020

Keywords

  • C Hermite interpolation
  • Extremal interpolant
  • Pythagorean hodograph curve
  • Quaternion
  • Quintic
  • Spatial

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