TY - JOUR
T1 - A new selection scheme for spatial Pythagorean hodograph quintic Hermite interpolants
AU - Han, Chang Yong
AU - Moon, Hwan Pyo
AU - Kwon, Song Hwa
N1 - Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/3
Y1 - 2020/3
N2 - 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 pϕ0,ϕ2 (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).
AB - 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 pϕ0,ϕ2 (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).
KW - C Hermite interpolation
KW - Extremal interpolant
KW - Pythagorean hodograph curve
KW - Quaternion
KW - Quintic
KW - Spatial
UR - http://www.scopus.com/inward/record.url?scp=85080895231&partnerID=8YFLogxK
U2 - 10.1016/j.cagd.2020.101827
DO - 10.1016/j.cagd.2020.101827
M3 - Article
AN - SCOPUS:85080895231
SN - 0167-8396
VL - 78
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
M1 - 101827
ER -