On the local existence of the quadratic geometric Hermite interpolant

Authors
Reif, U
Citation
U. Reif, On the local existence of the quadratic geometric Hermite interpolant, COMP AID G, 16(3), 1999, pp. 217-221
Citations number
3
Categorie Soggetti
Computer Science & Engineering
Journal title
COMPUTER AIDED GEOMETRIC DESIGN
ISSN journal
01678396 → ACNP
Volume
16
Issue
3
Year of publication
1999
Pages
217 - 221
Database
ISI
SICI code
0167-8396(199903)16:3<217:OTLEOT>2.0.ZU;2-0
Abstract
The quadratic geometric Hermite interpolant (GHI), as introduced by Hollig and Koch, is an interpolation scheme with maximal order and smoothness. Exi stence of the GHI depends on the given data. If the curve f, to be interpol ated at f (t(0)) and f (t(1)), is analytic, then nonzero curvature and smal l h : = t(1) - t(0) guarantee existence. An example of a C-infinity curve i s given to show that this conclusion does not hold if f is only smooth but not analytic. (C) 1999 Elsevier Science B.V. All rights reserved.