C 1 Hermite interpolation with PH curves by boundary data modification

We show how to create a new class of infinitely many PH Hermite interpolants for a given ordinary C 1 Hermite data-set, in a way that ameliorates the rapid shape transitions in PH quintic interpolants that occurs when boundary data has poor geometric compatibility. We first interpolate a Hermite dat...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 248; pp. 47 - 60
Main Authors Kong, Jae Hoon, Lee, Hyun Chol, Kim, Gwang Il
Format Journal Article
LanguageEnglish
Published 15.08.2013
Subjects
Asymmetry
Bending
Boundaries
Computation
Expenses
Interpolation
Mathematical models
Online AccessGet full text
ISSN0377-0427
DOI10.1016/j.cam.2013.01.016

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Summary:We show how to create a new class of infinitely many PH Hermite interpolants for a given ordinary C 1 Hermite data-set, in a way that ameliorates the rapid shape transitions in PH quintic interpolants that occurs when boundary data has poor geometric compatibility. We first interpolate a Hermite data-set using two asymmetric PH cubics, each of which satisfies the data at one boundary. Then we selectively apply one of three shape improvement techniques to the interpolant, so as to eliminate rapid shape transitions and produce C 1 PH curves with lower bending energy, at the expense of a small increase in arc-length.
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ISSN:0377-0427
DOI:10.1016/j.cam.2013.01.016