Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants

Hyeong In Choi; Rida T. Farouki; Song Hwa Kwon; Hwan Pyo Moon

doi:10.1016/j.cagd.2007.03.010

Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants

Hyeong In Choi
, Rida T. Farouki
, Song Hwa Kwon
, Hwan Pyo Moon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

A topological approach to identifying the "good" interpolant among the four distinct solutions to the first-order Hermite interpolation problem for planar quintic Pythagorean-hodograph curves is presented. An existence theorem is proved, together with a complete analysis of uniqueness/non-uniqueness properties. A simple formula for finding the "good" solution, without appealing to curve fairness or energy integrals, is also presented.

Original language	English
Pages (from-to)	411-433
Number of pages	23
Journal	Computer Aided Geometric Design
Volume	25
Issue number	6
DOIs	https://doi.org/10.1016/j.cagd.2007.03.010
State	Published - Aug 2008

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10.1016/j.cagd.2007.03.010

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abstract = "A topological approach to identifying the {"}good{"} interpolant among the four distinct solutions to the first-order Hermite interpolation problem for planar quintic Pythagorean-hodograph curves is presented. An existence theorem is proved, together with a complete analysis of uniqueness/non-uniqueness properties. A simple formula for finding the {"}good{"} solution, without appealing to curve fairness or energy integrals, is also presented.",

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AU - Choi, Hyeong In

AU - Farouki, Rida T.

AU - Kwon, Song Hwa

AU - Moon, Hwan Pyo

PY - 2008/8

Y1 - 2008/8

N2 - A topological approach to identifying the "good" interpolant among the four distinct solutions to the first-order Hermite interpolation problem for planar quintic Pythagorean-hodograph curves is presented. An existence theorem is proved, together with a complete analysis of uniqueness/non-uniqueness properties. A simple formula for finding the "good" solution, without appealing to curve fairness or energy integrals, is also presented.

AB - A topological approach to identifying the "good" interpolant among the four distinct solutions to the first-order Hermite interpolation problem for planar quintic Pythagorean-hodograph curves is presented. An existence theorem is proved, together with a complete analysis of uniqueness/non-uniqueness properties. A simple formula for finding the "good" solution, without appealing to curve fairness or energy integrals, is also presented.

UR - https://www.scopus.com/pages/publications/44849094498

U2 - 10.1016/j.cagd.2007.03.010

DO - 10.1016/j.cagd.2007.03.010

M3 - Article

AN - SCOPUS:44849094498

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VL - 25

SP - 411

EP - 433

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 6

ER -

Topological criterion for selection of quintic Pythagorean-hodograph Hermite interpolants

Abstract

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