Solvability of Hermite interpolation by spatial Pythagorean-hodograph cubics and its selection scheme

Song-Hwa Kwon

doi:10.1016/j.cagd.2009.11.002

Solvability of Hermite interpolation by spatial Pythagorean-hodograph cubics and its selection scheme

Computer Aided Geometric Design ◽

10.1016/j.cagd.2009.11.002 ◽

2010 ◽

Vol 27 (2) ◽

pp. 138-149 ◽

Cited By ~ 14

Author(s):

Song-Hwa Kwon

Keyword(s):

Hermite Interpolation ◽

Selection Scheme ◽

Pythagorean Hodograph

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Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

Advances in Computational Mathematics ◽

10.1007/s10444-003-2599-x ◽

2005 ◽

Vol 22 (4) ◽

pp. 325-352 ◽

Cited By ~ 34

Author(s):

Francesca Pelosi ◽

Rida T. Farouki ◽

Carla Manni ◽

Alessandra Sestini

Keyword(s):

Hermite Interpolation ◽

Pythagorean Hodograph ◽

Geometric Hermite Interpolation

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First order hermite interpolation with spherical Pythagorean-hodograph curves

Journal of Applied Mathematics and Computing ◽

10.1007/bf02831959 ◽

2007 ◽

Vol 23 (1-2) ◽

pp. 73-86 ◽

Cited By ~ 5

Author(s):

Gwang-Il Kim ◽

Jae-Hoon Kong ◽

Sunhong Lee

Keyword(s):

Hermite Interpolation ◽

First Order ◽

Pythagorean Hodograph

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A new selection scheme for spatial Pythagorean hodograph quintic Hermite interpolants

Computer Aided Geometric Design ◽

10.1016/j.cagd.2020.101827 ◽

2020 ◽

Vol 78 ◽

pp. 101827 ◽

Cited By ~ 2

Author(s):

Chang Yong Han ◽

Hwan Pyo Moon ◽

Song-Hwa Kwon

Keyword(s):

Selection Scheme ◽

Pythagorean Hodograph

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Hermite interpolation by Minkowski Pythagorean hodograph cubics

Computer Aided Geometric Design ◽

10.1016/j.cagd.2006.01.004 ◽

2006 ◽

Vol 23 (5) ◽

pp. 401-418 ◽

Cited By ~ 26

Author(s):

Jiří Kosinka ◽

Bert Jüttler

Keyword(s):

Hermite Interpolation ◽

Pythagorean Hodograph

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C˜2 Continuous Cubic Hermite Interpolation Splines with Second-Order Elliptic Variation

Tobacco Regulatory Science ◽

10.18001/trs.7.6.106 ◽

2021 ◽

Vol 7 (6) ◽

pp. 6317-6331

Author(s):

Jie Li ◽

Yaoyao Tu ◽

Shilong Fei

Keyword(s):

Shape Control ◽

Spline Function ◽

Hermite Interpolation ◽

Second Order ◽

Basis Functions ◽

Interpolation Spline ◽

Selection Scheme ◽

Spline Curve ◽

Spline Curves ◽

Two Parameters

In order to solve the deficiency of Hermite interpolation spline with second-order elliptic variation in shape control and continuity, c-2 continuous cubic Hermite interpolation spline with second-order elliptic variation was designed. A set of cubic Hermite basis functions with two parameters was constructed. According to this set of basis functions, the three-order Hermite interpolation spline curves were defined in segments 02, and the parameter selection scheme was discussed. The corresponding cubic Hermite interpolation spline function was studied, and the method to determine the residual term and the best interpolation function was given. The results of an example show that when the interpolation conditions remain unchanged, the cubic Hermite interpolation spline curves not only reach 02 continuity, but also can use the parameters to control the shape of the curves locally or globally. By determining the best values of the parameters, the cubic Hermite interpolation spline function can get a better interpolation effect, and the smoothness of the interpolation spline curve is the best.

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Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics

Abstract and Applied Analysis ◽

10.1155/2012/560246 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 3

Author(s):

Sunhong Lee ◽

Hyun Chol Lee ◽

Mi Ran Lee ◽

Seungpil Jeong ◽

Gwang-Il Kim

Keyword(s):

Complex Plane ◽

Hermite Interpolation ◽

Möbius Transformation ◽

Möbius Transformations ◽

Interpolation Problems ◽

Pythagorean Hodograph ◽

Improved Stability ◽

Mobius Transformation ◽

Extra Parameter ◽

Mobius Transformations

We present an algorithm forC1Hermite interpolation using Möbius transformations of planar polynomial Pythagoreanhodograph (PH) cubics. In general, with PH cubics, we cannot solveC1Hermite interpolation problems, since their lack of parameters makes the problems overdetermined. In this paper, we show that, for each Möbius transformation, we can introduce anextra parameterdetermined by the transformation, with which we can reduce them to the problems determining PH cubics in the complex planeℂ. Möbius transformations preserve the PH property of PH curves and are biholomorphic. Thus the interpolants obtained by this algorithm are also PH and preserve the topology of PH cubics. We present a condition to be met by a Hermite dataset, in order for the corresponding interpolant to be simple or to be a loop. We demonstrate the improved stability of these new interpolants compared with PH quintics.

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