First order hermite interpolation with spherical Pythagorean-hodograph curves

2007 ◽  
Vol 23 (1-2) ◽  
pp. 73-86 ◽  
Author(s):  
Gwang-Il Kim ◽  
Jae-Hoon Kong ◽  
Sunhong Lee
Keyword(s):  
Hermite Interpolation ◽  
First Order ◽  
Pythagorean Hodograph

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

2005 ◽  
Vol 22 (4) ◽  
pp. 325-352 ◽  
Author(s):  
Francesca Pelosi ◽  
Rida T. Farouki ◽  
Carla Manni ◽  
Alessandra Sestini
Keyword(s):  
Hermite Interpolation ◽  
Pythagorean Hodograph ◽  
Geometric Hermite Interpolation

scholarly journals Spaces of polynomial and nonpolynomial spline-wavelets

2019 ◽  
Vol 292 ◽  
pp. 04001
Author(s):  
Yu. K. Dem’yanovich ◽  
I. G. Burova ◽  
T. O. Evdokimovas ◽  
A. V. Lebedeva
Keyword(s):  
Interpolation Problem ◽  
Wavelet Decomposition ◽  
Hermite Interpolation ◽  
Uniform Grid ◽  
First Order ◽  
Spline Wavelets ◽  
Almost Everywhere

This paper, discusses spaces of polynomial and nonpolynomial splines suitable for solving the Hermite interpolation problem (with first-order derivatives) and for constructing a wavelet decomposition. Such splines we call Hermitian type splines of the first level. The basis of these splines is obtained from the approximation relations under the condition connected with the minimum of multiplicity of covering every point of (α, β) (almost everywhere) with the support of the basis splines. Thus these splines belong to the class of minimal splines. Here we consider the processing of flows that include a stream of values of the derivative of an approximated function which is very important for good approximation. Also we construct a splash decomposition of the Hermitian type splines on a non-uniform grid.

scholarly journals Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
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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