Hermite interpolation by Minkowski Pythagorean hodograph cubics

2006 ◽  
Vol 23 (5) ◽  
pp. 401-418 ◽  
Author(s):  
Jiří Kosinka ◽  
Bert Jüttler
Keyword(s):  
Hermite Interpolation ◽  
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

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

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.

scholarly journals $C^2$ Hermite interpolation by Pythagorean Hodograph space curves

2007 ◽  
Vol 76 (259) ◽  
pp. 1373-1392 ◽  
Author(s):  
Zbyněk Šír ◽  
Bert Jüttler
Keyword(s):  
Hermite Interpolation ◽  
Space Curves ◽  
Pythagorean Hodograph

scholarly journals Hermite interpolation by Pythagorean hodograph quintics

1995 ◽  
Vol 64 (212) ◽  
pp. 1589-1589 ◽  
Author(s):  
R. T. Farouki ◽  
C. A. Neff
Keyword(s):  
Hermite Interpolation ◽  
Pythagorean Hodograph

Pythagorean-hodograph cycloidal curves

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Jernej Kozak ◽  
Marjeta Krajnc ◽  
Mladen Rogina ◽  
Vito Vitrih
Keyword(s):  
Closed Form ◽  
Asymptotic Approximation ◽  
Hermite Interpolation ◽  
Approximation Order ◽  
Geometric Characterization ◽  
Closed Form Solutions ◽  
Order Analysis ◽  
Pythagorean Hodograph ◽  
Practical Tool ◽  
Curve Solution

AbstractIn the paper, Pythagorean-hodograph cycloidal curves as an extension of PH cubics are introduced. Their properties are examined and a constructive geometric characterization is established. Further, PHC curves are applied in the Hermite interpolation, with closed form solutions been determined. The asymptotic approximation order analysis carried out indicates clearly which interpolatory curve solution should be selected in practice. This makes the curves introduced here a useful practical tool, in particular in algorithms that guide CNC machines.

Sign in / Sign up

Export Citation Format

Share Document