Hermite Interpolation Using Möbius Transformations of Planar Pythagorean-Hodograph Cubics

Sunhong Lee, Hyun Chol Lee, Mi Ran Lee, Seungpil Jeong, Gwang-Il Kim
2012 Abstract and Applied Analysis  
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.
more » ... bius 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.
doi:10.1155/2012/560246 fatcat:rdriuzvgcfghtpyscnccx7gqkq