HERMITE INTERPOLATION USING PH CURVES WITH UNDETERMINED JUNCTION POINTS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 49, Issue 1, 2012, pp.175-195
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2012.49.1.175

Title & Authors

HERMITE INTERPOLATION USING PH CURVES WITH UNDETERMINED JUNCTION POINTS

Kong, Jae-Hoon; Jeong, Seung-Pil; Kim, Gwang-Il;

Kong, Jae-Hoon; Jeong, Seung-Pil; Kim, Gwang-Il;

Abstract

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki`s double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general Hermite interpolation problems. We also extend the UJP method to solve Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with junction points. Further generalizing the UJP method, we go on to solve Hermite interpolation problems using two PH quintics with a junction point, and we also show the possibility of applying the modi e UJP method to Hermite interpolation.

Keywords

Pythagorean hodograph (PH) curve;complex representation; Hermite interpolation; Hermite interpolation;undetermined junction point (UJP) method;

Language

English

Cited by

1.

2.

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