HERMITE INTERPOLATION USING PH CURVES WITH UNDETERMINED JUNCTION POINTS

Title & Authors
HERMITE INTERPOLATION USING PH CURVES WITH UNDETERMINED JUNCTION POINTS
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 $\small{C^1}$ Hermite interpolation problems. We also extend the UJP method to solve $\small{C^2}$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $\small{C^1}$ junction points. Further generalizing the UJP method, we go on to solve $\small{C^2}$ Hermite interpolation problems using two PH quintics with a $\small{C^1}$ junction point, and we also show the possibility of applying the modi e UJP method to $\small{G^2[C^1]}$ Hermite interpolation.
Keywords
Pythagorean hodograph (PH) curve;complex representation;$\small{C^1[C^2]}$ Hermite interpolation;$\small{G^2[C^1]}$ Hermite interpolation;undetermined junction point (UJP) method;
Language
English
Cited by
1.
TIME REPARAMETRIZATION OF PIECEWISE PYTHAGOREAN-HODOGRAPH $C^1$ HERMITE INTERPOLANTS,;;

Journal of applied mathematics & informatics, 2012. vol.30. 3_4, pp.381-393
1.
Planar C1 Hermite interpolation with PH cuts of degree (1,3) of Laurent series, Computer Aided Geometric Design, 2014, 31, 9, 689
2.
Minkowski Pythagorean-hodograph preserving mappings, Journal of Computational and Applied Mathematics, 2016, 308, 166
3.
C 1 Hermite interpolation with PH curves by boundary data modification, Journal of Computational and Applied Mathematics, 2013, 248, 47
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