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HERMITE INTERPOLATION USING PH CURVES WITH UNDETERMINED JUNCTION POINTS

김광일|정승필|공재훈
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회보 (Bulletin of the KMS)|제49권 제1호|pp. 175-195

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참고문헌

키워드

Pythagorean hodograph (PH) curvecomplex representationC1(C2) Hermite interpolationG2[C1] Hermite interpolationundetermined junction point (UJP) method
주제분류수학

초록

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 C1 Hermite interpolation problems. We also extend the UJP method to solve C2Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with C1 junction points. Further generalizing the UJP method, we go on to solve C2 Hermite interpolation problems using two PH quintics with a C1junction point, and we also show the possibility of applying the modi ed UJP method to G2[C1] Hermite interpolation.

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 C1 Hermite interpolation problems. We also extend the UJP method to solve C2Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with C1 junction points. Further generalizing the UJP method, we go on to solve C2 Hermite interpolation problems using two PH quintics with a C1junction point, and we also show the possibility of applying the modi ed UJP method to G2[C1] Hermite interpolation.

참고문헌 (33)

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관련 논문AI추천

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