A CLASS OF HERMITE PARAMETRIC CURVE AND INTERPOLATION SPLINE WITH SHAPE PARAMETERS

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Published: 2016-04-11

Page: 23-33


LIU CHENG-ZHI *

Department of Mathematics, Hunan Institute of Humanities, Science and Technology, Loudi 417000, China.

LI JUN-CHENG

Department of Mathematics, Hunan Institute of Humanities, Science and Technology, Loudi 417000, China.

LI BINGJUN

Department of Mathematics, Hunan Institute of Humanities, Science and Technology, Loudi 417000, China.

*Author to whom correspondence should be addressed.


Abstract

This paper proposes a class of Hermite parametric curve and interpolating spline with shape parameters, whose properties are analogous to the standard cubic parametric ones. What’s more, the shape of the curve can be modified by changing the value of the shape parameters while the interpolation condition need not to be changed. In order to obtain the optimal parameters, a mathematical model is established which is based on the fairing criterion, and the shape parameter solved by this model can make the curve satisfy C1 or C2 continuous as we need. Examples show that the shape parameters solved by the model can let the curves have good smoothness.

Keywords: Algebraic-trigonometric Hermite parametric spline curves, shape parameter, the energy optimization method.


How to Cite

CHENG-ZHI, L., JUN-CHENG, L., & BINGJUN, L. (2016). A CLASS OF HERMITE PARAMETRIC CURVE AND INTERPOLATION SPLINE WITH SHAPE PARAMETERS. Asian Journal of Mathematics and Computer Research, 12(1), 23–33. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/536

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