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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.8 P.1199~1209

http://doi.org/10.1631/jzus.2007.A1199


Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter


Author(s):  PAN Yong-juan, WANG Guo-jin

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   panyongjuan@zjut.edu.cn, wanggj@zju.edu.cn

Key Words:  Computer aided geometric design (CAGD), &alpha, -trigonometric polynomial curves, Interpolation, Convexity-preserving, Shape parameter


PAN Yong-juan, WANG Guo-jin. Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter[J]. Journal of Zhejiang University Science A, 2007, 8(8): 1199~1209.

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author="PAN Yong-juan, WANG Guo-jin",
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pages="1199~1209",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1199"
}

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%A WANG Guo-jin
%J Journal of Zhejiang University SCIENCE A
%V 8
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1199

TY - JOUR
T1 - Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter
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A1 - WANG Guo-jin
J0 - Journal of Zhejiang University Science A
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SP - 1199
EP - 1209
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Y1 - 2007
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A1199


Abstract: 
In computer aided geometric design (CAGD), it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However, most existing pertinent methods cannot generate convexity-preserving interpolating transcendental curves; even constructing convexity-preserving interpolating polynomial curves, it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above drawbacks. The basic idea is: first to construct a kind of trigonometric polynomial curves with a shape parameter, and interpolating trigonometric polynomial parametric curves with C2 (or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then, the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast, and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.

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Reference

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