CLC number: TP391

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Received: 2006-12-01

Revision Accepted: 2007-02-28

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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.

@article{title="Convexity-preserving interpolation of trigonometric polynomial curves with a shape parameter",

author="PAN Yong-juan, WANG Guo-jin",

journal="Journal of Zhejiang University Science A",

volume="8",

number="8",

pages="1199-1209",

year="2007",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.2007.A1199"

}

%0 Journal Article

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

%A PAN Yong-juan

%A WANG Guo-jin

%J Journal of Zhejiang University SCIENCE A

%V 8

%N 8

%P 1199-1209

%@ 1673-565X

%D 2007

%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

A1 - PAN Yong-juan

A1 - WANG Guo-jin

J0 - Journal of Zhejiang University Science A

VL - 8

IS - 8

SP - 1199

EP - 1209

%@ 1673-565X

Y1 - 2007

PB - Zhejiang University Press & Springer

ER -

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

**
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[1] Chang, G.Z., 1995. The Mathematics of Surfaces. Hunan Education Press, Changsha, p.15 (in Chinese).

[2] Farin, G., 2005. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide (5th Ed.). Morgan Kaufmann Publishers, San Diego, p.420.

[3] Fletcher, Y., McAllister, D.F., 1990. Automatic tension adjustment for interpolation splines. *IEEE Computer Graph. Appl*., **10**(1):10-17.

[4] Koch, P.E., Lyche, T., Neamtu, M., Schumaker, L.L., 1995. Control curves and knot insertion for trigonometric splines. *Adv. Comp. Math*., **3**:405-424.

[5] Loe, K.F., 1996. *α*-B-spline: a linear singular blending B-spline. *The Visual Computer*, **12**:18-25.

[6] Lyche, T., Winther, R., 1979. A stable recurrence relation for trigonometric B-splines. *J. Approx. Theory*, **25**:266-279.

[7] Peña, J.M., 1997. Shape preserving representations for trigonometric polynomial curves. *Computer Aided Geometric Design*, **14**(1):5-11.

[8] Schoenberg, I.J., 1964. On trigonometric spline interpolation. *J. Math. Mech*., **13**(5):795-825.

[9] Tai, C.L., Wang, G.J., 2004. Interpolation with slackness and continuity control and convexity-preservation using singular blending. *J. Comput. Appl. Math*., **172**(2):337-361.

[10] Walz, G., 1997a. Some identities for trigonometric B-splines with application to curve design. *BIT Numer. Math*., **37**:189-201.

[11] Walz, G., 1997b. Trigonometric Bézier and stancu polynomials over intervals and triangles. *Computer Aided Geometric Design*, **14**:393-397.

[12] Wang, G.Z., Chen, Q.Y., 2004. NUAT B-spline curves. *Computer Aided Geometric Design*, **21**:193-205.

[13] Wang, G.Z., Li, Y.J., 2006. Optimal properties of the uniform algebraic trigonometric B-splines. *Computer Aided Geometric Design*, **23**:226-238.

[14] Zhang, J.W., 1996. C-curves: an extension of cubic curves. *Computer Aided Geometric Design*, **13**(3):199-217.

[15] Zhang, J.W., 1997. Two different forms of C-B-splines. *Computer Aided Geometric Design*, **14**(1):31-41.

[16] Zhang, J.W., Krause, F.L., 2005. Extend cubic uniform B-splines by unified trigonometric and hyberolic basis. *Graph. Models*, **67**(2):100-119.

[17] Zhang, J.W., Krause, F.L., Zhang, H.U., 2005. Unifying C-curves and H-curves by extending the calculation to complex numbers. *Computer Aided Geometric Design*, **22**:865-883.

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