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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.9 P.1566-1571


Two-order Hermite vector-interpolating subdivision schemes

Author(s):  FAN Min, KANG Bao-sheng, ZHAO Hua

Affiliation(s):  Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China; more

Corresponding email(s):   min_fan@126.com

Key Words:  Two-order vectorial Hermite element, Hermite-interpolating subdivision schemes, Geometric features

FAN Min, KANG Bao-sheng, ZHAO Hua. Two-order Hermite vector-interpolating subdivision schemes[J]. Journal of Zhejiang University Science A, 2006, 7(9): 1566-1571.

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journal="Journal of Zhejiang University Science A",
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T1 - Two-order Hermite vector-interpolating subdivision schemes
A1 - FAN Min
A1 - KANG Bao-sheng
A1 - ZHAO Hua
J0 - Journal of Zhejiang University Science A
VL - 7
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SP - 1566
EP - 1571
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A1566

A family of two-order Hermite vector-interpolating subdivision schemes is proposed and its convergence and continuity are analyzed. The iterative level can be estimated for given error. The sufficient conditions of C2 continuity are proved. geometric features of subdivision curves, such as line segments, cusps and inflection points, are obtained by appending some conditions to initial vectorial Hermite sequence. An algorithm is presented for generating geometric features. For an initial sequence of two-order Hermite elements from unit circle, the numerical error of the 4th subdivided level is O(10−4).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Dyn, N., Levin, D., 1995. Analysis of Hermite-type Subdivision Schemes. In: Chui, C.K., Schumaker, L.L. (Eds.), Approximation Theory VIII, V. 2: Wavelets and Multilevel Approximation. World Scientific Publishing, Singapore, p.117-124.

[2] Dyn, N., Levin, D., 1999. Analysis of Hermite-Interpolatory Subdivision Schemes. In: Dubuc, S., Deslauriers, G. (Eds.), Spline Functions and the Theory of Wavelets. CRM Proc. Lecture Notes 18, AMS, Providence, RI, p.105-113.

[3] Dyn, N., Gregory, J., Levin, D., 1991. Analysis of uniform binary subdivision schemes for curve design. Constructive Approximation, 7(1):127-147.

[4] Jüttler, B., Schwanecke, U., 2002. Analysis and design of Hermite subdivision schemes. The Visual Computer, 18(5-6):326-342.

[5] Merrien, J., 1992. A family of Hermite interpolants by bisection algorithms. Numerical Algorithms, 2(2):187-200.

[6] Merrien, J., 1999. Interpolants D’Hermite C2 obtenus par subdivision. Mathematical Modelling and Numerical Analysis, 33(1):55-65.

[7] Shi, F.Z., 2001. Computer Aided-Geometric Design and NURBS. Higher Education Press, Beijing, p.419-421 (in Chinese).

[8] Wang, G.J., Wang, G.Z., Zheng J.M., 2001. Computer Aided-Geometric Design. Higher Education Press, Beijing, p.338-347 (in Chinese).

[9] Zhang, J.Q., 2003. Research on Generating Subdivision Surface and Applying to Surface Modelling. Ph.D Thesis, Zhejiang University (in Chinese).

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