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Received: 2006-02-28

Revision Accepted: 2006-05-03

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.9 P.1550-1560


A family of quasi-cubic blended splines and applications

Author(s):  SU Ben-yue, TAN Jie-qing

Affiliation(s):  School of Computer & Information, Hefei University of Technology, Hefei 230009, China; more

Corresponding email(s):   subenyue@sohu.com

Key Words:  Blended spline interpolation, C2 continuity, Global parameters, Local parameters, Quasi-cubic spline, Trigonometric polynomials

SU Ben-yue, TAN Jie-qing. A family of quasi-cubic blended splines and applications[J]. Journal of Zhejiang University Science A, 2006, 7(9): 1550-1560.

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T1 - A family of quasi-cubic blended splines and applications
A1 - SU Ben-yue
A1 - TAN Jie-qing
J0 - Journal of Zhejiang University Science A
VL - 7
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A1550

A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter α, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter α, where dpi(α,t) is linear with respect to dα for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.

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