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A family of quasi-cubic blended splines and applications

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第9期7卷 1550-1560页

作者： SU Ben-yue TAN Jie-qing School of Computer ＆ Information Hefei University of Technology Hefei 230009 China Department of Mathematics Anqing Teachers College Anqing 246011 China Institute of Applied Mathematics Hefei University of Technology Hefei 230009 China

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 a, 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 a, where dpi（a,t） is linear with respect to da 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 C^2 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.

关键词： blended spline interpolation C^2 continuity Global parameters Local parameters Quasi-cubic spline Trigonometric polynomials

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