| A family of quasi-cubic blended splines and applications |
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| 作者姓名： | SU Ben-yue TAN Jie-qing |
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| 作者单位： | [1]School of Computer ＆ Information, Hefei University of Technology, Hefei 230009, China [2]Department of Mathematics, Anqing Teachers College, Anqing 246011, China [3]Institute of Applied Mathematics, Hefei University of Technology, Hefei 230009, China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (Nos. 10171026 and 60473114), the Research Funds forYoung Innovation Group, Education Department of Anhui Prov-ince (No. 2005TD03) and the Natural Science Foundation of An-hui Provincial Education Department (No. 2006KJ252B), China |
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| 摘 要： | INTRODUCTION Bézier curves and uniform B-spline curves are powerful tools for constructing free form curves and surfaces (FFC/FFS). But they cannot represent the arcs, hyperbola, sphere, cylinders and other transcendental curves and surfaces exactly. In order to avoid the in- conveniences, many bases are presented in other new spaces (Zhang, 1996; Pe?a, 1997; Walz, 1997; Sánchez-Reyes, 1998; Mainar et al., 2001). Note that, these existing methods can deal with both polynomial curve…
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| 关 键 词： | 样条内插 全局参数 局部参数 三角多项式 |
| 收稿时间： | 2006-02-28 |
| 修稿时间： | 2006-05-03 |
A family of quasi-cubic blended splines and applications |
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| SU Ben-yue TAN Jie-qing.A family of quasi-cubic blended splines and applications[J].Journal of Zhejiang University Science,2006,7(9):1550-1560. |
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| Authors: | Ben-yue Su Jie-qing Tan |
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| Institution: | (1) School of Computer & Information, Hefei University of Technology, Hefei, 230009, China;(2) Department of Mathematics, Anqing Teachers College, Anqing, 246011, China;(3) Institute of Applied Mathematics, Hefei University of Technology, Hefei, 230009, China |
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| Abstract: | 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 dp
i(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.
Project supported by the National Natural Science Foundation of China (Nos. 10171026 and 60473114), the Research Funds for
Young Innovation Group, Education Department of Anhui Province (No. 2005TD03) and the Natural Science Foundation of Anhui
Provincial Education Department (No. 2006KJ252B), China |
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| Keywords: | Blended spline interpolation C2 continuity Global parameters Local parameters Quasi-cubic spline Trigonome- tric polynomials |
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