| A new method for automatically constructing convexity-preserving interpolatory splines |
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| 作者姓名： | PAN Yongjuan WANG Guojin |
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| 作者单位： | Institute of Images and Graphics, Zhejiang University, Hangzhou 310027, China;State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China;Department of Applied Methematics, Zhejiang University of Technology, Hangzhou 310032,China,Institute of Images and Graphics, Zhejiang University, Hangzhou 310027, China;State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (Grant No.60173034) and the Major State Basic Research Development Program of China (Grant No. 2002CB312101) |
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| 摘 要： | Constructing a convexity-preserving interpolating curve according to the given planar data points is a problem to be solved in computer aided geometric design (CAGD). So far, almost all methods must solve a system of equations or recur to a complicated iterative process, and most of them can only generate some function-form convexity-preserving interpolating curves which are unaccommodated with the parametric curves, commonly used in CAGD systems. In order to overcome these drawbacks, this paper proposes a new method that can automatically generate some parametric convexity-preserving polynomial interpolating curves but dispensing with solving any system of equations or going at any iterative computation. The main idea is to construct a family of interpolating spline curves first with the shape parameter a as its family parameter; then, using the positive conditions of Bernstein polynomial to respectively find a range in which the shape parameter a takes its value for two cases of global convex data points and piecewise convex data points so as to make the corresponding interpolating curves convexity-preserving and C2(or G1) continuous. The method is simple and convenient, and the resulting interpolating curves possess smooth distribution of curvature. Numerical examples illustrate the correctness and the validity of theoretical reasoning.
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| 关 键 词： | computer aided geometric design B spline curve interpolation convexity-preserving shape paramete |
A new method for automatically constructing convexity-preserving interpolatory splines |
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| PAN Yongjuan,WANG Guojin.A new method for automatically constructing convexity-preserving interpolatory splines[J].Progress in Natural Science,2004,14(6):524-535. |
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| Authors: | PAN Yongjuan WANG Guojin |
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| Institution: | 1. Institute of Images and Graphics, Zhejiang University, Hangzhou 310027, China;State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China;Department of Applied Methematics, Zhejiang University of Technology, Hangzhou 310032,China
2. Institute of Images and Graphics, Zhejiang University, Hangzhou 310027, China;State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China |
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| Abstract: | Constructing a convexity-preserving interpolating curve according to the given planar data points is a problem to be solved in computer aided geometric design (CAGD). So far, almost all methods must solve a system of equations or recur to a complicated iterative process, and most of them can only generate some function-form convexity-preserving interpolating curves which are unaccommodated with the parametric curves, commonly used in CAGD systems. In order to overcome these drawbacks, this paper proposes a new method that can automatically generate some parametric convexity-preserving polynomial interpolating curves but dispensing with solving any system of equations or going at any iterative computation. The main idea is to construct a family of interpolating spline curves first with the shape parameter a as its family parameter; then, using the positive conditions of Bernstein polynomial to respectively find a range in which the shape parameter a takes its value for two cases of global convex data points and piecewise convex data points so as to make the corresponding interpolating curves convexity-preserving and C2(or G1) continuous. The method is simple and convenient, and the resulting interpolating curves possess smooth distribution of curvature. Numerical examples illustrate the correctness and the validity of theoretical reasoning. |
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| Keywords: | computer aided geometric design B spline curve interpolation convexity-preserving shape paramete |
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