摘要
In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving in-terpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above draw-backs. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C2(or G1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.
In computer aided geometric design(CAGD) ,it is often needed to produce a convexity-preserving interpolating curve according to the given planar data points. However,most existing pertinent methods cannot generate convexity-preserving interpolating transcendental curves;even constructing convexity-preserving interpolating polynomial curves,it is required to solve a system of equations or recur to a complicated iterative process. The method developed in this paper overcomes the above drawbacks. The basic idea is:first to construct a kind of trigonometric polynomial curves with a shape parameter,and interpolating trigonometric polynomial parametric curves with C^2(or G^1) continuity can be automatically generated without having to solve any system of equations or do any iterative computation. Then,the convexity of the constructed curves can be guaranteed by the appropriate value of the shape parameter. Performing the method is easy and fast,and the curvature distribution of the resulting interpolating curves is always well-proportioned. Several numerical examples are shown to substantiate that our algorithm is not only correct but also usable.
基金
Project supported by the National Basic Research Program (973) of China (No. 2004CB719400)
the National Natural Science Founda-tion of China (Nos. 60673031 and 60333010)
the National Natural Science Foundation for Innovative Research Groups of China (No. 60021201)
关键词
计算机辅助几何设计
α-三角多项式曲线
凸性
形状参量
Computer aided geometric design (CAGD), α-trigonometric polynomial curves, Interpolation, Convexity-preserving, Shape parameter