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| 一类平面参数曲线的保单调插值 |
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潘永娟1,2,3, 王国瑾1,2
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1.浙江大学,计算机图像图形研究所,浙江,杭州,310027;2.浙江大学,CAD&CG国家重点实验室,浙江,杭州,310027;3.浙江工业大学,应用数学系,浙江,杭州,310032
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| 摘要: |
| 曲线、曲面的保形插值是几何外形设计的一个重点和难点课题,而保单调和保凸是保形的两个基本内容.研究了一类带有形状可调参数的平面参数曲线的保单调插值方法.其基本思想是:首先构造带有形状可调参数(的一类平面(-B样条插值曲线,再把其一阶导矢的两个分量分别转化为Bernstein多项式,从而利用Bernstein多项式的正性条件,得到此曲线为单调的充要条件,即形状参数(的取值范围,简单、快捷地实现此参数样条曲线的保单调插值.实例计算及绘图验证了理论推导的正确性与有效性.该方法的方便、有效使其易于在工程实践中获得广泛应用. |
| 关键词: 插值 (-B样条曲线 形状参数 保单调 Bernstein多项式 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60173034 (国家自然科学基金); the National Grand Fundamental Research 973 Program of China under Grant No.2002CB312101 (国家重点基础研究发展规划(973) |
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| Monotonicity-Preserving Interpolation with a Kind of Plane Parameter Curve |
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PAN Yong-Juan,WANG Guo-Jin
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| Abstract: |
| In the geometric shape design, shape preserving interpolation of curve/surface is an important and difficult subject in which both monotonicity-preserving and convexity-preserving interpolation are two basic contents. In this paper, the monotonicity-preserving interpolation of a kind of plane parameter curve with a shape control parameter is investigated. The basic idea is as follows: first, a kind of plane α-B-spline interpolation curve with a shape control parameter a is constructed; then, by converting the first derivatives of the curve into Bernstein polynomial, the positive conditions of Bernstein polynomial can be used to get the necessary and sufficie nt conditions for the monotonicity of α-B-spline interpolation curves, i.e., the range of the parameter a. Therefore, monotone-preserving interpolating curves can be obtained succinctly. Numerical examples illustrate the correctness and the validity of theoretical reasoning. In virtue of its convenience and efficiency, this method is hopeful to be widely applied to engineering and practice. |
| Key words: interpolation α-B-spline shape parameter monotonicity-preserving Bernstein polynomial |
