图学学报
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摘要: 提出了一种全新的广义Bézier 曲线。首先,从Lupas q-模拟Bernstein 算 子出发,得到了一组有理函数,该函数带有一个形状参数,是经典Bernstein 基函数的自然 推广。然后,构造了相应的广义Bézier 曲线,本文称之为Lupas q-Bézier 曲线,并研究了 其基本性质。Lupas q-Bézier 曲线具有与经典Bézier 曲线相类似的升阶公式和de Casteljau 算法。
关键词: 计算机辅助几何设计, Lupas q-模拟Bernstein 算子, Lupas q-Bé, zier 曲线, 升阶公式, de Casteljau 算法
Abstract: This paper presents a novel generalization of Bézier curves. Firstly, a class of rational functions with one shape parameter is presented. It comes from the Lupas q-analogue of Bernstein operator and is a natural extension to classical Bernstein basis. Then, the corresponding generalized Bézier curves, the so-called Lupas q-Bézier curves, are also constructed and their properties are studied. The new generalized Bézier curves share the degree evaluation and de Casteljau algorithm of the classical Bézier curves.
Key words: computer aided geometric design, Lupas q-analogue of Bernstein operator; Lupas q-Bézier curves, degree elevation, de Casteljau algorithm
韩力文, 楚 瑛, 李 丁, 刘 凤. 基于Lupas q-模拟Bernstein 算子的广义Bézier 曲线[J]. 图学学报.
Han Liwen, Chu Ying, Li Ding, Liu Feng. Generalized Bézier Curves Based on Lupas q-analogue of Bernstein Operator[J]. Journal of Graphics.
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http://www.txxb.com.cn/CN/Y2013/V34/I4/63