基于Lupas q-模拟Bernstein算子的广义Bézier曲线  

Generalized Bézier Curves Based on Lupas q-analogue of Bernstein Operator

作　　者：韩力文[1,2] 楚瑛[1] 李丁[1] 刘凤[1] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050024 [2]河北省计算数学与应用重点实验室,河北石家庄050024

出　　处：《图学学报》2013年第4期63-68,共6页Journal of Graphics

基　　金：国家自然科学基金资助项目(61170107);河北省教育厅自然科学研究项目(Q2012041)

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。This paper presents a novel generalization of B6zier 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 B6zier curves, the so-called Lupas q-B6zier curves, are also constructed and their properties are studied. The new generalized B6zier curves share the degree evaluation and de Casteljau algorithm of the classical B6zier curves.

关 键 词：计算机辅助几何设计 Lupasq-模拟Bernstein算子 Lupasq-Bézier曲线 升阶公式 deCasteljau算法 

分 类 号：O241.5[理学—计算数学]