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

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.