基于Lupas q-模拟Bernstein 算子的广义Bézier 曲线

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。

Generalized Bézier Curves Based on Lupas q-analogue ofBernstein Operator

This paper presents a novel generalization of Bézier curves. Firstly, a class ofrational functions with one shape parameter is presented. It comes from the Lupas q-analogue ofBernstein operator and is a natural extension to classical Bernstein basis. Then, the correspondinggeneralized Bézier curves, the so-called Lupas q-Bézier curves, are also constructed and theirproperties are studied. The new generalized Bézier curves share the degree evaluation and deCasteljau algorithm of the classical Bézier curves.