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