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Applications of Lupas q-analogue Bernstein Operator in CAGD


Academic Report

Title: Applications of Lupas q-analogue Bernstein Operator in CAGD

Reporter: Prof. Liwen Han (Hebei normal University)

Time: September 7, 2017 PM 15:30

Location: A#1101 room, Innovation Park Building 

Contact: Prof. Chungang Zhu (tel: 84708351-8315)


Abstract: Bernstein polynomials and Bézier curves/surfaces are of fundamental importance for Computer Aided Geometric Design (CAGD). Recently, the rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials involving q-integers. In 1987, Romanian mathematician Alexandru Lupas introduced the first q-analogue of Bernstein polynomials. Regrettably, the operators proposed by Lupas remained unnoticed for a long while due to the very limited availability of his article published in regional conference proceedings. Today, this situation has changed and Lupas q-analogues become one of the most popular q-analogues of the Bernstein polynomials.

In this talk, the applications of Lupas q-analogue Bernstein operator in CAGD will be discussed. New generalizations of Bernstein–Bézier curves and surfaces based on Lupas q-analogue Bernstein operator are introduced and their geometric characteristic and some applications are discussed. Moreover, Lupas q-analogue Bernstein operator are used to implement more stable barycentric rational interpolation.

The brief introduction to the reporter: Liwen Han is a professor of College of mathematics and information science, Hebei Normal University. He received a doctorate degree from Jilin University in 2002. From 1999 to 2003, he taught at Jilin University and he was introduced to Hebei Normal University in 2003. In October 2003, he won second prize of  “China Computational Mathematics Federation Excellent Young Paper”. Now he engages in computer-aided geometric design and calculation of geometric.