Weighted Lupaş -Bézier curves

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• 作者：Li-Wen Han^a ; ^b ; ^{hanliwen@sina.com" class="auth_mail" title="E-mail the corresponding author} ; Ya-Sha Wu^a ; ^{xingyunsha@126.com" class="auth_mail" title="E-mail the corresponding author} ; Ying Chu^a ; ^{chuyingyouxiang@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Lupaş qq-analogue of Bernstein operator ; Weighted Lupaş qq-Bernstein basis ; Normalized totally positive basis ; Rational Bé ; zier curve ; Conic sections ; Shape parameter
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：308
• 期：Complete
• 页码：318-329
• 全文大小：790 K

文摘

This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q$q$-integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q$q$–Bézier curves, is constructed based on a set of Lupaş q$q$-analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q$q$–Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q$q$–Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q$q$–Bézier curves.