Weighted Lupas q-Bezier curves

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:308

Article

Han, Li-Wen^1,2  Wu, Ya-Sha¹  Chu, Ying¹ 

[1] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] Hebei Prov Key Lab Computat Math & Applicat, Shijiazhuang 050024, Hebei, Peoples R China

关键词: Lupas q-analogue of Bernstein operator;    Weighted Lupas q-Bernstein basis;    Normalized totally positive basis;    Rational Bezier curve;    Conic sections;    Shape parameter;   

DOI  :  10.1016/j.cam.2016.06.017

来源: Elsevier

【 摘 要 】

This paper is concerned with a new generalization of rational Bernstein-Bezier curves involving q-integers as shape parameters. A one parameter family of rational Bernstein-Bezier curves, weighted Lupas q-Bezier curves, is constructed based on a set of Lupas q-analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bezier 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 Lupas q-Bezier curves have more modeling flexibility than classical rational Bernstein-Bezier curves and Lupas q-Bezier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q-Bezier curves. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free