Lupaş blending functions with shifted knots and q -Bézier curves

Journal of inequalities and applications

article

Kottakkaran Sooppy Nisar¹  Vinita Sharma²  Asif Khan² 

[1] Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University;Department of Mathematics, Aligarh Muslim University

关键词: q -integers;    Degree elevation;    De Casteljau-type algorithm;    Lupaş q -Bernstein operators with shifted knots;    Bézier curve;    Tensor product;    Shape preserving;   

DOI  :  10.1186/s13660-020-02450-5

学科分类：电力

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce blending functions of Lupaş q-Bernstein operators with shifted knots for constructing q-Bézier curves and surfaces. We study the nature of degree elevation and degree reduction for Lupaş q-Bézier Bernstein functions with shifted knots for $t \in [\frac{a}{[\mu ]_{q}+b} , \frac{[\mu ]_{q}+a}{[\mu ]_{q}+b} ]$ . For the parameters $a=b=0$ , we get Lupaş q-Bézier curves defined on $[0,1]$ . We show that Lupaş q-Bernstein functions with shifted knots are tangent to fore-and-aft of its polygon at end points. We present a de Casteljau algorithm to compute Bernstein Bézier curves and surfaces with shifted knots. The new curves have some properties similar to q-Bézier curves. Similarly, we discuss the properties of the tensor product for Lupaş q-Bézier surfaces with shifted knots over the rectangular domain.

【 授权许可】

CC BY