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.

中文翻译：

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带有移动结和q- Bézier曲线的Lupaş混合功能

在本文中，我们介绍了Lupaşq-Bernstein算子与平移结的混合函数，以构造q-Bézier曲线和曲面。我们研究了$ t \ in [\ frac {a} {[\ mu] _ {q} + b}，\ frac {[\ mu]中带有移位结的Lupaşq-BézierBernstein函数的度升高和度降低的性质] _ {q} + a} {[\ mu] _ {q} + b}] $。对于参数$ a = b = 0 $，我们获得在$ [0,1] $上定义的Lupaşq-Bézier曲线。我们显示，带有移动结的Lupaşq-Bernstein函数在端点处与其多边形的前后切线。我们提出了一种de Casteljau算法，以计算带结移动的BernsteinBézier曲线和曲面。新曲线的某些特性类似于q-贝塞尔曲线。同样，我们讨论了在矩形域上具有平移结的Lupaşq-Bézier曲面的张量积的性质。