用加权lupaku后量子bsamzier曲线逼近二次曲线

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2022-01-01 DOI:10.1515/dema-2022-0016

Asif Khan, M. Iliyas, Khalid Khan, M. Mursaleen

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引用次数: 0

摘要

摘要本文研究了加权lupaku后量子Bernstein混合函数和利用基(p,q) \左(p,q) -整数构造的bsamzier曲线。这些混合函数形成归一化的全正基。由于加权lupaku后量子bsamzier曲线的理性性质和正权，它们有助于从几何的角度进行研究。研究了它们的度高程特性和de Casteljau算法。证明了二次加权lupaku后量子bsamzier曲线可以表示二维平面上的二次曲线。用图形分析的方法讨论了权值的几何解释和加权后量子bsamzier曲线的二次曲线表示。这种新的广义加权lupakq后量子bsamzier曲线与经典的理性bsamzier曲线、lupakq q - bsamzier曲线和加权lupakq q - bsamzier曲线相比，由于额外的参数pp和q q，对特定控制点和控制多边形提供了更好的逼近和灵活性。

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Approximation of conic sections by weighted Lupaş post-quantum Bézier curves

Abstract This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via ( p , q ) \left(p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter p p and q q in comparison to classical rational Bézier curves, Lupaş q q -Bézier curves and weighted Lupaş q q -Bézier curves.

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.