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 pp and qq in comparison to classical rational Bézier curves, Lupaş qq-Bézier curves and weighted Lupaş qq-Bézier curves.

Keywords

• post-quantum integers
• weighted lupaş post-quantum bézier curve
• rational bézier curve
• normalized totally positive basis
• shape parameter
• conic sections
• 65d17
• 41a10
• 41a25
• 41a36