Lupa\c{s} post quantum blending functions and B\'{e}zier curves over arbitrary intervals

Abstract

In this paper, we extend properties of rational Lupa\c{s}-Bernstein blending functions, Lupa\c{s}-B\'{e}zier curves and surfaces over arbitrary compact intervals $[\alpha,\beta ]$ in the frame of post quantum-calculus. The de-Casteljau's algorithm based on post quantum-integers is derived. A two parameter family as Lupa\c{s} post quantum Bernstein functions over arbitrary compact intervals are constructed to establish their degree elevation and reduction properties. Some of their basic properties for Lupa\c{s} post quantum B\'{e}zier curves are studied. Some fundamental properties over arbitrary intervals for these surfaces as well as de Casteljau algorithm and degree evaluation properties are discussed. Post quantum-Lupa\c{s}-Bernstein operators over arbitrary compact intervals are constructed with the help of rational Lupa\c{s}-Bernstein functions. The derived results on arbitrary compact intervals are important from computational point of view. Graphical representations are added to demonstrate consistency to theoretical findings.