In this paper, we extend the properties of rational Lupaş-Bernstein blending functions, Lupaş- Bézier curves and surfaces over arbitrary compact intervals [α, β] in the frame of post quantum-calculus and derive the de-Casteljau’s algorithm based on post quantum-integers. We construct a two parameter family as Lupaş post quantum Bernstein functions over arbitrary compact intervals and establish their degree elevation and reduction properties. We also discuss some fundamental properties over arbitrary intervals for these curves such as de Casteljau algorithm and degree evaluation properties. Further we construct post quantum Lupaş Bernstein operators over arbitrary compact intervals with the help of rational Lupaş- Bernstein functions. At the end some graphical representations are added to demonstrate consistency of theoretical findings