Algorithms and Identities for B$\acute{e}$zier curves via Post Quantum Blossom

Abstract

In this paper, a new analogue of blossom based on post quantum calculus is introduced. The post quantum blossom has been adapted for developing identities and algorithms for Bernstein bases and B$\acute{e}$zier curves. By applying the post quantum blossom, various new identities and formulae expressing the monomials in terms of the post quantun Bernstein basis functions and a post quantun variant of Marsden's identity are investigated. For each post quantum B$\acute{e}$zier curves of degree $m,$ a collection of $m!$ new, affine invariant, recursive evaluation algorithms are derived.