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.

13 pages, 4 figures, name of two more authors who contributed in revised form added, slight change in title of the paper

References in corpus (3)

• Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series
• Approximation properties of (p;q)-variant of Stancu-Schurer operators(Revised)
• Some Approximation Results by $(p,q)$-analogue of Bernstein-Stancu Operators (Revised)