Algorithms and Identities for Bézier 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 basis and B´ezier curves. By applying the post-quantum blossom, various new identities and formulae expressing the monomials in terms of the post-quantum Bernstein basis and a post-quantum variant of Marsden’s identity are investigated. For each post-quantum B´ezier curves of degree m, a collection of m! new, affine invariant, recursive evaluation algorithms are derived.

Key words and phrases. post-quantum integers; post-quantum blossom; de Casteljau algorithm; Marsden’s identity; post-quantum Bernstein polynomials; post-quantum B´ezier curve; quantum Bernstein polynomials.

2020 Mathematics Subject Classification. MSC: primary 65D17; secondary 41A10, 41A25, 41A36