q-Bernstein basis functions on a triangulated domain

Abstract

In this paper, we propose generalized q-Bernstein basis functions based on a triangulated domain using q-real. Proofs of some geometric and algebraic properties are given. These include the partition of unity, degree raising and the q-De Casteljau algorithm. Finally, we introduce the generalized q-Bernstein polynomial functions of degree n. We have constructed these polynomials on the triangle with the parameter q, which can be used to improve the rendering given by standard Bernstein polynomials.

Keywords: q-Bernstein basis; q-Integers; q-Bernstein polynomials.

MSC (2020): 65D07, 65D17, 65D10.