Quantum (q, h)-Bézier surfaces based on bivariate (q, h)-blossoming

Abstract

We introduce the (q, h)-blossom of bivariate polynomials, and we define the bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces on rectangular domains using the tensor product. Using the (q, h)-blossom, we construct recursive evaluation algorithms for (q, h)-Bézier surfaces and we derive a dual functional property, a Marsden identity, and a number of other properties for bivariate (q, h)-Bernstein polynomials and (q, h)-Bézier surfaces. We develop a subdivision algorithm for (q, h)-Bézier surfaces with a geometric rate of convergence. Recursive evaluation algorithms for quantum (q, h)-partial derivatives of bivariate polynomials are also derived.

Keywords

• bézier surface
• bivariate (q
• h)-blossom
• bivariate (q
• h)-bernstein basis
• marsden identity
• quantum differentiation
• recursive evaluation
• subdivision
• 41xx
• 65d15
• 65d17