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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.

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