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

Jegdić Ilija, Simeonov Plamen, Zafiris Vasilis

Demonstratio Mathematica

2019

Vol. 52, nr 1

451--466

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. Usingthe (q, h)-blossom, we construct recursive evaluation algorithms for (q, h)-Bézier surfaces and we derive adual functional property, a Marsden identity, and a number of other properties for bivariate (q, h)-Bernsteinpolynomials and (q, h)-Bézier surfaces. We develop a subdivision algorithm for (q, h)-Bézier surfaces witha geometric rate of convergence. Recursive evaluation algorithms for quantum (q, h)-partial derivatives ofbivariate polynomials are also derived.