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

[摘要] 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.

[学科分类] 外科医学

[关键词] Bézier surface;bivariate (q;h)-blossom;bivariate (q;h)-Bernstein basis;Marsden identity;quantum differentiation;recursive evaluation;subdivision