Affiliation:
1. Texas Southern University , USA
2. University of Houston – Downtown , USA
Abstract
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.
Reference25 articles.
1. [1] Goldman R., Simeonov P., Quantum Bernstein bases and quantum Bézier curves, J. Comput. Appl. Math., 2015, 288, 284–303
2. [2] Goldman R., Simeonov P., Novel polynomial Bernstein bases and Bézier curves based on a general notion of polynomial blossoming, Numer. Algorithms, 2016, 72(3), 605–634.
3. [3] Simeonov P., Zafiris V., Goldman R., h-Blossoming: A new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves, Comput. Aided Geom. Design, 2011, 28(9), 549–565
4. [4] Simeonov P., Zafiris V., Goldman R., q-Blossoming: A new approach to algorithms and identities for q-Bernstein bases and q-Bézier curves, J. Approx. Theory, 2012, 164(1), 77–104
5. [5] Jegdić I., Larson J., Simeonov P., Algorithms and identities for (q, h)-Bernstein polynomials and (q, h)-Bézier curves – a non-blossoming approach, Anal. Theory Appl., 2016, 32, 373–386
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献