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

• Autorzy: Jegdić Ilija , Simeonov Plamen , Zafiris Vasilis

Identyfikatory

DOI

10.1515/dema-2019-0029

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Bezier surface; bivariate (q, h)-blossom; bivariate (q, h)-Bernstein basis; Marsden identity; quantum differentiation; recursive evaluation; subdivision

PL

płaty Béziera; wzór Marsdena; wielomiany Bernsteina; różnicowanie; rekurencja

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 451--466
• Opis fizyczny: Bibliogr. 25 poz., rys.

Twórcy

autor

Jegdić Ilija

• Texas Southern University, USA

autor

Simeonov Plamen

• University of Houston – Downtown

autor

Zafiris Vasilis

• University of Houston – Downtown

Bibliografia

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• [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] 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] 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
• [6] Simeonov P., Goldman R., Quantum B-splines, BIT, 2013, 53(1), 193-223
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• [20] Goldman R., Barry P., Shape parameter deletion for Pólya curves, Numer. Alg., 1991, 1, 121-137
• [21] Ramshaw L., Bézier and B-spline curves as multiaflne maps, Theoretical foundations of computer graphics and CAD (Il Ciocco, 1987), 757-776, NATO Adv. Sci. Inst. Ser. F, Comput. Systems Sci., 40, Springer-Verlag Berlin, 1988
• [22] Ramshaw L., Blossoms are polar forms, Comput. Aided Geom. Design, 1989, 6(4), 323-358
• [23] Jegdić I., Algorithms and identities for bivariate (h1, h2)-blossoming, Int. J. Appl. Math., 2017, 30(4), 321-343
• [24] Goldman R., Simeonov P., Formulas and algorithms for quantum differentiation of quantum Bernstein bases and quantum Bézier curves based on quantum blossoming, Graph. Models, 2012, 74, 326-334
• [25] Andrews G., Askey R., Roy R., Special Functions, Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, 1999

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).