Algorithms and Identities for $(q,h)$-Bernstein Polynomials and $(q,h)$-Bézier Curves — A Non-Blossoming Approach

Algorithms and Identities for $(q,h)$-Bernstein Polynomials and $(q,h)$-Bézier Curves — A Non-Blossoming Approach

Year:    2016

Author:    I. Jegdić, J. Larson, P. Simeonov

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 373–386

Abstract

We establish several fundamental identities, including recurrence relations, degree elevation formulas, partition of unity and Marsden identity, for quantum Bernstein bases and quantum Bézier curves. We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bézier curves. Our proofs use standard mathematical induction and other elementary techniques.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2016.v32.n4.5

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 4 : pp. 373–386

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Bernstein polynomials Bézier curves Marsden's identity recursive evaluation.

Author Details

I. Jegdić

J. Larson

P. Simeonov

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