Volume 32, Issue 4
Algorithms and Identities for $(q,h)$-Bernstein Polynomials and $(q,h)$-Bézier Curves — A Non-Blossoming Approach

Anal. Theory Appl., 32 (2016), pp. 373-386.

Published online: 2016-10

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• 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.

• Keywords

Bernstein polynomials, Bézier curves, Marsden's identity, recursive evaluation.

11C08, 65DXX, 65D15, 65D17

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@Article{ATA-32-373, author = { and I. Jegdić and and 21603 and and I. Jegdić and and J. Larson and and 21604 and and J. Larson and P. and Simeonov and and 21605 and and P. Simeonov}, title = {Algorithms and Identities for $(q,h)$-Bernstein Polynomials and $(q,h)$-Bézier Curves — A Non-Blossoming Approach}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {4}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n4.5}, url = {http://global-sci.org/intro/article_detail/ata/4677.html} }
TY - JOUR T1 - Algorithms and Identities for $(q,h)$-Bernstein Polynomials and $(q,h)$-Bézier Curves — A Non-Blossoming Approach AU - I. Jegdić , AU - J. Larson , AU - Simeonov , P. JO - Analysis in Theory and Applications VL - 4 SP - 373 EP - 386 PY - 2016 DA - 2016/10 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n4.5 UR - https://global-sci.org/intro/article_detail/ata/4677.html KW - Bernstein polynomials, Bézier curves, Marsden's identity, recursive evaluation. AB -

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.

I. Jegdić, J. Larson & P. Simeonov. (1970). Algorithms and Identities for $(q,h)$-Bernstein Polynomials and $(q,h)$-Bézier Curves — A Non-Blossoming Approach. Analysis in Theory and Applications. 32 (4). 373-386. doi:10.4208/ata.2016.v32.n4.5
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