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

I. Jegdic, J. Larson & P. Simeonov

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 Bezier curves. We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bezier curves. Our proofs use standard mathematical induction and other elementary techniques.
  • Keywords

Bernstein polynomials Bezier curves Marsden's identity recursive evaluation

  • AMS Subject Headings

11C08 65DXX 65D15 65D17

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COPYRIGHT: © Global Science Press

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@Article{ATA-32-373, author = {I. Jegdic, J. Larson and P. Simeonov}, title = {Algorithms and Identities for (q,h)-Bernstein Polynomials and (q,h)-Bezier 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 Bezier curves. We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bezier 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)-Bezier Curves--A Non-Blossoming Approach AU - I. Jegdic, J. Larson & P. Simeonov 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 KW - Bezier curves KW - Marsden's identity KW - 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 Bezier curves. We also develop two term recurrence relations for quantum Bernstein bases and recursive evaluation algorithms for quantum Bezier curves. Our proofs use standard mathematical induction and other elementary techniques.
I. Jegdic, J. Larson & P. Simeonov. (1970). Algorithms and Identities for (q,h)-Bernstein Polynomials and (q,h)-Bezier 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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