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 - <p style="text-align: justify;">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 B<span style="text-align: justify;">é</span>zier curves. Our proofs use standard mathematical induction and other elementary techniques.</p>