Computer Aided Geometric Design
Geometric applications of bivariate q-Bernstein and q-orthogonal polynomials
MATH'08 Proceedings of the American Conference on Applied Mathematics
h-Blossoming: A new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves
Computer Aided Geometric Design
h-Blossoming: A new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves
Computer Aided Geometric Design
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
Generalized Bézier curves and surfaces based on Lupaş q-analogue of Bernstein operator
Journal of Computational and Applied Mathematics
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We introduce a new variant of the blossom, the q-blossom, by altering the diagonal property of the standard blossom. This q-blossom is specifically adapted to developing identities and algorithms forq-Bernstein bases and q-Bezier curves over arbitrary intervals. By applying the q-blossom, we generate several new identities including an explicit formula representing the monomials in terms of the q-Bernstein basis functions and a q-variant of Marsden's identity. We also derive for each q-Bezier curve of degree n, a collection of n! new, affine invariant, recursive evaluation algorithms. Using two of these new recursive evaluation algorithms, we construct a recursive subdivision algorithm for q-Bezier curves.