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

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.