B\'ezier representation of the constrained dual Bernstein polynomials

TL;DR

This paper derives explicit Bezier coefficient formulas for constrained dual Bernstein basis polynomials using Hahn polynomials, enabling efficient computation and applications in computer-aided geometric design.

Contribution

It introduces explicit formulas and recursive schemes for constrained dual Bernstein polynomials, linking them to Hahn polynomials, with practical applications in CAGD.

Findings

Explicit Bezier coefficient formulas derived

Efficient recursive computation scheme developed

Applications demonstrated in CAGD

Abstract

Explicit formulae for the B\'ezier coefficients of the constrained dual Bernstein basis polynomials are derived in terms of the Hahn orthogonal polynomials. Using difference properties of the latter polynomials, efficient recursive scheme is obtained to compute these coefficients. Applications of this result to some problems of CAGD is discussed.