Chebyshev–Bernstein bases Original Research Article

From a design point of view, extended Chebyshev spaces are interesting in so far as they provide useful shape parameters. In such spaces, the blossoming principle generates de Casteljau type algorithms, which makes it natural to define Chebyshev–Bernstein bases as the dual bases of the linear functional giving the control points. Such bases share the same properties as the Bernstein bases in polynomial spaces. In particular they are the optimal shape preserving bases. This also holds in piecewise smooth extended Chebyshev spaces.