A universal approach to blossoming with applications to Bernstein bases and Bézier curves for arbitrary function spaces

Abstract We present a general constructive approach to blossoming for arbitrary finite dimensional univariate function spaces by altering the diagonal property of the classical blossom. We apply this approach to blossoming to develop the corresponding theory of Bernstein bases and Bézier curves including de Casteljau type algorithms for evaluation and subdivision as well as a Marsden identity for arbitrary finite dimensional univariate function spaces.