Properties of an h-Bernstein-like basis and curves

Blossoming is a useful technique to study bases and curve representations in computer-aided geometric design. Recently Simeonov et al. (Comput Aided Geom Des 28:549–565, 2011) have used a blossom generalization, namely the h-blossom, to derive new results about the h-Bernstein basis and h-Bézier curves that have previously been studied in approximation theory and computer-aided geometric design. This paper introduces a basis related to the h-Bernstein basis. There is a close relationship between this new basis and the h-Bernstein basis, between the new basis and the h-blossom, and between the new basis and “progressive” curves. This paper explores these relationships and uses them to derive properties both of the new basis itself, and of curves represented in terms of the new basis.