h-Blossoming: A new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves Original Research Article

A new variant of the blossom, the h-blossom, is introduced by altering the diagonal property of the standard blossom. The significance of the h-blossom is that the h-blossom satisfies a dual functional property for h-Bézier curves over arbitrary intervals. Using the h-blossom, several new identities involving the h-Bernstein bases are developed including an h-variant of Marsdenʼs identity. In addition, for each h-Bézier curve of degree n, a collection of n! new, affine invariant, recursive evaluation algorithms are derived. Using two of these recursive evaluation algorithms, a recursive subdivision procedure for h-Bézier curves is constructed. Starting from the original control polygon of an h-Bézier curve, this subdivision procedure generates a sequence of control polygons that converges rapidly to the original h-Bézier curve.