Arbitrarily high degree elevation of Bézier representations Original Research Article

In this paper we present fast algorithms to raise the degree n of a simplicial Bézier representation of degree n to arbitrarily high degree. Each Bézier point of some (n + r)th degree representation can be computed in a simplicial recursive scheme of depth n. In the case of curves the recurrence relation reveals that the (n + r)th degree Bézier polygon can also be obtained by inserting r knots into some nth degree spline which provides a very fast algorithm. Furthermore, a short new proof is given for the fact that the Bézier nets of a multivariate polynomial converge to the polynomial under repeated degree elevation.