Generalizing rational degree elevation

Abstract

A generalization of the well-known degree elevation algorithms for Bézier curves is presented. This generalized degree elevation extends the expressive power of rational polynomials. In particular, it allows a given curve to be represented equivalently by a family of control point and weight distributions, without affecting its parameterization. Some control over the control point distribution is demonstrated. The effects of reparameterization in conjunction with degree elevation are also explored, and techniques for detecting degeneracy in the presence of reparameterization are described.