Computer Aided Geometric Design 22 (2005) 183–197 www.elsevier.com/locate/cagd Fast degree elevation and knot insertion for B-spline curves Qi-Xing Huang a , Shi-Min Hu a,∗ , Ralph R. Martin b a Department of Computer Science and Technology, Tsinghua University, Beijing 100084, PR China b School of Computer Science, Cardiff University, Cardiff, CF24 3AA, United Kingdom Received 30 April 2004; received in revised form 15 October 2004; accepted 10 November 2004 Available online 30 November 2004 Abstract We give a new, simple algorithm for simultaneous degree elevation and knot insertion for B-spline curves. The method is based on the simple approach of computing derivatives using the control points, resampling the knot vector, and then computing the new control points from the derivatives. We compare our approach with previous algorithms and illustrate it with examples.  2004 Elsevier B.V. All rights reserved. Keywords: B-splines; Degree elevation; Knot insertion 1. Introduction Several methods have been given for degree elevation of B-spline curves (Cohen et al., 1985; Liu and Wayne, 1997; Prautzsch, 1984; Prautzsch and Piper, 1991; Pigel and Tiller, 1994), the fastest of which is Prautzsch and Piper’s algorithm (Prautzsch and Piper, 1991). Unfortunately, their algorithm suffers from being complicated and hard to implement. On the other hand, Piegl and Tiller’s (1994) algorithm is more straightforward, and easier to understand. It splits the B-spline curve into Bézier curve pieces, raises the degree of each piece, and then recombines the degree-elevated Bézier curves to produce the new B-spline curve. Liu’s algorithm (Liu and Wayne, 1997) has the benefits of being both simple to implement and fast. It takes the approach of computing the new control points using a series of knot insertions followed by a series of knot deletions. * Corresponding author. E-mail address: shimin@tsinghua.edu.cn (S.-M. Hu). 0167-8396/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cagd.2004.11.001