C 1 NURBS representations of G 1 composite rational Bézier curves

This paper is concerned with the re-representation of a G 1 composite rational Bezier curve. Although the rational Bezier curve segments that form the composite curve are G 1 continuous at their joint points, their homogeneous representations may not be even C 0 continuous in the homogeneous space. In this paper, an algorithm is presented to convert the G 1 composite rational Bezier curve into a NURBS curve whose nonrational homogeneous representation is C 1 continuous in the homogeneous space. This re-representation process involves reparameterization using Mobius transformations, smoothing multiplication and parameter scaling transformations. While the previous methods may fail in some situations, the method proposed in this paper always works.