C1 NURBS representations of G1 composite rational Bezier 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.