C1 NURBS representations of G1 composite rational Bézier curves.

This paper is concerned with the re-representation of a G1 composite rational Bézier curve. Although the rational Bézier curve segments that form the composite curve are G1 continuous at their joint points, their homogeneous representations may not be even C0 continuous in the homogeneous space. In this paper, an algorithm is presented to convert the G1 composite rational Bézier curve into a NURBS curve whose nonrational homogeneous representation is C1 continuous in the homogeneous space. This re-representation process involves reparameterization using Möbius transformations, smoothing multiplication and parameter scaling transformations. While the previous methods may fail in some situations, the method proposed in this paper always works. [ABSTRACT FROM AUTHOR]