Subdivision Algorithm and G¹ Condition for C-Bézier Curves

C-Bézier curves are an extension of cubic Bézier curves.In addition to having many properties that Bézier curves have,they have the adjustable shape parameter α,and can represent arcs precisely.This paper presents the subdivision algorithm and G¹ condition of C-Bézier curves based on the analysis of C-Bézier basis functions and terminal properties.The results have definite geometric meanings that are useful for the shape modification and representation of C-Bézier curves.The results can also be extended to surface modeling with C-Bézier.