Abstract:

Complex curve approximation is a basic problem in CAGD, and the traditional de Casteljau algorithm is commonly used with the fixed parameter value of 0.5. To achieve better subdivided curves in approximation, we consider two different choices of the subdivision parameters for the planar Bézier curves. The two choices of the parameter are associated with convex hull area minimization and convex hull flat minimization. The definitions and algorithms of the parameters are proposed in both cases. By analyzing the parameters for different types of curves, we find that the optimal parameter volues are close to 0.5 when the curve segments are short enough. This fact indicates that it is reasonable to select the parameter value of 0.5 for the small curve segments. For some complex curves the least flat method improves the efficiency of the subdivision by more than 50%, compared to the traditional de Casteljau method. For other curves, the two methods have similar efficiency.

Key words: planar Bézier curve, subdivision parameter, polygon flatting, convex hull area