We study the validity of Zipf's Law in a data set of Chinese city sizes. Previous investigations are restricted to log-log rank-size regression for a fixed sample. In contrast, we use rolling sample regression methods in which the sample is changing with the truncation point. The intuition is that if the distribution is Pareto with a coefficient one (Zipf's… (More)
Subdivision scheme is a discrete modeling method that breaches old model of surface modeling, namely, from discrete data to continuous data and last to discrete data. The method is simple, small computing and fast in modeling. This paper presents a classification standard of subdivision scheme, discusses and compares several subdivision schemes in brief.
The shape features of planar trigonometric Bézier curves with two shape parameters are analyzed. The necessary and sufficient conditions are derived for these curves having one or two inflection points, a loop or a cusp, or be locally or globally convex. All conditions are completely characterized by the relative position of the control polygon's side… (More)