| ¡¡ | Chinese Journal of Computers Full Text |
| Title | Shape Analysis of Rational C-B¨¦zier Curve |
| Authors | WU Rong-Jun1) YE Zheng-Lin2) LUO Wei-Min1) |
| Address | 1)(Department of Applied Mathematics and Applied Physics, Xi¡¯an Institute of Post and Telecommunications, Xi¡¯an 710121) 2)(Department of Applied Mathematics, Northwestern Polytechnical University, Xi¡¯an 710072) |
| Year | 2007 |
| Issue | No.11(2055¡ª2059) |
| Abstract & Background | Abstract In this paper the authors analyze the shape features like singularities, inflection points and local or global convexity of rational C-B¨¦zier curve, then give the necessary and sufficient conditions for this curve having one or two inflection points, or a loop, or a cusp, or being local or global convex in terms of the relative position of its control polygons¡¯ side vectors. The authors also discuss the influences of weight coefficients on the shape diagram of this curve. keywords rational C-B¨¦zier curve; singular points; inflection points; local convexity; global convexity background This work is supported by the Natural Science Foundation of Shaanxi Province of China under grant No.2004A12 and Special Research Project of Educational Department of Shaanxi Province under grant No.05JK289. Distribution of singular points, inflection points and convexity (local or global) of parametric curves is very important in designing curves. In this paper the authors apply the method used in (Ye and Wu 2005), which is based on theory of envelope and continuous bijection, to rational C-B¨¦zier curve, obtain the distribution regions of singular points and inflection points without much difficulty. Furthermore, the envelope of the regions, which indicate local convexity, are found to be two of boundary curves of region which indicates a loop, so the complete shape diagram, which is geometrical visual, is got, and easy to judge. |