计算机工程与应用 ›› 2012, Vol. 48 ›› Issue (3): 165-168.

• 图形、图像、模式识别 • 上一篇    下一篇

一类三次曲线的形状分析

吴晓勤,陈福来,朱秀云   

  1. 湖南科技大学 数学与计算科学学院,湖南 湘潭 411201
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2012-01-21 发布日期:2012-01-21

Shape analysis of class of cubic curves

WU Xiaoqin, CHEN Fulai, ZHU Xiuyun   

  1. School of Mathematics & Computation Science, Hunan University of Science & Technology, Xiangtan, Hunan 411201, China
  • Received:1900-01-01 Revised:1900-01-01 Online:2012-01-21 Published:2012-01-21

摘要: 基于包络理论与拓扑映射的方法,对一类带有形状参数的三次曲线进行了形状分析,得出了曲线上含有奇点、拐点和曲线为局部凸或全局凸的充分必要条件,这些条件完全由控制多边形和形状参数所决定。进一步讨论了形状参数对形状分布图的影响及其对曲线形状的调节能力。

关键词: 三次曲线, 形状参数, 奇点, 拐点, 局部凸, 全局凸

Abstract: This paper considers the shape features of the class of cubic curves based on the theory of envelop and topological mapping. Necessary and sufficient conditions are derived for this curve having one or two inflection points, a loop or a cusp, or be locally or globally convex. Those conditions are completely decided by control polygon and the shape parameter. Furthermore, it discusses the influences of shape parameter on the shape distribution diagram and the ability for adjusting the shape of the curve.

Key words: cubic curve, shape parameter, singularities, inflection points, local convexity, global convexity