文章摘要
易于拼接且形状可调的Bézier曲线曲面
Bézier curves and surfaces which are easy to piece and shape adjustable
  
DOI:
中文关键词: 曲线曲面设计  Bézier方法  形状参数  几何连续  切线多边形
英文关键词: curve and surface design  Bézier method  shape parameter  geometric continuity  tangent polygonBézier
基金项目:国家自然科学基金资助项目(11261003);江西省教育厅项目(GJJ14493)
作者单位
严兰兰 东华理工大学 理学院江西 南昌 330013 
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中文摘要:
      为了增强Bézier曲线曲面形状表示的灵活性,同时简化Bézier曲线曲面的光滑拼接条件,构造了3组含参数的多项式基函数,并由它们定义了结构分别类似于二次、三次、四次Bézier曲线曲面的新曲线曲面.它们不仅保留了Bézier曲线曲面的基本性质,而且还具有形状可调性,并且由新曲线曲面构成的组合曲线曲面可以在简单的条件下实现G2或G3光滑拼接.另外还给出了构造与给定多边形相切的曲线的方法,该方法简单有效,而且曲线对给定的多边形是保形的.
英文摘要:
      In order to enhance the shape representation flexibility and simplify the smooth connecting conditions of Bézier curve and surface, three groups of polynomial basis functions with shape parameter were constructed. Based on them, three kinds of new curves and surfaces, which had the similar structure with the quadratic, cubic and quartic Bézier curve and surface respectively, were defined. The new curves and surfaces not only posess the basic properties of Bézier curve and surface, but also have shape adjustability. Furthermore, under simple conditions, the composite curves and surfaces consist of the new curves and surfaces achieve G2 or G3 continuity. Besides, the method of constructing curves tangent to the given polygons is presented. This method is simple and effective. And the curves are conformal to the given polygons.
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