三次有理Bézier曲线的形状调整方法  

Some Methods for Shape Modification of Cubic Rational Bézier Curves

作　　者：韩旭里[1] 肖鸣宇[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410083

出　　处：《计算机工程与应用》2005年第15期70-72,119,共4页Computer Engineering and Applications

基　　金：湖南省自然科学基金项目(编号:01JJY2095);教育部留学回国人员科研基金项目(编号:教外司犤2001犦498号)资助

摘　　要：给出了两类调整三次有理Bézier曲线形状的方法。一类方法是使曲线通过给定的插值点,从而实现曲线的形状调整。另一类方法是将曲线上的点作为控制多边形两边连线段上的分点,通过调整分线段的比例,实现对曲线的形状调整。针对不同情况,分别给出了权因子的计算公式。计算方法简单,使用方便,并使三次有理Bézier曲线的形状调整更加具体和明确。同时,由计算结果得到了任意三次有理Bézier曲线不相交的充分必要条件。Two kinds of the methods for shape modification of cubic rational Bézier curves are presented in this paper.One of the methods is to let the generated curves pass through the given interpolation point such that the shape modification is achieved.Another method is to generate curves by setting the proportion of dividing a line segment which connects two edges of the given control polygon.The computing formulas for the weights of cubic rational Bézier curves are given respectively for different cases.The given computing methods are simple and useful.According to the given methods,people can adjust the shape of cubic rational Bézier curves exactly.A sufficient and necessary condition for which arbitrary two cubic rational Bézier curves do not intersect is also gotten.

关 键 词：有理BÉZIER曲线 权因子 形状修改 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]