摘要
点/曲线的最近距离在几何造型中有着较广泛的应用,特别是在实时性要求很高的应用中,最近距离计算的效率也相应地面临越来越高的要求.为此,提出混合基于控制多边形的细分位置快速估算、分类剔除,以及渐进求根法等技术的点到NURBS曲线最近距离的快速计算方法.首先将平方距离函数转化为Bézier形式;然后根据对应的控制多边形信息来快速估算细分位置,并根据分类技术进行剔除;最后使用高阶收敛的渐进求根方法计算出相应的最近点.该方法只需要一次Bézier形式的转换,具有比圆裁剪更好的裁剪效果.数值实例结果表明,与已有的圆裁剪等方法相比,混合的快速计算方法可以具有更高的裁剪效率和计算效率.
Point projection problem of NURBS curves has a wide application in geometric modeling system.A fast approach is presented for computing the minimum distance between a point and a NURBS curve.It combines a control-polygon-based method for searching the subdivision position,the classification based clipping method with progressive root-finding technique.It firstly translates the square distance function into Bézier form; and then,estimates the subdivision positions by using the control polygon,and does the clippings based on classification; finally it computes the minimum distance by using progressive root-finding technique.It can achieve a better clipping effect than the circle-clipping methods.Numerical examples show that the new method can achieve better clipping efficiency and better computational efficiency than those of circle clipping method and other prevailing methods.
作者
王龙权
陈小雕
陈立庚
Wang Longquan;Chen Xiaodiao;Chen Ligeng(School of Computer,Hangzhou Dianzi University,Hangzhou 310018)
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2019年第1期26-30,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(61672009)
关键词
NURBS曲线
点投影
圆裁剪
分类剔除
渐进求根
NURBS curve
point projection
circle-clipping
classification clipping
progressive root-finding method
