NURBS曲面逆节点插入法  

Method of inserting reverse knots into NURBS curved surfaces

作　　者：毛虎平[1] 孙振山 韩啸 高亚洲 贾峰[1] MAO Hu-ping;SUN Zhen-shan;HAN Xiao;GAO Ya-zhou;JIA Feng(School of Energy and Power Engineering,North University of China,Taiyuan 030051)

机构地区：[1]中北大学能源与动力工程学院,山西太原030051

出　　处：《机械设计》2023年第3期41-47,共7页Journal of Machine Design

基　　金：国家自然科学基金(51275489);山西省自然科学基金(201701D121082)。

摘　　要：针对工程中对控制点的特殊需求,提出了一种非均匀有理B样条曲面逆节点插入方法。从分析NURBS控制多边形的边及其相关联的节点出发,通过齐次坐标投影确定必须插入节点所在区间,利用插入控制点对控制多边形的边分割与需插入节点对参数区间的分割等比例映射,获得过任意点并与控制多边形对边相交的等参线,得到对应插入节点,再从插入节点出发反方向确定所有需要插入的控制点,协同实现某特殊需求控制点插入的任务。数值算例验证了文中方法对于NURBS曲面插入控制点的有效性,且具有明显的几何和物理意义。In view of the special requirements of control points in engineering,the method of inserting the reverse knots into the non-uniform rational B-spline surfaces is proposed.Firstly,the analysis is conducted on the edges of the NURBS control polygon and the related knots;the interval where the knots must be inserted is computed by means of homogeneous coordinates projection;the isoparametric curve is obtained,which meets the special requirements of the control points and intersects the opposite edge of the control polygon;the corresponding inserted knot is obtained.Then,all the control points to be inserted are computed from the inserted knot in the opposite direction,in order to insert the control points with special requirements in a collaborative manner.The numerical examples have verified that this method of inserting control points into NURBS surfaces is effective with great importance in geometry and physics.

关 键 词：NURBS 控制点 曲面 逆节点插入 

分 类 号：TB92[一般工业技术—计量学]