基于第2类Coons曲面的插值型细分方法  

Interpolatory subdivision scheme based on type 2 Coons surface

作　　者：周元迪 李亚娟[1] 邓重阳[1] ZHOU Yuandi;LI Yajuan;DENG Chongyang(School of Sciences,Hangzhou Dianzi University,Hangzhou 310018,China)

机构地区：[1]杭州电子科技大学理学院,杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2024年第5期31-38,共8页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金项目(61872121)。

摘　　要：提出基于第2类Coons曲面的插值型细分方法,可定义于任意拓扑下的四边形网格。第1步,设置初始网格点在每条边上的切矢。第2步,在每1层细分中,首先由网格边上的2个点及切矢结合德卡斯特里奥算法构造曲线边界,将参数中心点设为新边点,并计算两端点、新边点的新切矢;然后,在4条曲线边界上设定跨界导矢,给出端点扭矢并构造第2类Coons曲面,将采样曲面的参数中心点作为新面点,同时计算面点和邻边的新切矢。第3步,设置形状参数调整规则点的切矢,最后迭代得到极限曲面。数值算例表明,相比于Kobbelt细分方法及4点曲面细分方法,提出方法能得到光滑度更高的插值曲面,且易于控制。收敛性、连续性分析证明,插值曲面至少为G^(1)连续。An interpolatory subdivision method based on type 2 Coons surface is proposed,which is defined on quadrilateral meshes of any topology.Step 1,set the tangent vector of the initial grid point on each edge.Step 2,in each layer of subdivision,the curve boundary is constructed from two points and tangent vectors on the mesh edge by combining with the De Casteljau's algorithm.The center point of curve parameter is set as the new edge point,and the new tangent vector of two endpoints and new edge point is calculated.And then,set the boundary derivative on the boundary of four curves,and give the endpoint torsion vector to construct type 2 Coons surface.The parameter center point of the sampling surface is taken as the new surface point,and the new tangent vector on the connection edge of the surface point and the edge point is calculated.Step 3,set the shape parameters to adjust the tangent vector of the regular points,and finally,the limit surface is iteratively obtained.Numericals examples shows that,compared with Kobbelt subdivision method and 4-point surface subdivision method,the proposed method which can obtain interpolatory surfaces with higher smoothness is controllable easily.Convergence and continuity analysis prove that the interpolation surface is at least G~1 continuous.

关 键 词：插值 第2类Coons曲面 曲面细分 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]