基于四边形网格均值坐标的K-2环网格曲面构造

Construction of K-2 ring mesh surface based on quad mean value coordinates

为在曲面造型中避免产生扭曲、褶皱等现象,将四边形网格中内点的K-2环网格作为控制网格,提出一种简单、灵活的曲面构造方法。给定一个K-2环控制网格,构造一个与其具有同样拓扑结构的平面网格。再将平面网格拓展成空间四边形网格,同时在平面网格内进行采样。然后计算采样点关于空间四边形网格顶点的四边形网格均值坐标,最后利用四边形网格均值坐标生成曲面,保证曲面上的每一点都满足C^(∞)。在这个过程中设置了一个全局形状因子h,用于控制曲面与初始控制网格的逼近程度,通过实例证明,h越小,曲面越逼近初始控制网格。

In order to avoid distortions and wrinkles in the surface modeling,the K-2 ring mesh at the inner point of the quad mesh served as the control mesh,a simple and flexible surface construction method was proposed.With a given K-2 ring control mesh,a planar mesh with the same topologyit was constructed.Then the plane mesh was expanded into a spatial quad mesh,and samples were made in the plane mesh.The quad mean value coordinates of the sampling points were later calculated with respect to the vertices of the spatial quad mesh.Finally,the surface was generated using the quad mean value coordinates to ensure that each point on the surface meets C^(∞).In this process,a global shape factor h was set to control the degree of approximation between the surface and the initial control mesh.It is proved through examples that the smaller h is,the closer the surface is to the initial control mesh.