多边形网格的非流形封闭三角形网格正则化

Construction of Non-manifold Closed Regular Triangle Mesh from Polygonal Mesh

为了提高基于网格模型的算法与应用的效率和稳定性,提出一种将任意多边形网格模型转化为正则三角网格模型的算法.首先对输入多边形网格模型中非三角形的面片进行三角剖分,然后查找并移除模型中的重合或重叠元素,再通过模型内部三角形求交对模型进行边和面的分割,从而修正模型的拓扑结构;在求交的过程中,根据边和三角形的位置关系对共面求交进行细致的分类处理,减少了求交次数,提高了算法的稳定性;最后循环搜索在网格模型中可以确定法向的种子三角形,通过拓扑结构调整与之相邻的三角形的法向,最终构成一个或多个法向确定的闭合曲面.实验结果表明,该算法能够将多边形网格转化为正则三角形网格模型.

To improve the efficiency and the stability of algorithms based on polygonal meshes, an algorithm to regularize a polygonal mesh into a regular triangle mesh is proposed. First, triangularize the input mesh and remove the coincident or overlapped elements. Then split the faces and edges of the model by computing the intersection of triangles and justifying the topology. During the process of intersection, an algorithm according to the classification of the relationship between the edges and the coplanar triangles is used to reduce the time cost and improve the efficiency. Find a seed triangle with the determined normal, adjust its neighbors according to the topology continuity, and at last one or more normal-determined closed surfaces are obtained. Experiments show that the algorithm can well convert a polygonal mesh to a regular triangle mesh.