中文摘要：

针对散乱点云数据在三角剖分过程中产生的拓扑缺陷，提出一种基于数学形态学运算和拓扑规则的网格拓扑修补算法。通过交互的方式选择需要修改的区域，使用自适应分层栅格的缺陷识别技术提取有拓扑缺陷的网格的顶点，从而确定待修复区域的边界，然后利用数学形态学的开启运算和闭合运算去除该修复区域的拓扑缺陷，并利用基于柄体理论的拓扑运算法则对该区域进行局部拓扑修改，生成二维流形的三角网格。应用实例表明，由于不需要对整个点云数据重新进行三角剖分，简化数据处理的过程，该算法具有运算速度快、结果准确性好的优点，并能较好地消除网格中的拓扑缺陷，有效地提高三角网格的显示精度，最终得到具有几何一致性和网格单元拓扑一致性的三角网格模型。

英文摘要：

For the topological defects generated during unorganized point cloud triangulation, a new method is presented for mesh repair based on mathematical morphology and topology rule. The repaired areas are chosen with the interactive ways, and the mesh vertexs with potential topological errors are found out by means of a defect detecting technology based on adaptive hierarchical grid so as to determine the boundary need to be repaired. Opening and closing of mathematical morphology being used, the topology of the model can be modified. The local topology repair is able to be finished and a 2-manifold triangle mesh is generated quickly through topological mesh operators based on Handlebody theory. Experimental results show that the triangulation of the whole point cloud is no longer needed so that the data processing is simplified. The proposed algorithm is fast and accurate, and the topological defects can be eliminated satisfactorily and output precision of triangular meshes can be improved efficiently. The triangular mesh model with geometrical and topological consistency is able to be formed.