中文摘要：

利用Voronoi图及其对偶Delaunay三角网研究平面离散点集拓扑邻近稳定区域的计算方法,给出拓扑邻近稳定区域的概念,证明点的拓扑邻近稳定区域必须满足的两个条件,给出点的拓扑邻近稳定区域定量计算模型,并通过试验证明其正确性。

英文摘要：

A method to maintain the neighboring relations between each two points in discrete points set is studied based on the Delaunay triangulation or the Voronoi diagram.A new concept of the topology stable area is put forward firstly,then the two conditions which the points in the topology stable area should be met are proved by the empty circle rule of the Delaunay triangulation,A novel calculation model of the topology stable area of the plane discrete points based on the Voronoi diagram is presented and it＇s correctness is proved by the experiment.