ABSTRACT The aim of this article is to describe a convenient but robust method for defining neighbourhood relations among buildings based on ordinary Delaunay diagrams (ODDs) and area Delaunay diagrams (ADDs). ODDs and ADDs are defined as a set of edges connecting the generators of adjacent ordinary Voronoi cells (points representing centroids of building polygons) and a set of edges connecting two centroids of building polygons, which are the generators of adjacent area Voronoi cells, respectively. Although ADDs are more robust than ODDs, computation time of ODDs is shorter than that of ADDs (the order of their computation time complexity is O(nlogn)). If ODDs can approximate ADDs with a certain degree of accuracy, the former can be used as an alternative. Therefore, we computed the ratio of the number of ADD edges to that of ODD edges overlapping ADDs at building and regional scales. The results indicate that: (1) for approximately 60% of all buildings, ODDs can exactly overlap ADDs with extra ODD edges; (2) at a regional scale, ODDs can overlap approximately 90% of ADDs with 10% extra ODD edges; and (3) focusing on judging errors, although ADDs are more accurate than ODDs, the difference is only approximately 1%.

中文翻译：

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基于普通德劳内图和面积德劳内图的邻域关系比较：定义建筑物邻域关系的应用

摘要本文的目的是描述一种方便但稳健的方法，用于定义基于普通德劳内图 (ODD) 和面积德劳内图 (ADD) 的建筑物之间的邻域关系。ODDs 和 ADDs 被定义为连接相邻普通 Voronoi 单元（代表建筑物多边形质心的点）的生成器的一组边和连接建筑物多边形的两个质心的一组边，它们分别是相邻区域 Voronoi 单元的生成器。尽管 ADDs 比 ODDs 更健壮，但 ODDs 的计算时间比 ADDs 短（它们的计算时间复杂度的顺序是 O(nlogn)）。如果 ODD 可以以一定的精度近似 ADD，则可以使用前者作为替代。所以，我们计算了建筑和区域尺度上 ADD 边的数量与与 ADD 重叠的 ODD 边的数量之比。结果表明：（1）对于大约 60% 的建筑物，ODD 可以与具有额外 ODD 边的 ADD 精确重叠；(2) 在区域尺度上，ODDs 可以与大约 90% 的 ADDs 重叠，并有 10% 的额外 ODD 边缘；(3) 专注于判断错误，虽然ADDs比ODDs更准确，但差异只有1%左右。