A comparison of neighbourhood relations based on ordinary Delaunay diagrams and area Delaunay diagrams: an application to define the neighbourhood relations of buildings
A comparison of neighbourhood relations based on ordinary Delaunay diagrams and area Delaunay diagrams: an application to define the neighbourhood relations of buildings
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DOI：
10.1080/13658816.2020.1748191
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发表时间：
2020-04
影响因子：
5.7
通讯作者：
Hiroyuki Usui;Akihiro Teraki;Kei-ichi Okunuki;Toshiaki Satoh
中科院分区：
文献类型：
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作者：
Hiroyuki Usui;Akihiro Teraki;Kei-ichi Okunuki;Toshiaki Satoh
摘要本文的目的是描述一种基于普通Delaunay图(ODDS)和面积Delaunay图(ADDS)来定义建筑物之间邻里关系的方便而稳健的方法。ODDS和ADD被定义为连接相邻普通Voronoi单元(代表建筑多边形质心的点)生成元的一组边和连接两个建筑多边形质心的一组边，它们分别是相邻区域Voronoi单元的生成器。虽然ADDS比ODDS更健壮，但ODDS的计算时间比ADDS更短(其计算时间复杂度的量级为O(Nlogn))。如果赔率能够以一定的精度近似加法，则前者可以作为一种选择。因此，我们在建筑物和区域尺度上计算了添加边的数目与奇数边重叠添加的数目的比率。结果表明：(1)对于大约60%的建筑物，赔率可以精确地重叠ADDS和额外的奇边；(2)在区域尺度上，赔率可以重叠大约90%的ADS和10%的额外奇边；以及(3)专注于判断错误，尽管ADD比ODDS更准确，但差异只有大约1%。
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%.