When generalizing a group of objects, displacement is an essential operation to resolve the conflicts arising between them due to enlargement of their symbol sizes and reduction of available map space. Although there are many displacement methods, most of them are rather complicated. Therefore, more practical methods are still needed. In this article, a new building displacement approach is proposed. For this purpose, buildings are grouped and zones are created for them in the blocks via Voronoi tessellation and buffering. Linear patterns are then detected through buffer analyses and the respective zones are narrowed to be able to preserve these patterns. After all the buildings are displaced inside their zones, grid points are generated and then weighted through kernel density estimation and buffer analyses to find suitable locations. Accordingly, the buildings are displaced toward the computed locations iteratively. The proposed approach directly enforces minimum distance and positional accuracy constraints while several indirect mechanisms are used for preserving spatial patterns and relationships. For the quality evaluation of the displacement, the angle, length and shape comparison measures are introduced, computed based on the (Delaunay) triangles or the azimuth comparison measure of the connection lines, generated for the buildings. The quality evaluation criteria are yielded according to the visual assessment of the displacement quality and the quantitative analysis of the measures. The findings demonstrate that the proposed approach is quite effective and practical for zonal building displacement.

中文翻译：

---

建筑物综合中基于网格点权重的区域位移方法

概括一组对象时，位移是解决由于符号大小增加和可用地图空间减少而导致它们之间发生冲突的基本操作。尽管置换方法很多，但大多数方法都相当复杂。因此，仍然需要更实用的方法。在本文中，提出了一种新的建筑物位移方法。为此，通过Voronoi细分和缓冲在建筑物中对建筑物进行分组并为其创建区域。然后通过缓冲区分析检测线性模式，并缩小各个区域的范围以能够保留这些模式。在所有建筑物在其区域内移位后，生成网格点，然后通过核密度估计和缓冲区分析加权以找到合适的位置。因此，建筑物迭代地移向计算位置。所提出的方法直接强制了最小距离和位置精度约束，同时使用了几种间接机制来保留空间模式和关系。为了对位移进行质量评估，引入了角度，长度和形状比较量度，这些量度是根据建筑物产生的（Delaunay）三角形或连接线的方位角比较量度来计算的。根据位移质量的视觉评估和措施的定量分析得出质量评估标准。研究结果表明，所提出的方法对于区域建筑物位移是相当有效和实用的。所提出的方法直接强制了最小距离和位置精度约束，同时使用了几种间接机制来保留空间模式和关系。为了对位移进行质量评估，引入了角度，长度和形状比较量度，这些量度是根据建筑物产生的（Delaunay）三角形或连接线的方位角比较量度来计算的。根据位移质量的视觉评估和措施的定量分析得出质量评估标准。研究结果表明，所提出的方法对于区域建筑物位移是相当有效和实用的。所提出的方法直接强制了最小距离和位置精度约束，同时使用了几种间接机制来保留空间模式和关系。为了对位移进行质量评估，引入了角度，长度和形状比较量度，这些量度是根据建筑物产生的（Delaunay）三角形或连接线的方位角比较量度来计算的。根据位移质量的目测评估和措施的定量分析得出质量评估标准。研究结果表明，所提出的方法对于区域建筑物位移是相当有效和实用的。