A Zonal Displacement Approach via Grid Point Weighting in Building Generalization

Abstract

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.

A spatial contextual immune genetic algorithm to building cartographic displacement

“…Therefore, for the constraints C31 and C33, a kind of DSZs is constructed by overlapping the Voronoi tessellation and buffer areas of the buildings. Since Voronoi tessellation is a wonderful tool to express spatial relations and structures in Computational Geometry and has been widely used to identify and describe the spatial relations, structures, and patterns of building groups in map generalization (Ai et al, 2015; Basaraner, 2011; Peng et al, 1995; Sahbaz & Basaraner, 2021; Wei, He, et al, 2018), we use it to restrict the displacement range of buildings, thus preventing topology errors and maintain the spatial relations and patterns. Meanwhile, the buffer zone with the size R for each building is used to delimit the movement area in terms of constraint C2 for each building.…”

“…However, most of spatial relations and patterns are ill‐defined; and the related constraints cannot be easily evaluated by scalar geometric measures as components of the objective function. Therefore, enhanced data models (e.g., DT; Højholt, 2000; Peng et al, 1995), Voronoi tessellation (Ai et al, 2015; Basaraner, 2011; Peng et al, 1995; Sahbaz & Basaraner, 2021; Wei, He, et al, 2018), MST (Bader, 2001; Wang, Guo, Wei, et al, 2017), and proximity graph (Liu et al, 2014; Ruas, 1998; Sun, Guo, Liu, Lv, et al, 2016) should be used to identify, represent, and preserve those spatial characteristics during the displacement process.…”

“…Fei (2004) adopted a raster‐vector hybrid data structure to deal with the graphic conflict between roads and buildings caused by the widening of road symbols in large‐scale topographic maps. Basaraner (2011) proposed an iterative zonal displacement approach for buildings, in which building groups and displacement zones are created in the blocks via Voronoi tessellation and buffering, and relevant criteria are defined to control the displacement iteratively; and recently, Sahbaz and Basaraner (2021) put forward a new zonal displacement approach via grid point weighting. Ai et al (2015) put forward the displacement algorithm of building group based on a vector field model, in which a scalar field is constructed based on a constrained Delaunay triangulation (CDT) skeleton to control the displacement and propagation of buildings caused by road widening.…”

“…During map generalization, proximity conflicts or symbol overlaps often occur between adjacent buildings or between buildings and other adjacent objects (e.g., roads) because of map scale reduction or symbol exaggeration (Liu et al, 2014). To remove these conflicts, several generalization operators have been employed, such as contextual selection (Wang, Guo, Liu, et al, 2017), aggregation (Ai & Zhang, 2007; Li et al, 2004; Shen et al, 2019), displacement (Ai et al, 2015; Bader, 2001; Bader et al, 2005; Basaraner, 2011; Bobrich, 2001; Burghardt & Meier, 1997; Fei, 2004; Harrie, 1999, 2003; Harrie & Sarjakosk, 2002; Højholt, 2000; Huang et al, 2017; Li et al, 2020; Lichtner, 1979; Liu et al, 2014; Lonergan & Jones, 2001; Mackaness, 1994; Mackaness & Purves, 2001; Peng et al, 1995; Pilehforooshha, et al, 2021; Ruas, 1998; Sahbaz & Basaraner, 2021; Sester, 2005; Sun, Guo, Liu, Lv, et al, 2016; Sun, Guo, Liu, Ma, et al, 2016; Wang, Guo, Wei, et al, 2017; Ware & Jones, 1998; Ware et al, 2002, 2003; Wei, He, et al, 2018; Wilson et al, 2003), and typification (Mao et al, 2012; Regnauld, 2001; Shen et al, 2016; Yan et al, 2021). Among these operators, displacement may be the most frequently used one in a map production environment (Ai et al, 2015; Foerster & Stoter, 2008).…”

“…To satisfy the cartographic constraints of building displacement, various algorithms have been proposed over the years. Those algorithms can be divided into two categories: sequential algorithms (Ai et al, 2015; Basaraner, 2011; Fei, 2004; Lichtner, 1979; Mackaness, 1994; Peng et al, 1995; Pilehforooshha et al, 2021; Ruas, 1998; Wei, Guo, et al, 2018) and optimization algorithms (Bader, 2001; Bader et al, 2005; Bobrich, 2001; Burghardt & Meier, 1997; Harrie, 1999, 2001, 2003; Højholt, 2000; Huang et al, 2017; Li et al, 2020; Liu et al, 2014; Lonergan & Jones, 2001; Mackaness & Purves, 2001; Pilehforooshha et al, 2021; Sahbaz & Basaraner, 2021; Sester, 2005; Sun, Guo, Liu, Lv, et al, 2016; Sun, Guo, Liu, Ma, et al, 2016; Wang, Guo, Wei, et al, 2017; Ware et al, 2002, 2003; Ware & Jones, 1998; Wilson et al, 2003) (see details in Sections 2.1 and 2.2). In sequential algorithms, buildings are handled based on a trial and error strategy.…”