An Algorithm based on the Weighted Network Voronoi Diagram for Point Cluster Simplification

Abstract

Points on maps that stand for geographic objects such as settlements are generally connected by road networks. However, in the existing algorithms for point cluster simplification, points are usually viewed as discrete objects or their distances are considered in Euclidean spaces, and therefore the point cluster generalization results obtained by these algorithms are sometimes unreasonable. To take roads into consideration so that point clusters can be simplified in appropriate ways, the network Voronoi diagram is used and a new algorithm is proposed in this paper. First, the weighted network Voronoi diagram is constructed taking into account the weights of the points and the properties of the related road segments. Second, the network Voronoi polygons are generated and two factors (i.e., the area of the network Voronoi polygon and the total length of the dilated road segments in the polygon) are considered as the basis for point simplification. Last, a Cartesian coordinate system is built based on the two factors and the point clusters are simplified by means of the “concentric quadrants”. Our experiments show that the algorithm can effectively and correctly transmit types of information in the process of point cluster simplification, and the results are more reasonable than that generated by the ordinary Voronoi-based algorithm and the weighted Voronoi-based algorithm.

Real-Time Displacement of Point Symbols Based on Spatial Distribution Characteristics

“…The second problem of the proposed method is that only the spatial relations of points are taken into consideration during the displacement process. This is unreasonable, because the relations among the points are not pure geometric relations but are also affected by the road network [34]. Hence network data should be considered to make the generalization results more practical and less confusing for users, especially in the visualization of city map.…”

Opening Gated Communities and Neighborhood Accessibility Benefits: The Case of Seoul, Korea

“…A Voronoi diagram consists of a Voronoi cell, the Voronoi space that surrounds a Voronoi cell, a Voronoi vertex, and a Voronoi foam [ 34 ]. Voronoi diagrams have been used widely for the delimitation of maritime zones and mapping coastal boundaries [ 35 ] and for mechanical engineering and robotics [ 36 , 37 ] as well as in urban planning and architecture for analyzing or designing indoor circulation, path planning, and service area studies [ 38 , 39 , 40 , 41 , 42 ]. In particular, the Voronoi diagram can describe the service area of the city network more accurately than can the traditional Euclidian network method [ 43 ].…”

Methods for Inferring Route Choice of Commuting Trip From Mobile Phone Network Data

“…Voronoi diagram is a popular method for partitioning space into sub-regions based on a set of pre-defined points in the space. It is widely used in the fields of spatial analysis and urban planning, such as service area delimitation [37] and map generalization [38]. As it is for space partitioning based on the distance to a set of seed points, the Voronoi diagram can be directly applied in our case to partition the entire area into sub-areas (or Voronoi cells) based on the cell tower locations-i.e., generating a coverage zone of each cell tower-which can then be used as a spatial reference in measuring a distance from the route (d ij ).…”