Joint generalization of city points and road network for sma

城市点与路网集成的小比例尺制图综合

Joint generalization of city points and road network for

small-scale mapping

1*T. E. Samsonov1,2, A. M. Krivosheina1 Lomonosov Moscow State University, Faculty of Geography, 1 Leninskiye Gory, Moscow, Russia, 119234

*Email: tsamsonov@geogr.msu.ru

2Delaunay Laboratory of Discrete and Computational Geometry, Yaroslavl State University,

150000, Sovetskaya Str. 14, Yaroslavl, Russian Federation

1. Introduction

Multiscale cartographic web services such as Google Maps, Microsoft Bing and OpenStreetMap are produced using large amounts of spatial data that is initially prepared in large and intermediate scales. Since these services are published in multiscale environment a problem of data generalization for small scales arises. Usually this task is solved by selection of objects by their attributes. The smaller scale is, the more important object classes are selected. However, this strategy is only suitable for territories with mostly uniform distribution of settlements, for example, Western Europe. Large and climatically diverse regions, such as Russia, Australia, and Northern Africa are notable for their extremely non-uniform pattern of topographic elements. Attribute selection does not work in such cases, since in sparsely populated areas we should depict even some of the smallest cities and low-category roads to show that the territory is lived-in. At the same time the ratio of population densities between densely and sparsely populated territories should be retained as far as possible.

Another important aspect of small-scale mapping is that road network generalization should correspond strongly to location of generalized city points. Every selected road should start and finish at the city point or another road. If two cities are connected in the source map, this connection should be retained after generalization. A brief survey of web services mentioned above shows that the rules of small-scale generalization are often violated. This leads to inadequate representation of the territory with lots of road dangles and only the largest cities retained.

This study aims to develop an algorithm for joint generalization of settlement points and road network with regulation of settlements distribution density over the territory.

2. Background

Small-scale representation of settlements and roads is usually implemented using point set and network generalization algorithms. Li (2007) singles out two types of algorithms for point set generalization: selective omission and structural simplification. The first group includes settlement-spacing, distribution-coefficient, gravity-modeling, set-segmentation, quadrant-reduction (Langran and Poicker 1986) and circle-growth (van Kreveldt et al. 1995) algorithms. The second group of algorithms simplifies the set of points by removing some of them on the basis of various characteristics. One of the most popular strategies is to use Voronoi-based generalization, which ranks points according to their Voronoi areas and thematic importance and iteratively removes points with smallest weights (Ai and Liu 2002, Yan and Weibel 2008). Qian et al (2006) introduced the polarization transformation approach.

For simplification of geographical networks graph theory is usually used (Mackaness and