城市点与路网集成的小比例尺制图综合

Beard 1993). Using various measures the importance of individual edges and nodes can be determined (Li and Choi 2002). Thomson and Brooks (2007) generalized road networks using “strokes” with the assumption that the most probable edges for traveling are those with minimal travel cost.

Analysis of the generalization techniques reveals the following problems:

Most of the algorithms for point generalization are global, so they do not allow adjustment of generalization parameters to the characteristics of local pattern and density of objects. For example, Ai and Liu (2002) algorithm preserves point distribution pattern well. However it does not consider cartographic requirements, which compel generalization thresholds to tighten in densely populated regions to free the space for symbols and labels. At the same time generalization thresholds should be relaxed in sparsely populated regions to show the presence of habitation. Recent progress in hydrography generalization with regional parameterization (Buttenfield Stanislawski and Brewer 2011) shows that this technique can be successfully applied to build more cartographically oriented generalization process.

The task of joint generalization of point and network features and its cartographic application is not developed enough. An experience in agent-based generalization (Touya and Duchene 2011) that combines multiple layers and criteria together shows that collaborative generalization strategy gives the most satisfying results. However it is applied primarily to the large-scale maps, while the small-scale generalization is different because of increasing competition between objects and attention to patterns and clusters instead of individual objects.

3. Methodology and results

We solve the task of joint generalization in two steps. At first, the city points are generalized, and then the road network is adjusted to generalized set of points.

The problem of point density regulation is treated by clustering the points into regions of various densities and then generalizing each region independently with individual percentage of omitted points. We based Voronoi polygons removal on three factors:

Voronoy polygon area A with weight wa.

City population P with weight wp.

City administrative status S with weight ws.

Both population and administrative statuses were classified into 5 categories from 1 to 5 and the weight Wi of every point is calculated as:

Wi=waAi wpPi wsSi

Using the weights wa, wp and ws we can control the influence of each factor on the importance of the point.

The main difference from previous Voronoy-based techniques is that we:

do not generalize all the points in one set, but do this operation by subsets of points with different clustering tolerance;

do not freeze adjacent neighbours of currently deleted point, but increment their neighbour index Ni — the number of deleted neighbours — and use it along with weight in point sorting; this simplifies algorithm and derives additional useful information about generalization cores (see further).

The outline of the algorithm is as follows:

1. Define several levels Lj of clustering tolerance. For example these levels can be 25, 50, 100 and 200 kilometres. The polygonal cluster is a group of points in which the distances from every point to its two nearest neighbours is less than defined threshold Tj.