An Improved Map Transformation Algorithm Considering the Balance of Features Density in Cartographical Region
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摘要: 制图区域要素密度分布不均衡会增加地图表达难度，常规地图表达方式无法解决视觉不平衡的问题。在Gastner-Newman地图变形算法的基础上，提出了一种顾及制图区域要素密度平衡和公众地图认知一致性的地图变换算法。首先，设计多种变形单元尺度以及配置制图要素密度权重组合；然后，代入线性扩散方程，构建变形格网并映射各离散控制点；最后，生成多种变形地图结果。开展了地图认知实验，获得56份问卷结果，针对中国广西南宁市青秀区行政区划图的形态控制，应控制S周长 > 0.975、S周长面积比 > 0.961、S形状比 > 0.966，能兼顾地图形变以及公众认知的一致性。为解决地图要素密度不均衡的问题提供了新的思路，变形后的地图达到视觉平衡，同时，通过调整形变权重参数实现了公众地图认知的一致性。Abstract:Objectives In the case of uneven distribution of map features, the density difference breaks the visual balance and reduces the beauty of the map. A large number of spatial features are concentrated in the small area, resulting in the contradiction between the display of features and the size of the area. Map details are not prominent, which increases difficulties in obtaining spatial information and is not conducive to decision analysis. The uneven distribution of feature density in mapping area increases the difficulty of map expression. Conventional map expression cannot solve the problem of visual imbalance.Methods Based on Gastner-Newman cartogram algorithm, this paper proposes a map transformation algorithm that balances the feature density and achieve consistent public perception. Various cartograms can be generated through five steps: Designing deformation unit scales, configuring density weight combination of features, applying linear diffusion equation, constructing deformation grids and mapping discrete control points.Results Taking Qingxiu district of Nanning city, China as the research area, we select two scale deformation units of sub-district and custom grid, and configure density weights with different combinations of point of interest and road network geometry features to generate various cartograms. The deformation measurement values of the deformation map are calculated respectively. After cognitive experiments, 56 questionnaires were obtained. Regarding the morphological control of the administrative map of Qingxiu District in Nanning, the parameters configurations should be controlled as in Sperimeter > 0.975, Sperimeter area ratio > 0.961 and Sshape ratio > 0.966. In this way, public cognition can be consistent.Conclusions This study provides a new idea to solve the problem of uneven density of map features. The deformed map reaches visual balance.The area where the original features are dense increases while the area where the features are sparse decreases. By adjusting the deformation weight parameters to maintain the consistency of public map cognition. Subsequently, we will further study how to determine the optimal parameter combination to achieve the optimal deformation expression and cognitive effect.
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Keywords:
- map load /
- information entropy /
- visual balance /
- map generalization /
- map cognition
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图 8 待测试变形地图不一致率与其形变度量指标关系
Figure 8. Relationship Between Inconsistency Rate of Cartogram to be Tested and Its Deformation Measurement Index
表 1 研究区域数据统计
Table 1 Statistics of Research Regional Features
行政区划名称 面积/km² POI个数 POI密度/(个·km-2) 路网数量/km 路网密度
/(km·km-2)新竹街道 5.1 2 540 498 61.1 12 建政街道 9.6 1 032 107.5 74.2 7.7 中山街道 12.7 1 326 104.4 105.6 8.3 南湖街道 32.9 1 212 36.8 174 5.3 津头街道 37.7 1 606 42.7 197.8 5.2 南阳镇 94.9 21 0.2 19.7 0.2 刘圩镇 159.7 24 0.2 33 0.2 伶俐镇 236.3 43 0.2 59.7 0.3 长塘镇 276.6 792 2.7 258.6 0.9 合计 856.5 8 596 983.7 
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表 2 认知实验结果
Table 2 Cognitive Experiment Results
变形地图编号 形变度量指标 不一致票数 不一致率 重叠面积比 S周长 S周长面积比 S形状比 S1-9-1 0.746 0.926 0.892 0.908 40 0.714 S1-7-3 0.746 0.926 0.891 0.909 40 0.714 S1-3-7 0.746 0.925 0.891 0.908 40 0.714 S1-5-5 0.747 0.927 0.893 0.910 38 0.679 S1-POI 0.776 0.948 0.914 0.931 36 0.643 S2-POI 0.775 0.972 0.953 0.963 31 0.554 S1-1-9 0.814 0.971 0.954 0.960 30 0.536 S2-8-2 0.794 0.974 0.957 0.967 29 0.518 S2-5-5 0.803 0.983 0.966 0.975 28 0.500 S2-7-3 0.787 0.975 0.961 0.966 28 0.500 S2-3-7 0.802 0.983 0.968 0.975 27 0.482 S2-9-1 0.770 0.969 0.949 0.961 27 0.482 S2-4-6 0.797 0.983 0.967 0.975 26 0.464 S2-6-4 0.797 0.981 0.965 0.973 25 0.446 S1-2-8 0.814 0.971 0.949 0.960 25 0.446 S2-1-9 0.811 0.991 0.975 0.983 24 0.429 S2-2-8 0.810 0.990 0.974 0.982 22 0.393 S2-路网 0.948 1.000 1.000 1.000 18 0.321 S1-4-6 0.952 0.999 0.998 0.999 16 0.286 S1-6-4 0.954 0.998 0.997 0.997 15 0.268 S1-路网 0.885 0.982 0.966 0.974 10 0.179 S1-8-2 0.951 0.996 0.992 0.994 10 0.179 注: S周长表示变形前后周长的相似度；S周长面积比表示变形前后周长面积比的相似度；S形状比表示变形前后形状比的相似度；S1-路网、S2-路网表示只考虑路网权重；S1-POI、S2-POI表示只考虑POI权重
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