面向双/多变量的连续面域拓扑图可视化方法

doi:10.11947/j.AGCS.2019.20180353

测绘学报 ›› 2019, Vol. 48 ›› Issue (6): 756-766.doi: 10.11947/j.AGCS.2019.20180353

面向双/多变量的连续面域拓扑图可视化方法

李响¹, 王丽娜², 张卫东³, 杨飞¹, 杨振凯¹

1. 信息工程大学地理空间信息学院, 河南郑州 450052;
2. 郑州轻工业大学计算机与通信工程学院, 河南郑州 450001;
3. 61512部队, 北京 100088

收稿日期:2018-07-23 修回日期:2019-03-18 出版日期:2019-06-20 发布日期:2019-07-09
通讯作者: 王丽娜 E-mail:wln_map@126.com
作者简介:李响(1982-),男,博士,副教授,主要研究方向为互联网地理数据获取与分析和地理信息可视化。E-mail:lixiangzzchxy@163.com
基金资助:
地理信息工程国家重点实验室开放基金（SKLGIE2016-Z-4-2）；国家重点研发计划项目（2016YFB0502300；2017YFC1200300）；国家自然科学基金（41671455）

A visualization method of continuous area cartogram for two or multiple variables

LI Xiang¹, WANG Lina², ZHANG Weidong³, YANG Fei¹, YANG Zhenkai¹

1. Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450052, China;
2. School of Computer and Communication Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China;
3. 61512 Troops, Beijing 100088, China

Received:2018-07-23 Revised:2019-03-18 Online:2019-06-20 Published:2019-07-09
Supported by:
The Open Foundation of State Key Laboratory of Geo-information Engineering (No. SKLGIE 2016-Z-4-2);The National Key Research and Development Program (Nos. 2016YFB0502300;2017YFC1200300);The National Natural Science Foundation of China(No. 41671455)

摘要/Abstract

摘要： 面域拓扑图是一种利用区域面积大小定量表达区域属性信息的可视化方法。由于其区域面积本身已经表示某一变量，因此这更有利于双/多变量的制图表达。针对目前基于面域拓扑图的双/多变量表达方法中存在的难以表达相邻区域之间基本状况和不利于不同地理现象的空间分布规律及差异表达的问题，本文提出一种面向双/多变量的连续面域拓扑图可视化方法。首先通过格网密度补偿和积分步长逐步试探的方法对基于扩散模型的连续面域拓扑图生成算法进行部分优化，完成基本变量的表达，然后分别通过空间内插和符号扩展完成第2和第3变量在连续面域拓扑图中的表达。最后以慕尼黑市人口密度和银行/ATM分布（双变量）数据以及奥格斯堡市人口密度数据、幼儿园分布以及规模数据（多变量）为试验数据进行可视化，并通过实证分析验证了该方法的有效性和优越性。

关键词: 地理信息可视化, 双/多变量制图, 连续面域拓扑图, 扩散算法

Abstract: Area cartogram is a visualization method that quantitatively represents regional attribute information by using the area size. Area cartogram is more conductive to the bivariate/multivariate mapping because the area size itself participates in the expression of variables. Now, bivariate/multivariate mapping based on area cartogram is difficult to express the basic situation between adjacent regions, and it is also difficult to express the spatial distribution of different geographical phenomena, to detect differences between two or more variables and spatial patterns. A method of a continuous Area cartogram for two or multiple variables has been proposed in this paper. Firstly, compensation of grid density and the progressive heuristics of the integration step are used to improve and optimize the classic algorithm of continuous area cartogram-"the diffusion-based method for producing density equalizing maps". Then, the first variable is visualized by area cartogram and the second or more variables are visualized by interpolating location on a continuous Area cartogram and symbolization. Finally, we use the population density and bank/ATM distribution data in Munich (bivariate mapping), the population density, kindergarten distribution and scale data in Augsburg (multivariate mapping) as case studies. This method is proved to be more effective and superior by the experiment results.

Key words: geovisualization, bivariate/multivariate mapping, continuous area cartogram, the diffusion-based method for producing density equalizing maps

中图分类号:

P208

李响, 王丽娜, 张卫东, 杨飞, 杨振凯. 面向双/多变量的连续面域拓扑图可视化方法[J]. 测绘学报, 2019, 48(6): 756-766.

LI Xiang, WANG Lina, ZHANG Weidong, YANG Fei, YANG Zhenkai. A visualization method of continuous area cartogram for two or multiple variables[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(6): 756-766.

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面向双/多变量的连续面域拓扑图可视化方法

A visualization method of continuous area cartogram for two or multiple variables

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