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

doi:10.11947/j.AGCS.2019.20180353

Abstract

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

CLC Number:

P208

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.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://xb.chinasmp.com/EN/10.11947/j.AGCS.2019.20180353

http://xb.chinasmp.com/EN/Y2019/V48/I6/756

References

[1] ELMER M E. Symbol considerations for bivariate thematic mapping[D]. Madison:University of Wisconsin-Madison, 2012.
[2] CHERNOFF H. The use of faces to represent points in k-dimensional space graphically[J]. Journal of the American Statistical Association, 1973, 68(342):361-368.
[3] LEONOWICZ A. Two-variable Choropleth maps as a useful tool for visualization of geographical relationship[J]. Geografija, 2006, 42(1):33-37.
[4] 曾兴国, 杜清运, 任福. 一种采用Mashup的网络地图多变量制图方法[J]. 武汉大学学报(信息科学版), 2015, 40(9):1215-1219. ZENG Xingguo, DU Qingyun, REN Fu. A web multi-variate mapping method based on Mashup[J]. Geomatics and Information Science of Wuhan University, 2015, 40(9):1215-1219.
[5] 王丽娜, 江南, 李响, 等. Cartogram表示方法研究综述[J]. 计算机辅助设计与图形学学报, 2017, 29(3):393-405. WANG Lina, JIANG Nan, LI Xiang, et al. A survey of cartogram[J]. Journal of Computer-Aided Design & Computer Graphics, 2017, 29(3):393-405.
[6] 艾廷华. 适宜空间认知结果表达的地图形式[J]. 遥感学报, 2008, 12(2):347-354. AI Tinghua. Maps adaptable to represent spatial cognition[J]. Journal of Remote Sensing, 2008, 12(2):347-354.
[7] HENNIG B D. Rediscovering the world:gridded cartograms of human and physical space[D]. Sheffield:University of Sheffield, 2011.
[8] DORLING D. Area cartograms:their use and creation[C]//Concepts and Techniques in Modern Geography. Norwich:University of East Anglia, 1996.
[9] TOBLER W. Thirty five years of computer cartograms[J]. Annals of the Association of American Geographers, 2004, 94(1):58-73.
[10] SPECKMANN B, KREVELD M V, FLORISSON S. A linear programming approach to rectangular cartograms[M]//RIEDL A, KAINZ W, ELMES G A. Progress in Spatial Data Handling. Berlin, Heidelberg:Springer, 2006:529-546.
[11] KEIM D A, PANSE C, NORTH S C. Medial-axis-based cartograms[J]. IEEE Computer Graphics and Applications, 2005, 25(3):60-68.
[12] 张军海, 胡文亮, 韩宪生. 拓扑图传递量化信息的方法[J]. 地图, 2001(1):3-6. ZHANG Junhai, HU Wenliang, HAN Xiansheng. Method for representing quantitative information in topological map[J]. Cartography, 2001(1):3-6.
[13] 艾廷华, 周梦杰, 陈亚婕. 专题地图属性信息的LOD表达与TreeMap可视化[J]. 测绘学报, 2013, 42(3):453-460. AI Tinghua, ZHOU Mengjie, CHEN Yajie. The LOD representation and TreeMap visualization of attribute information in thematic mapping[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(3):453-460.
[14] SLINGSBY A, DYKES J, WOOD J. Rectangular hierarchical cartograms for socio-economic data[J]. Journal of Maps, 2010, 6(1):330-345.
[15] BUCHIN K, EPPSTEIN D, LÖFFLER M, et al. Adjacency-preserving Spatial TreeMaps[M]//DEHNE F, IACONO J, SACK J R. Algorithms and Data Structures. Berlin, Heidelberg:Springer, 2011(6844):159-170.
[16] HUGH H. Multivariate mapping[EB/OL]. (2016-11-08)[2019-03-15]. http://www.geotechcenter.org/uploads/2/4/8/8/24886299/16_multivariate_mapping_s12.ppt.
[17] NUSRAT S, ALAM M J, SCHEIDEGGER C, et al. Cartogram visualization for bivariate geo-statistical data[J]. IEEE Transactions on Visualization and Computer Graphics, 2018, 24(10):2675-2688.
[18] GASTNER M T, NEWMAN M E J. Diffusion-based method for producing density-equalizing maps[J]. Proceedings of the National Academy of Sciences of the United States of America, 2004, 101(20):7499-7504.
[19] 张珣, 钟耳顺, 张小虎, 等. 一种尺度效应指数修正的格网数据示意地图制图算法[J]. 武汉大学学报(信息科学版), 2015, 40(8):1100-1104. ZHANG Xun, ZHONG Ershun, ZHANG Xiaohu, et al. A modified algorithm to construct gridded area cartograms by scale effect index[J]. Geomatics and Information Science of Wuhan University, 2015, 40(8):1100-1104.
[20] OYANA T J, RUSHOMESA R I, BHATT L M. Using diffusion-based cartograms for visual representation and exploratory analysis of plausible study hypotheses:the small and big belly effect[J]. Journal of Spatial Science, 2011, 56(1):103-120.
[21] 陈谊, 赵云芳, 杜晓敏. 变形统计地图构建方法综述[J]. 系统仿真学报, 2016, 28(9):1970-1978. CHEN Yi, ZHAO Yunfang, DU Xiaomin. Overview of cartogram algorithm[J]. Journal of System Simulation, 2016, 28(9):1970-1978.
[22] LI Ziqiang, ARYANA S. Diffusion-based cartogram on spheres[J]. Cartography and Geographic Information Science, 2017, 45(5):464-475.
[23] ZAITSEV V F, POLYANIN A D. Handbook of exact solutions for ordinary differential equations[M]. 2nd ed. Boca Raton:CRC Press, 2002.
[24] CHENG A H D, CHENG D T. Heritage and early history of the boundary element method[J]. Engineering Analysis with Boundary Elements, 2005, 29(3):268-302.
[25] SVLI E, MAYERS D F. An introduction to numerical analysis[M]. Cambridge:Cambridge University Press, 2003.