{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:41:07Z","timestamp":1759920067565,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T00:00:00Z","timestamp":1736553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42201490","212300410303"],"award-info":[{"award-number":["42201490","212300410303"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006407","name":"Natural Science Foundation of Henan Province","doi-asserted-by":"publisher","award":["42201490","212300410303"],"award-info":[{"award-number":["42201490","212300410303"]}],"id":[{"id":"10.13039\/501100006407","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>The rectangular cartogram is a geospatial visualization method that blends the characteristics of maps and charts. By simplifying geographic regions into rectangles and using the area of each rectangle to represent statistical data, it enables efficient geovisualization. This paper summarizes and analyzes the advantages and limitations of two main approaches used in current rectangular cartogram construction algorithms. To address the issues of high computational cost and inadequate preservation of adjacency and relative positional relationships in existing algorithms, we propose and implement a new rectangular cartogram construction algorithm. This algorithm simplifies the layout computation process while ensuring that the adjacency and relative positional relationships between regions during the layout generation process have only minor errors. In adjusting rectangle areas to match attribute values, the algorithm adopts a \u201cregion-by-region placement\u201d strategy, ensuring that errors in area accuracy remain within a small range, while also keeping errors in adjacency and relative positional relationships minimal. Finally, by comparing the results of our algorithm with those of existing algorithms using real-world data with varying distribution characteristics, we demonstrate its effectiveness. The results show that the proposed algorithm not only improves computational efficiency but also effectively displays the adjacency and relative positional relationships between regions.<\/jats:p>","DOI":"10.3390\/ijgi14010025","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T05:40:40Z","timestamp":1736746840000},"page":"25","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A New Construction Method for Rectangular Cartograms"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-3187-9857","authenticated-orcid":false,"given":"Lina","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0766-8903","authenticated-orcid":false,"given":"Haoxun","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7490-6962","authenticated-orcid":false,"given":"Xiang","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450052, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5890-1388","authenticated-orcid":false,"given":"Pengfei","family":"Lu","sequence":"additional","affiliation":[{"name":"Institute of Surveying and Mapping, Information Engineering University, Zhengzhou 450052, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-6411-0382","authenticated-orcid":false,"given":"Yaru","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Zhengzhou University of Light Industry, Zhengzhou 450001, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1109\/MCG.1983.263019","article-title":"An Effective Graphic \u201cVocabulary\u201d","volume":"3","author":"McCleary","year":"1983","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_2","first-page":"393","article-title":"A Survey of Cartogram","volume":"29","author":"Wang","year":"2017","journal-title":"J. Comput. -Aided Des. Comput. Graph."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hennig, B.D. (2011). Rediscovering the World: Gridded Cartograms of Human and Physical Space. [Ph.D. Thesis, University of Sheffield].","DOI":"10.1007\/978-3-642-34848-8_3"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1111\/j.1467-8306.2004.09401004.x","article-title":"Thirty Five Years of Computer Cartograms","volume":"94","author":"Tobler","year":"2004","journal-title":"Ann. Assoc. Am. Geogr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/MCG.2005.64","article-title":"Medial-axis-based cartograms","volume":"25","author":"Keim","year":"2005","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"292","DOI":"10.2307\/208794","article-title":"The Rectangular Statistical Cartogram","volume":"24","author":"Raisz","year":"1934","journal-title":"Geogr. Rev."},{"key":"ref_7","first-page":"8","article-title":"Rectangular Statistical cartograms of the World","volume":"35","author":"Raisz","year":"1936","journal-title":"J. Geogr."},{"key":"ref_8","first-page":"347","article-title":"Maps Adaptable to Represent Spatial Cognition","volume":"12","author":"Ai","year":"2008","journal-title":"Nat. Remote Sens. Bull."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1111\/cgf.12932","article-title":"The state of the art in cartograms","volume":"35","author":"Nusrat","year":"2016","journal-title":"Comput. Graph. Forum"},{"key":"ref_10","first-page":"1970","article-title":"Overview of Cartogram Algorithm","volume":"28","author":"Chen","year":"2016","journal-title":"J. Syst. Simul."},{"key":"ref_11","first-page":"526","article-title":"Research on Information Heritage Based on Cartogram Method","volume":"26","author":"Zhao","year":"2016","journal-title":"China Popul.\u00b7Resour. Environ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1080\/00087041.2018.1534358","article-title":"Cartograms for Use in Forecasting Weather-Driven Natural Hazards","volume":"56","author":"Pappenberger","year":"2019","journal-title":"Cartogr. J."},{"key":"ref_13","first-page":"327","article-title":"Drawing social networks using area-labeling rectangular cartograms","volume":"13","author":"Lin","year":"2012","journal-title":"J. Internet Technol."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, L., Li, X., Ding, L., Yu, X., and Hu, T. (2022). Visualization and Analysis of Transport Accessibility Changes Based on Time Cartograms. ISPRS Int. J. Geo-Inf., 11.","DOI":"10.3390\/ijgi11080432"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1080\/15230406.2023.2264755","article-title":"Effectiveness of animated choropleth and proportional symbol cartograms for epidemiological dashboards","volume":"51","author":"Kronenfeld","year":"2024","journal-title":"Cartogr. Geogr. Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Dorling, D. (2011). Area Cartograms: Their Use and Creation. The Map Reader, Wiley-Blackwell.","DOI":"10.1002\/9780470979587.ch33"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2376","DOI":"10.1109\/TVCG.2022.3151227","article-title":"Multicriteria Optimization for Dynamic Demers Cartograms","volume":"28","author":"Nickel","year":"2022","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7499","DOI":"10.1073\/pnas.0400280101","article-title":"Diffusion-based method for producing density-equalizing maps","volume":"101","author":"Gastner","year":"2004","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1111\/j.0033-0124.1976.00371.x","article-title":"Noncontiguous area Cartograms","volume":"28","author":"Olson","year":"1976","journal-title":"Prof. Geogr."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4631","DOI":"10.1109\/TVCG.2023.3275925","article-title":"Effectiveness of Area-to-Value Legends and Grid Lines in Contiguous Area Cartograms","volume":"30","author":"Fung","year":"2024","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Jia, F., Wang, W., Yang, J., Li, T., Song, G., and Xu, Y. (2023). Effectiveness of Rectangular Cartogram for Conveying Quantitative Information: An Eye Tracking-Based Evaluation. ISPRS Int. J. Geo-Inf., 12.","DOI":"10.3390\/ijgi12020039"},{"key":"ref_22","unstructured":"Skowronnek, A. (2024, November 13). Beyond Choropleth Maps: A Review of Techniques to Visualize Quantitative Areal Geodata. Available online: https:\/\/alsino.io\/static\/papers\/BeyondChoropleths_AlsinoSkowronnek.pdf."},{"key":"ref_23","first-page":"453","article-title":"The LOD Representation and TreeMap Visualization of Attribute Information in Thematic Mapping","volume":"42","author":"Ai","year":"2013","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_24","unstructured":"Buchin, K., Eppstein, D., L\u00f6ffler, M., N\u00f6llenburg, M., and Silveira, R.I. Adjacency-Preserving Spatial Treemaps. Proceedings of the Algorithms and Data Structures."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"330","DOI":"10.4113\/jom.2010.1090","article-title":"Rectangular Hierarchical Cartograms for Socio-Economic Data","volume":"6","author":"Slingsby","year":"2010","journal-title":"J. Maps"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Scheibel, W., Limberger, D., and D\u00f6llner, J. (2020, January 8\u201310). Survey of treemap layout algorithms. Proceedings of the 13th International Symposium on Visual Information Communication and Interaction, Eindhoven, The Netherlands.","DOI":"10.1145\/3430036.3430041"},{"key":"ref_27","unstructured":"Xu, J., and Shen, H.-W. (2023). VMap: An Interactive Rectangular Space-filling Visualization for Map-like Vertex-centric Graph Exploration. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0304-3975(95)00257-X","article-title":"Regular edge labeling of 4-connected plane graphs and its applications in graph drawing problems","volume":"172","author":"Kant","year":"1997","journal-title":"Theor. Comput. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.comgeo.2006.06.002","article-title":"On rectangular cartograms","volume":"37","author":"Speckmann","year":"2007","journal-title":"Comput. Geom."},{"key":"ref_30","unstructured":"van Kreveld, M., and Speckmann, B. (2005, January 9\u201316). Rectangular cartogram computation with sea regions. Proceedings of the 22nd International Cartographic Conference, A Coru\u00f1a, Spain. Available online: https:\/\/research-portal.uu.nl\/en\/publications\/rectangular-cartogram-computation-with-sea-regions."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Riedl, A., Kainz, W., and Elmes, G.A. (2006). A Linear Programming Approach to Rectangular Cartograms. Progress in Spatial Data Handling: 12th International Symposium on Spatial Data Handling, Springer.","DOI":"10.1007\/3-540-35589-8"},{"key":"ref_32","unstructured":"Buchin, K., Speckmann, B., and Verdonschot, S. Evolution Strategies for Optimizing Rectangular Cartograms. Proceedings of the Geographic Information Science."},{"key":"ref_33","unstructured":"Heilmann, R., Keim, D.A., Panse, C., and Sips, M. (2004, January 10\u201312). RecMap: Rectangular Map Approximations. Proceedings of the IEEE Symposium on Information Visualization, Austin, TX, USA."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v086.c01","article-title":"Rectangular statistical cartograms in R: The recmap package","volume":"86","author":"Panse","year":"2018","journal-title":"J. Stat. Softw."},{"key":"ref_35","unstructured":"(2023, May 20). Recmap. Available online: https:\/\/github.com\/cpanse\/recmap.git."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1111\/cgf.12647","article-title":"Quantitative Measures for Cartogram Generation Techniques","volume":"34","author":"Alam","year":"2015","journal-title":"Comput. Graph. Forum"}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/14\/1\/25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:26:57Z","timestamp":1759919217000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/14\/1\/25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,11]]},"references-count":36,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["ijgi14010025"],"URL":"https:\/\/doi.org\/10.3390\/ijgi14010025","relation":{},"ISSN":["2220-9964"],"issn-type":[{"type":"electronic","value":"2220-9964"}],"subject":[],"published":{"date-parts":[[2025,1,11]]}}}