Abstract: The popularity and availability of digital tools has boosted the use of thematic maps in infographics and data visualizations Unlike general purpose maps, thematic maps are aimed at communicating the spatial distribution of a particular topic or theme, such as population density, voter preference or income Since thematic maps have been more often studied and tailored for European and North American countries, some of them need adjustment to properly represent Brazilian states, according to their needs The aim of this paper is to present the hexagonal hierarchical cartogram, which represents Brazilian states in a normalized geographical format using single-hue color scales to show magnitude We demonstrate its use by mapping average grades obtained by students of all Brazilian states in a national exam called ENEM (Exame Nacional do Ensino Medio)

Abstract: Cartogram drawing is a technique for showing geography-related statistical information, such as demographic and epidemiological data. The idea is to distort a map by resizing its regions according to a statistical parameter by keeping the map recognizable. This article describes an R package implementing an algorithm called RecMap which approximates every map region by a rectangle where the area corresponds to the given statistical value (maintain zero cartographic error). The package implements the computationally intensive tasks in C++. This paper's contribution is that it demonstrates on real and synthetic maps how package recmap can be used, how it is implemented and how it is used with other statistical packages.

Abstract: A travel-time cartogram is an effective method for representing travel time distances from a given point to the other points on a map and the geographic space is deformed accordingly. Compared with other map representations, users can identify travel-time distances on travel-time cartograms more easily because of the geometric deformations according to travel time. However, there are challenges when generating travel-time cartograms, including inconsistent map scales, topological errors and a lack of spatial deformation visualization. In this paper, we suggest a framework for addressing these challenges. More specifica lly, we propose: (1) three design principles to keep the scale of the transformed map the same with its original map; (2) a number of constraints to adjust topological errors generated by the process of transformation based on Moving Least Squares (MLS); and (3) 2-D and 3-D visualization methods to represent travel-time cartograms and their deformation. We use the travel time of trains from Munich to other selected cities in Bavaria as a case study. The results show that our method is applicable and the visualizations depict the time distance relationship between Munich and other cities from different perspectives.

Abstract: A map is often a useful way to visualize big-data sets that vary by region. For example, voting patterns by region, income levels by region, or tweet frequency by location are just some examples of data that benefit from being placed on a map. However, measuring any regional activity and placing it on a map is usually disappointing. Typically, whenever a bar chart or pie chart is placed on a map, it either covers something else up or visually disappoints in other ways. A heat-map overlaid on top of a map is better, but it tends to show areas of high activity but gives no way of highlighting areas between average levels and below average levels of activity. In this paper we show several examples of cartograms that solve this problem. A cartogram is a map in which a regional variable – such as population, Senate representation, income, patents issued, or tweet activity – is substituted for land area. The geometry or space of the map is distorted to convey the information of the regional variable in a much more realistic and visually persuasive manner.

Abstract: A three-dimensional cartogram is a thematic 3D map on which the volume of each region is linearly proportional to an extensive property enclosed within. This work formulated a 3D cartogram using a linear diffusion process. The 3D cartogram algorithm may be applied to a uniform Cartesian grid such that the distribution of the property of interest, such as the hydrocarbon pore volume in each cell, is equalized throughout the transformed domain. The spatial distortion of the grid cells serves as the qualitative indicator of this property, and the color may be used to visualize the spatial distribution of another property, such as permeability. Such a 3D cartogram on which a second property is mapped is a two-variable 3D cartogram.

Abstract: . The article provides an overview of the features of the Magrit web application: a free online thematic mapping tool, presenting a strong pedagogical dimension and making possible to mobilize all the elements necessary for the realization of a thematic map. In this tool, several simple modes of representation are proposed such as proportional maps or choropleth maps. Other, more complex modes are also available such as smoothed maps and cartograms. Each map can be finalized thanks to layout and customization features (projection, scale, orientation, toponyms, etc.) and exported in vector format. Magrit is therefore a complete, light and versatile tool particularly adapted to cartography teaching at the university.

Abstract: This paper introduces hexograms as a method for mapping areal data. It builds on the idea of balanced cartograms that reduce geographic distortion, combining those with hexagonal binning to create nontessellating tile maps of geographical distributions. The aim is to produce less geographically distorted representations of neighbourhood and other areal data than those resulting from conventional cartograms, whilst also avoiding the problem of invisibility found in traditional choropleth maps. The process behind the method is introduced with examples of its application. The code to reproduce some of the maps is available for R.

Abstract: This study uses an equal population cartogram to plot the intercity railway network in Mainland China.

Abstract: A planar cartogram is a two-dimensional map, on which the area of each closed region is in direct proportion to a chosen extensive property. To date, various algorithms have been proposed to construct planar cartograms. This work extends the two-dimensional, diffusion-based, topologically invariant cartogram algorithm proposed by Gastner and Newman onto spheres. Unlike its planar counterpart, the spherical formulation does not require boundary conditions and is invariant to the rotation of input data on the sphere. An implementation of this spherical cartogram transformation is designed to generate readable topology-preserving cartograms on spheres. Lastly, the method is illustrated with applications to global data such as worldwide human population, gross domestic product (purchasing power parity), carbon dioxide emissions and regional data such as the Electoral College of the United States presidential election of 2016.

Abstract: We describe bivariate cartograms , a technique specifically designed to allow for the simultaneous comparison of two geo-statistical variables. Traditional cartograms are designed to show only a single statistical variable, but in practice, it is often useful to show two variables (e.g., the total sales for two competing companies) simultaneously. We illustrate bivariate cartograms using Dorling-style cartograms, yet the technique is simple and generalizable to other cartogram types, such as contiguous cartograms, rectangular cartograms, and non-contiguous cartograms. An interactive feature makes it possible to switch between bivariate cartograms, and the traditional (monovariate) cartograms. Bivariate cartograms make it easy to find more geographic patterns and outliers in a pre-attentive way than previous approaches, as shown in Fig. 2 . They are most effective for showing two variables from the same domain (e.g., population in two different years, sales for two different companies), although they can also be used for variables from different domains (e.g., population and income). We also describe a small-scale evaluation of the proposed techniques that indicates bivariate cartograms are especially effective for finding geo-statistical patterns, trends and outliers.

Abstract: Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts, cartograms can represent correctly which regions share common borders, resulting in insightful visualizations that can be the basis for further spatial statistical analysis. Computer programs can assist data scientists in preparing cartograms, but developing an algorithm that can quickly transform every coordinate on the map (including points that are not exactly on a border) while generating recognizable images has remained a challenge. Methods that translate the cartographic deformations into physics-inspired equations of motion have become popular, but solving these equations with sufficient accuracy can still take several minutes on current hardware. Here we introduce a flow-based algorithm whose equations of motion are numerically easier to solve compared with previous methods. The equations allow straightforward parallelization so that the calculation takes only a few seconds even for complex and detailed input. Despite the speedup, the proposed algorithm still keeps the advantages of previous techniques: With comparable quantitative measures of shape distortion, it accurately scales all areas, correctly fits the regions together, and generates a map projection for every point. We demonstrate the use of our algorithm with applications to the 2016 US election results, the gross domestic products of Indian states and Chinese provinces, and the spatial distribution of deaths in the London borough of Kensington and Chelsea between 2011 and 2014.

Abstract: Cartograms are maps in which areas of geographic regions, such as countries and states, appear in proportion to some variable of interest, such as population or income. Cartograms are popular visualizations for geo-referenced data that have been used for over a century to illustrate patterns and trends in the world around us. Despite the popularity of cartograms, and the large number of cartogram types, there are few studies evaluating the effectiveness of cartograms in conveying information. Based on a recent task taxonomy for cartograms, we evaluate four major types of cartograms: contiguous, non-contiguous, rectangular, and Dorling cartograms. We first evaluate the effectiveness of these cartogram types by quantitative performance analysis (time and error). Second, we collect qualitative data with an attitude study and by analyzing subjective preferences. Third, we compare the quantitative and qualitative results with the results of a metrics-based cartogram evaluation. Fourth, we analyze the results of our study in the context of cartography, geography, visual perception, and demography. Finally, we consider implications for design and possible improvements.