Choropleth map

Abstract: It is now technologically feasible to produce virtually continuous shades of grey by using automatic map drawing equipment. It is therefore no longer necessary for the cartographer to \"quantize\" data by combining values into class intervals. As a simple illustration an automatic line plotter can be programmed to draw lines virtually any distance apart (Fig. 1). Thus, one can obtain any desired density of inked area to white area. For example, if the geographical data, symbolized by z, are normalized to lie in the range from zero to one, then an appropriate spacing of orthogonal lines of width w is given by s = (w/z) • [1 + (1 — z)].

Abstract: Trumbo’s (1981) ideas on bivariate choropleth design have been underexplored and underutilized. He noted that effective map design (including color selection) is directly informed by the intended goal or use of the map (i.e., what questions might the map answer), and he identified three common spatial relationships that can be displayed by a bivariate choropleth: inverse relationships, a range of one variable within another, and direct relationships. Each is best suited to answering different map readers’ questions. Trumbo also suggested sample color palettes to focus the map reader’s attention on pertinent data. In consultation with Trumbo, we extended his ideas, first by creating focal models that illustrate his three spatial relationships. We then constructed sample maps to examine each of the focal models, and finally compared each model by mapping the same two data sets (of obesity and inactivity). We investigated the visual differences in each of the resulting maps, and asked spatial questions regarding the relationships between obesity and inactivity. Our work validates Trumbo’s ideas on bivariate choropleth map design, and we hope our focal models guide cartographers towards making color choices by linking their map purpose to the appropriate focal model.

Abstract: Statistical data associated with geographic regions is nowadays globally available in large amounts and hence automated methods to visually display these data are in high demand. There are several well-established thematic map types for quantitative data on the ratio-scale associated with regions: choropleth maps, cartograms, and proportional symbol maps. However, all these maps suffer from limitations, especially if large data values are associated with small regions. To overcome these limitations, we propose a novel type of quantitative thematic map, the necklace map. In a necklace map, the regions of the underlying two-dimensional map are projected onto intervals on a one-dimensional curve (the necklace) that surrounds the map regions. Symbols are scaled such that their area corresponds to the data of their region and placed without overlap inside the corresponding interval on the necklace. Necklace maps appear clear and uncluttered and allow for comparatively large symbol sizes. They visualize data sets well which are not proportional to region sizes. The linear ordering of the symbols along the necklace facilitates an easy comparison of symbol sizes. One map can contain several nested or disjoint necklaces to visualize clustered data. The advantages of necklace maps come at a price: the association between a symbol and its region is weaker than with other types of maps. Interactivity can help to strengthen this association if necessary. We present an automated approach to generate necklace maps which allows the user to interactively control the final symbol placement. We validate our approach with experiments using various data sets and maps.