Throughout March and April 2009, international air travelers departing from Mexico were unknowingly transporting a novel influenza A (H1N1) virus¹ to cities around the world. We analyzed the flight itineraries for all passengers departing from commercial airports in Mexico between March and April 2008, using data from the International Air Transport Association (IATA). The purpose of this analysis was to show how travelers — and consequently to predict how H1N1 — would disseminate worldwide during the initial wavefront of this epidemic. We analyzed IATA data from March and April 2008 for the following reasons: the data accounted for more than 95% of all passenger trips worldwide via commercial airlines, they included information on the flight origins and destinations of actual passengers, data on passenger itineraries for the period from March through April 2009 were unavailable at the time of this analysis, the global pattern of passenger departures from Mexico between March and April varies minimally from year to year, and the epidemic in Mexico was largely unrecognized during the period from March through April 2009, with passenger departures presumably following their usual seasonal pattern.

Background. Every year millions of pilgrims from around the world gather under extremely crowded conditions in Mecca, Saudi Arabia to perform the Hajj.

A new method of cartographic line simplification is presented. Regular hexagonal tessellations are used to sample lines for simplification, where hexagon width, reflecting sampling fidelity, is varied in proportion to target scale and drawing resolution. Tesserae constitute loci at which new sets of vertices are defined by vertex clustering quantization, and these vertices are used to compose simplified lines retaining only visually resolvable detail at target scale. Hexagon scaling is informed by the Nyquist–Shannon sampling theorem. The hexagonal quantization algorithm is also compared to an implementation of the Li–Openshaw raster-vector algorithm, which undertakes a similar process using square raster cells. Lines produced by either algorithm using like tessera widths are compared for fidelity to the original line in two ways: Hausdorff distances to the original lines are statistically analyzed, and simplified lines are presented against input lines for visual inspection. Results show that hexagonal quantization offers advantages over square tessellations for vertex clustering line simplification in that simplified lines are significantly less displaced from input lines. Visual inspection suggests lines produced by hexagonal quantization retain informative geographical shapes for greater differences in scale than do those produced by quantization in square cells. This study yields a scale-specific cartographic line simplification algorithm, following Li and Openshaw's natural principle, which is readily applicable to cartographic linework. Open-source Java code implementing the hexagonal quantization algorithm is available online.

Epidemics and pandemics are geographical in nature and constitute spatial, temporal, and thematic phenomena across large ranges of scales: local infections with a global spread; short-term decisions by governments and institutions with long-term effects; and diverse effects of the disease on many aspects of our lives. Pandemics pose particular challenges to their visual representation by cartographic means. This article briefly summarizes some of these challenges and outlines ways to approach these. We discuss how to use the information usually available for telling the story of an epidemic, illustrated by the example of the 2019–2020 COVID-19 pandemic. The maps attached to this article demonstrate the discussed cartographic means.

Cartographic generalization research has focused almost exclusively in recent years on topographic mapping, and has thereby gained an incorrect reputation for having to do only with reference or positional data. The generalization research community needs to broaden its scope to include thematic cartography and geovisualization. Generalization is not new to these areas of cartography, and has in fact always been involved in thematic geographic visualization, despite rarely being acknowledged. We illustrate this involvement with several examples of famous, public-audience thematic maps, noting the generalization procedures involved in drawing each, both across their basemap and thematic layers. We also consider, for each map example we note, which generalization operators were crucial to the formation of the map’s thematic message. The many incremental gains made by the cartographic generalization research community while treating reference data can be brought to bear on thematic cartography in the same way they were used implicitly on the well-known thematic maps we highlight here as examples.

An automated method of variable digital elevation model (DEM) smoothing is presented. Using variably sized kernels to perform filtering, the method is driven by the entropy of local z-values in the DEM, i.e. the amount of information necessary to convey the elevation variety in the neighborhood of each pixel. This paper presents the method in service of low-pass filtering in order to smooth the raster, though other neighborhood-based filters could be implemented as well. When used in smoothing, the method successfully retains detail in areas of higher relief variation and suppresses it in areas of lower variation, thereby retaining more salient features like ridges, peaks, or incised valleys, while diminishing flatter ones. Varying the neighborhood size with which entropy calculations are made allows for filtering through continuous map scale, enabling multi-scale representation. The method also includes a simple correction for smoothed pixels such that their z-value range reflects that of the input DEM, thereby ensuring that subsequent products such as generated contour lines remain within correct ranges. Several illustrations are given of the method's results.