Map Projections

Map Projection Research

5707.4 - Minimizing error for spatial binning in a projected world

Wednesday, July 5
5:10 PM - 5:30 PM
Location: Maryland B

When working with datasets containing a large number of point features, the density of marks representing those features can lead to clutter and overlapping symbols. To minimize clutter and make spatial patterns more apparent, we can aggregate point symbols into polygonal bins and symbolize the bins according to count or density. The polygonal bins in use are typically either standard political geographies (e.g., Census enumeration units) or regular polygons (e.g., squares or hexagons). While aggregation into political geographies is common for choropleth mapping, these polygons tend to be irregular in shape and size and, therefore, will show different levels of detail across the map. Regular polygons provide a method for aggregation of the data at a consistent level of detail, since all the polygons are the same size and shape. The consistency restores the reader’s attention to the visual encodings, such as hue and lightness to represent count or density, by eliminating distracting size and shape variation in the symbols.

Unfortunately, regular spatial bins can confuse the reader because the bins’ consistent size and shape on the plane cannot reflect consistent size and shape on the sphere. That inconsistency is due to the impossibility of preserving both area and angle on a map. Bins of consistent shape and size across the map must distort one, or both, of these properties. Even a map reader educated in principles of map projections is unlikely to recognize this distortion or to be able to accommodate for the distortion in their assessment of the spatial pattern. The user probably expects that all bins are guaranteed to be equal and directly comparable for assessing either count or density of points, but the inevitable distortion from projection means that the expectations of the us-er’s mental model cannot be met.

Recognizing that any map suffers from this problem of distortion, what can we do to minimize errors in interpreting binned spatial data? In this presentation we introduce the idea of a ‘safe zone’. This safe zone is the area for which the error from binning stays within some specified tolerance. A safe zone can be calculated for any projection, and in this presentation we demonstrate the calculation and application for spatial binning on the Web Mercator projection, the most common projection when using Web mapping tile services (e.g., Google Maps, Mapbox, etc.). The safe zone calculation we demonstrate for Web Mercator is based on establishment of a reference scale for the dataset and assessing the inflation or deflation of scale away from this reference. The upper and lower bounds of the safe zone can be calculated by identifying the maximum latitude that does not exceed the permissible inflation or deflation of scale.

By restricting binning to a safe zone we can minimize perceptual errors in interpreting spatially binned data.

Sarah E. Battersby

Senior Research Scientist
Tableau Research

Sarah Battersby is a Senior Research Scientist at Tableau Software. She is a past president of the Cartography and Geographic Information Society (CaGIS) and is a member of the ICA Commission on Map Projections. Sarah's primary area of focus is cognitive cartography. Her work emphasizes how we can help people visualize and use spatial information more effectively. Her research has covered a variety of areas, including perception in dynamic map displays, geospatial technologies and spatial thinking abilities, and the impact of map projection on spatial cognition.


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Daniel Strebe

Senior Software Engineer
Tableau Software

Daniel ('daan') Strebe is a Senior Software Engineer on the Maps Front-End Team at Tableau Software. daan is a past-Chair of the ICA Commission on Map Projections.


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Michael P. Finn

Research Cartographer
US Geological Survey, Center of Excellence for Geographical Information Science

Michael P. Finn is a Research Cartographer in the USGS Center of Excellence for Geospatial Information Science. He holds a BS in Geography with a Minor in Cartography and Map Technology from Southwest Missouri State University (now Missouri State University) and an MS in Civil Engineering from Virginia Polytechnic Institute & State University. Mike has worked as a Computer and IT Specialist, and a Research Cartographer with the US Geological Survey for the past 17 years. He also has 10 years of experience with the US Air Force and 7 years with the Defense Mapping Agency.

Mike serves or has served on the Boards of Directors of the Cartography and Geographic Information Society (CaGIS), the American Society for Photogrammetry and Remote Sensing (ASPRS), and the Cyberinfrastructure Specialty Group of the Association of American Geographers (AAG). He has also served as the Director of the GIS Division for ASPRS. Mike is currently serving as President of CaGIS after serving as President-Elect in 2015 and Vice President in 2014. In addition, Mike is a member of the Editorial Board for the journal Cartography and Geographic Information Science.

For international scientific service, Mike is currently serving as Vice-Chair of the International Cartographic Association (ICA) Commission on Open Source Geospatial Technologies for the 2015 – 2019 term. In addition, he is and has been an active member of the ICA Commission on Map Projections. Mike is currently serving as a Co-Chair of the International Society for Photogrammetry & Remote Sensing’s (ISPRS) Technical Commission IV (TC – Geodatabases and Location Based Services), Working Group 4 (Geospatial Data Infrastructure) for the XXIIIrd ISPRS Congress (2012 – 2016) and was previously Co-Chair of the TC IV (Geodatabases and Digital Mapping), WG 1 (Geospatial Data Infrastructure) for the XXIInd ISPRS Congress (2008 – 2012).


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Bojan Šavrič

Software Development Engineer
Environmental Systems Research Institute

Bojan Šavrič is a Software Development Engineer for Projection Engine team at Esri, Inc. He holds a Ph.D. in geography and Diploma degree in geodetic engineering. His main research interests are map projections, mathematical techniques in cartography, and the development of tools for cartographers. Bojan is also a member of the International Cartographic Association Commission on Map Projections.


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5707.4 - Minimizing error for spatial binning in a projected world

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