Posts Tagged ‘cartograms’

Announcing IndieMapper (Axis Maps)

Tuesday, March 17th, 2009

[Editor's note: The same folks at Axis Maps who brought us Finder! and Maker! from GeoCommons (blog post) announce IndieMapper, a new tool for cartographers by cartographers to make awesome maps. When released (summer 2009?), this online, Flash-based solution will fill a nitch between full bore GIS systems and manual compilation in Illustrator. I hope they'll add an "embed this map" option for people who want to publish their maps straight to the web for their 2.0 release. Screenshots below.]

Republished from the Axis Maps IndieMapper blog.
Add yourself to their email list to get the 411 on the first release.

Note: David Heyman of Axis Maps was at SXSW Interactive 2009 this weekend in the NeoCartography: Mapping Design and Usability Evolved session.

Welcome to indiemapper.com! We’re very excited that you’ve taken the time to learn about our project. Put your email address in the subscription box below so we can tell you about indiemapper developments and most importantly… the launch!

A little about indiemapper:

  1. It’s big. We’re not satisfied with the current tools available for making maps. They’re too expensive and their cartographic functionality doesn’t always give us everything we need. We’re building indiemapper to replace those tools. It takes in shapefiles and spits out a vector file to Illustrator, just like GIS. It supports multiple projections, just like GIS. Labeling, map layout, data classification, just like GIS. If you need it to make a map, it’s in there.
  2. It’s focused. The problem with the existing tools for making maps is that they aren’t designed exclusively for making maps. You’re only using about 10% of the software to make your map (but paying for all 100%). We built indiemapper for only one purpose: making maps.
  3. It’s visual. If I want to reclassify my data, why do I need to go into the map properties dialog box, select the symbology tab, click on the data classification button that opens up a new window, move the tabs around in that new window, click OK in the new window, click OK in the first window I opened and then wait for my map to redraw to see if the classification looks good? With indiemapper, every update is live and every control is easily accessible. No more hunting. No more waiting.
  4. It’s online. Updates are available as soon as they’re released. No more waiting for service packs or paying for upgrades. And Mac users: Get ready… we are 100% platform independent. Use it on a Mac, use it on Windows, even try out Linux (you might like it!)

I could go on and on, and I will, right here on this blog. Check back here for a discussion on functionality, coding, design, cartography, all things indiemapper. We’ll be releasing some free tools along the way that we’ll want to tell you about too. Most importantly, we want your feedback so let us have it!

Top features:
  • Fast, visual editing.
  • Nothing more than 2 clicks away.
  • Rolling release with constant updates.
  • Choropleth mapping.
  • Dot density mapping.
  • Proportional symbol mapping.
  • Cartograms.
  • Unlimited undos.
  • Colors from ColorBrewer.
  • Type from TypeBrewer.
  • Basemaps from Natural Earth.
  • Map layout for print and screen.
  • Load data from shapefile and KML formats.
  • Export to vector SVG.
  • Export to JPG.
Screenshots:
PROJECTIONS:
  • Visual selection process
  • Re-project vector data on-the-fly
  • Filter by projections that preserve area / shape / direction
  • Learn more about projection best practices
  • Create custom standard lines / centering
DATA LAYERS:
  • Manage multiple thematic data layers
  • Create new layers on-the-fly from attributes of existing datasets
  • Control editability / visibility
  • Instantly access style / label options for each data layer
CHOROPLETH MAPS
  • Create both classed and unclassed choropleth maps
  • Select from built-in automatic classification routines or set your own breaks
  • Visually set manual class breaks using interactive live-updating histogram
  • Automatically select built-in ColorBrewer color ramps
  • Create your own custom color ramps
  • Every change is updated on the map instantly

Noncontiguous Area Cartograms (IndieMaps)

Monday, March 2nd, 2009

[Editor's note: Zach Johnson promotes his Actionscript 3 class for producing non-continuous cartograms and gives background on why these are better (and easier to construct) than Gaster-Newman continuous cartograms.]

Excerpted from IndieMaps blog by Zach Johnson.
View full blog post from Dec. 4, 2008.

Fully contiguous cartograms have stretched and distorted borders but perfectly maintained topologies. Like the Gastner-Newman diffusion-based cartograms we see all over the place. Though all sorts of cartogram designs have been produced, those with perfect topology preservation (fully contiguous cartograms) receive the majority of academic and popular press attention.

< snip >

Judy Olson (Wisconsin Geography alum natch) wrote the only academic article to focus specifically on this cartogram symbology in 1976. She believed noncontiguous cartograms held three potential advantages over contiguous cartograms (I’ve three more below):

  1. “the empty areas, or gaps, between observation units are meaningful representations of discrepancies of values, these discrepancies generally being a major reason for constructing a cartogram”
  2. production of noncontiguous cartograms involves “only the discrete units for which information is available and only the lines which can be accurately relocated on the original map appear on the noncontiguous cartogram”
  3. because of perfect shape preservation, “recognition of the units represented is relatively uncomplicated for the reader”

Despite these inherent advantages (along with ease of production), all the early value-by-area cartograms I’ve seen maintain contiguity. Some took the radical step of abstracting features to geometric primitives, like Levasseur’s early French examples (which may not have been cartograms) and Erwin Raisz’s early American “rectangular statistical cartograms”. But in many ways the noncontiguous design is the more radical cartogram, as it actually breaks the basemap apart — rather than skewing shared borders it abandons them.

my [his] AS3 classes

Olson outlines a technique — the projector method — for manually producing such cartograms. A projector capable of precise numeric reduction/enlargement was required, but not much else, and accurate cartograms could be produced in minutes. A scaling factor was calculated for each enumeration unit, the projector was set to this value, and the projected borders were traced, keeping units centered on their original centers.

My [his] AS3 NoncontiguousCartogram class works similarly. It takes an array of objects containing geometry and attribute properties and creates a noncontiguous cartogram. I include methods for creating the input array from a shapefile/dbf combo, but using KML, WKT, or geoJSON representations wouldn’t be too hard. Methods are included for projecting this lat/long linework (to Lambert’s Conformal Conic projection at least). The NoncontiguousCartogram class draws the input geography, figures the area of each feature, and scales figures according to their density in the chosen thematic variable.

It’s all good/in ActionScript 3, so can be used in Flash or Flex. The zip distribution includes the following:

  • the main NoncontiguousCartogram.as class
  • two example applications and the data needed to run them
  • utility classes, including some that make creating cartograms from shp/dbf input quite easy
  • Edwin Van Rijkom’s SHP and DBF libraries, which are used to load the shapefiles in both of the included examples
  • Keith Peters’ MinimalComps AS3 component library, for the components used in one of the examples
  • Grant Skinner’s gTween class, which is required by the NoncontiguousCartogram class for tween transitions

Browse all the above or download the zip.

<snip>

more advantages

In my thesis research last spring, noncontiguous cartograms performed quite well: subjects rated them highly on aesthetics and could locate and estimate the areas of features with relatively high accuracy. I would add the following to Olson’s list of noncontiguous cartogram advantages.

  1. Olson concentrates on the perfect shape preservation of noncontiguous cartograms. The form (well, those with units centered on the original enumeration unit centroids, as in Olson’s projector method) also perfectly preserves the location of the features on the resultant transformed cartogram. Not only are features easier to recognize, but locations within the transformed units can be accurately located as well (cities or mountain ranges from the original geography can be accurately plotted on the transformed cartogram).
  2. Because units are separate on the transformed cartogram, their figure-ground is increased and areas of features can therefore be more accurately estimated.
  3. Many cartogram designs (including most manual cartograms and the Gastner-Newman-produced cartograms) sacrifice some accuracy for shape recognition. This is a defensible tradeoff, especially as area estimation is notoriously inaccurate and nonlinear. Yet it’s a tradeoff that noncontigous cartograms need not make, as they can always perfectly represent the data with relative areas without sacrificing shape preservation.

Thus, noncontiguous cartograms seem to excel at the cartogram’s two main map-reading tasks: shape recognition and area estimation. This is mediated somewhat by the chief advantage of contiguous cartograms: compactness. Because no space is created between enumeration units, contiguous cartogram enumeration units can be larger than those on noncontiguous cartograms, all other things equal. The increased size on contiguous cartograms may improves their legibility.

Read the full entry over at Indie Maps . . .

Early Cartograms (IndieMaps)

Monday, March 2nd, 2009

[Editor's note: Enjoy these examples of early cartograms from Zach Johnson's thesis research.]

Excerpted from IndieMaps.
Originally published there Dec. 8, 2009.

I’m kind of on a cartogram kick lately. I’m interested in the pioneers of the form, those who first thought to distort borders and explode topologies in order to convey the distribution of some thematic variable. When was the first cartogram produced, where, and by whom? I ran into a lot of material while researching my thesis; this post only begins the discussion.

1868

The honor typically goes to Émile Levasseur for the diagrammatic maps contained in his 1868 and 1875 economic geography textbooks.

early diagrammatic map by Levasseur

H. Gray Funkhouser (1937) wrote of these “colored bar graphs”,

squares proportional to the extent of surfaces, population, budget, commerce, merchant marine of the countries of Europe, the squares being grouped about each other in such a manner as to correspond to their geographical position

Interestingly, Waldo Tobler (2004) points out that the example printed by Funkhouser (above) was sized by land area and thus not a true value-by-area cartogram. I don’t have access to Levasseur’s texts, and it’s odd that the only available scan of Levasseur’s first cartogram shows a diagrammatic map, not a true cartogram.

1897

On the other hand is the image below, whose units are definitely sized to the data, but whose geographic arrangement is questionable. I first saw this page from an 1897 Rand McNally Atlas of the World in a SpatialCollective post; a high res version is available from the David Rumsey Map Collection.

a bubble chart, perhaps a circular cartogram, from an 1897 atlas

Circles on the left are sized proportional to population, those on the right to debt. Though the arrangement seems haphazard, geography is not ignored as the circles are grouped together by continent. I don’t really buy these as cartograms, but they’re certainly a predecessor to the circular cartogram form popularized by Danny Dorling nearly 100 years later.

Continue reading at IndieMaps . . .

E00Parser, an ActionScript 3 Parser for the Arc/Info Export Topological GIS Format (IndieMaps)

Monday, March 2nd, 2009

[Editor's note: Zach Johnson promo's his ActionScript 3 class for reading in .e00 GIS files to Flash. Useful for creating cartograms and other graphic representations reliant on topological relationships. Originally posted there Feb. 21, 2009.]

First off, why mess with such a retro format as Arc/Info Export (.e00)?– any code written for this ASCII file type in the last few years has been on how to go from e00 to pretty much anything (especially to the non-topological data format, the shapefile).

Put simply, topological information makes a lot of things possible for the intrepid ActionScripter.

Read more at IndieMaps . . .
Get the code . . .

Global Forces Converge to Drive up Oil Prices (Wash Post)

Thursday, January 8th, 2009

[Editor's note: January begins newspaper design association page contest season. We came across this graphic looking thru our 2008 work in the Washington Post and was reminded how it fits in with my geography and projections as network topology thesis. Lines on this map of "Major Global Trade Routes" of oil connect each geographic feature with related geographic features. Weights are given to each connection and represented visually. Overall the network is conformal to real geography in a top level abstract sense, but the connections (flow lines) between them shine. Kudos to Renée, now at the Wall Street Journal.]

Reprinted from The Washington Post, July 27, 2008.

In the time it takes most people to read this sentence, the world will have used up (forever) about 9,520 barrels of oil. At 40,000 gallons per second, it’s going fast.

The United States plays a central role in the global energy system as the largest consumer, the largest importer and the third-largest producer of oil in the world. With use of this finite resource rising at breakneck speed, will the world have enough to meet its needs, and will it be able to afford it?

TOP OIL PRODUCERS
Where does the oil come from? Just three countries — Saudi Arabia, Russia and the United States — pump about 31 percent of the world’s oil. More than 9 million barrels per day of crude oil (plus another 1 million barrels per day of liquids derived from natural gas) are being extracted from the reserves underneath Saudi Arabia, the world’s single largest oil producer.

TOP OIL CONSUMERS
Every day, the U.S. consumes more than 20 million barrels — almost one-fourth of all the oil used in the world and more than two times as much as the second-biggest consumer, China. Consumption in most developed countries, including Britain, France, Germany and Italy, hovers around 2 million barrels a day — barely a tenth of that used by the U.S.

Screenshots below and above. Download PDF.

Graphics reported by Brenna Maloney, graphics by Todd Lindeman — The Washington Post. Map by Renée Rigdon – The Washington Post.

Topology and Projections: 21st Century Cartography

Sunday, June 15th, 2008

maps splash walters gallery baltimore

The traveling map exhibit MAPS: FINDING OUR PLACE IN THE WORLD at the Walter’s in Baltimore, Maryland (via the Field Museum, Chicago) wrapped up last weekend. While looking at John Adam’s Road distance map of England and Wales I was put in mind of how map projections try to preserve several of:

  • Area
  • Distance
  • Shape, and
  • Direction/angle

Then the question arose: Might information (thematic) topology now be interchangable with purely geographical topology?

John Adam’s map from 1680 places towns in relative (not absolute) geographic lat-long coordinates in a rough framework that preserves their orientation to one another and in the rough-shape of their original geography. But the primary purpose of this map is to emphasize the relationship between towns and intra-town distances. Below by Royal Geographic Society.

john adams road map 1680

This topological focus (of NODES and EDGES in math-speak) is perfectly represented in Adam’s map. Circles (nodes) are inscribed with town names and straight lines (edges) connecting town circles are annotated with road distance (not straight-line geographic distance).

Modern scientific cartography, with an emphasis on visualization, might finally be loosening the geographic straight jacket to the point where purely lat-long geography doesn’t matter so much but the inter-connection (edges) of said features (nodes) gains emphases and is preserved.

I believe such thematic topology maps are “geographically” accurate and employ projection just like conventional cartography but these “projections” are as of now ad hoc and not properly defined or formalized and are often created manually. Efficient and effective mathematical formulas should be devised and listed along conventional map projections in publications like Snyder’s (USGS) Map Projections: A Working Manual.

The nearest we come to topologic maps are subway maps and cartograms. More on cartograms below.

new york subway map slice

This subway map of New York City is a topological map where the island area of Manhattan is relatively small geographically but is significantly exaggerated to accommodate the “accurate” display of the topological nodes and edges of subway stations and subway lines. (Dorling cartogram example below by Zach Johnson.)

zach johnson cartogram

Cartograms are a good example of topological maps:

  • Area of symbol represents the NODE weight alone.
  • Distance is based on EDGE weight first and and geographic distance second (trying to approximate the “relatedness” between each, eg close countries close, far countries far).
  • Direction is approximated.
  • Shape is approximated.

Zach Johnson has a good post on this topic on his blog (cartograms are the focus of his Masters Thesis).

Below a New York Times map showing the weighted electoral votes of the 48 contiguous states as the topological area of each state.

ny time cartogram example

Let us examine a map of water flow in a stream network (Kelso and Araya):

six rivers streamflow

One usually sees these maps with a conic projection to preserve equal-land-area. But the river segments are drawn exaggerated to their geographic width to represent the EDGE weight between nodes in the true geography space.

The map is dispensing with equal-land-area between nodes (the overall area and shape are preserved) and instead focusing on DISTANCE and DIRECTION between each node. The edges are “preserved” by exaggerating the stream centerlines to preserve the thematic variable. Overall SHAPE is preserved, but local land AREA is not.

Such topological maps are not diagrams because they are still rooted in land-geography; the placement of the nodes is guided by land geography but shift accordingly to best show the interrelationships between nodes. Ignoring the land-geography by listing the nodes and edges in a chart or table is not a map. A topological map takes a complex n-dimensioned space and represents that topology in a 2d dimensioned space.

precip swiss atlas

Some precipitation maps use “gridded” tightly spaced, regularized nodes and edges (above: Swiss Atlas, 2.0). The “weight” of rain and snow fall is indicated by color. Because of the spacing of the nodes and the hyper-localness of the mapped theme, this “topological map” manages to preserve both the topology and the geography.

nat geo 8th world atlas human chapter opener

The above example from the 8th Edition National Geographic Atlas of the World focuses on the quantity difference between nodes and represents that with height spikes (3d). If this were a topologic projection that needed to show the contents of each node (not the inter-relationship between nodes) the spike height would be flattened out into area alone (2.5d), leading to a grossly exaggerated land-area map but correct population-area cartogram such as:

mworlds_zj.png

Above from the Dutch company Mapping Worlds via Zach Johnson.

tom patterson relief example

Tom Patterson (above) uses this 2.5d term to talk about relief shading of land elevation. But I think it can be used to represent any map that is a representation of more than simply 2 variables (lat and long). Really, much of thematic cartography is 2.5d when it tries to represent complex datasets (like precipitation) with color and other visual variables.

So visualization / modern scientific cartography is focused on examining and preserving / projecting topological relationships. Often these are closely related to geographic space, but not always. That is why I am so fascinated by cartograms :)

How do we measure the “error” and “conformal”-ness in a topological map?

  • Area: Does this “view” of the topology preserve the node and edge weights?
  • Distance: Does this “view” preserve the inter-relations between nodes?
  • Direction: Both topological between nodes and geographically.
  • Shape: Purely geographical. This is what sets some cartograms above others.

For topologic shape:

Projecting a n-dimensioned topology onto a 2d surface has one or more points tangent to the 2d surface. An ideal solution shows all nodes and edges shown flattened out but this would likely require using an interrupted projection with dashed linkage lines between like-lobes content (I have seen this somewhere, need example).

For geographic shape and direction:

We are concerned with local shape (direct neighbors in the topology) and global shape. In the England example above for the Dorling cartogram the north-south direction axis tilts left in the topology. A “best” solution preserves this geographic orientation by rotating the topology network until it “conforms” more to the geography.

Finally, we can visualize this with a modified cartography cube from Zach Johnson:

cart cube zach johnson