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Mercator vs. well…not Mercator (Platte Carre)

Platte Carre and Mercator


(ArcWeb Explorer –Platte Carre– and Virtual Earth –Mercator–)

Distortion Options 

The act of flattening out the earth onto a flat surface guarantees that some distortion will take place.  Distortion is actually fundamental to projection -that’s its nature.  So distortion is unavoidable, but there are options when it comes to what kind of distortion your map can have and that depends on the projection that you choose.

In the GIS world, particularly the ESRI-based GIS world, Platte Carre is the default projection –so default, that often folks use and work with Platte Carre without realizing it.  Platte Carre is French for flat and square; the coordinate grid zones are warped into equally sized squares.

All of the big players in the online mapping world, however, are using the Mercator projection -with the exception of ESRI’s ArcWeb Explorer.  In this post, I’ll describe some of the differences between these projections.  Pictures help (bias admitted).

Imaginary Blue Islands

This example uses Tissot Circles to illustrate the different ways that Mercator and Platte Carre distort the earth.  In the globe on the left, pretend that those blue circles are imaginary islands of equal size and shape (round) on the earth.  The Mercator projection very obviously distorts the size of objects; things grow progressively larger the farther away they are from the equator.  Shape, however, is maintained -those imaginary blue islands are still round.  Platte Carre distorts shape. Specifically, the farther from the equator, the more squished things appear.

Why Platte Carre Gets Weird  

If you are setting up a tiled Map Web Service for the 2D environment that is global in extent and uses satellite or aerial imagery, then there is no better choice than good old Mercator.  Look at the difference between the airplanes below.  ESRI and Microsoft are using the same imagery provider, GlobeXplorer, for their coverage of the airport in Anchorage Alaska.  ESRI’s ArcWeb Explorer uses Platte Carre projection, and thus the aerial imagery appears to be flattened.  This squishing effect increases the farther one navigates from the equator.  The Virtual Earth version of the same airplane maintains its true shape.


(the Platte Carre squish effect)

In Mercator, objects at more extreme latitudes look much bigger than their equally-sized counterparts near the equator, though the average person would find more meaningful aerial imagery that has its shape intact, rather than the Platte Carre squish effect.

Mercator’s Size Distortion

Something’s got to give, so while Platte Carre is busy distorting shape (above), Mercator distorts relative size.  To give an idea of the magnitude of this size distortion, check out the airfields below.  They are both set to the same Virtual Earth zoom level of 16, however one is in Anchorage, Alaska and the other is in Honolulu, Hawaii.  Since Mercator inflates the size of objects the nearer they are to the poles, then what do the poles look like?  They don’t!

The Mercator Coverage Gap

At least Platte Carre covers the entire earth.  A Mercator map (and therefore, most of the public map web sites) cannot display the whole world.  What?!!!  Actually, Mercator maps of the world typically trim off the poles (85 – 90 degrees in the north, and -85 – -90 degrees in the south).  That’s right, these areas just don’t get mapped.  Check out this graphic.  The Mercator projection is created by putting a hypothetical light bulb in the center of the earth then projecting it’s image onto a cylinder (Mercator is a Cylindrical projection).

If a global Mercator map were to cover the poles, it would be infinitely tall.  VE, Google, and the rest trim it so that the image is square (around but not exactly 85 degrees).  Still I’ll take some missing polar regions over satellite/aerial imagery with a corrupt aspect ratio any day.

Speaking of Square…

Since a typical Mercator global map is square (because the poles that would extend into infinity have been trimmed), then defining zoom levels is cleaner because that square can be divided over and over and over again, each division a closer zoom level tile set where each tile covers a smaller area and has greater cartographic and imagery detail.  And again, since shape is maintained in the Mercator projection, imagery will look true to life.

The Overlay Issue

But wait, if the GIS world is largely wrapped up in Platte Carre (or sometimes mis-identified as WGS 84 -which is actually a datum), and the Software/Service companies are using Mercator isn’t there going to be an interoperability issue?  Yes.  Pulling in public WMS images (which are almost always Platte Carre) over a Mercator basemap service (like Virtual Earth, Google Maps, Yahoo Maps…) will definitely result in a serious and glaring misalignment.  If you are serious about pulling Public WMSs over a Mercator map, they can be run through the IDV Solutions Tile Server, which has a re-projection engine.

John Nelson / IDV Solutions / john.nelson@idvsolutions.com

 

One response

  1. it's me

    Thanks!

    March 9, 2009 at 12:30 am

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