We all know the usual view of the World:
We’ve got the world unwrapped around the North Pole, which appears at the top of the map. A
long time ago I got to wondering what it would look like if we used some point other than the North
Pole as this unwrap-point.
Back in 1997 I had a lot of time on my hands and was living in a Muslim country, so I did this by
hand using Mecca as the unwrap point. I had a cheap globe that I drew new longitude and latitude
lines on (as if Mecca was the North Pole), then transferred the map to graph paper. This took
forever, but was pretty cool to see the result. I recently decided to resurrect this effort, but
automated this time. I found a free source of coastline data in text format (http://www.ngdc.noaa.
gov/mgg/shorelines/shorelines.html), brought these 61,000 points into Excel, then did a whole
bunch of trig to wrap the map back onto a sphere. Then I’d rotate the sphere so some new point
was at the top and unwrap the map again. (Illustrated below.) This yielded some screwy-looking
Using Mecca, Saudi Arabia:
Using Brisbane, Australia:
Using Boston, USA:
As crazy as they look, it’s important to remember that they’re just as “correct” as the one we’re
used to seeing. The same logic is used to go from the sphere to the flat map. The same
distortion happens, but to different locations.
Below is a summary of how it works, but way cooler is the Java Applet.
The original data is a two-dimensional set of points with longitude as x and latitude as y.
Here's what it looks like plotted:
Some basic trig wraps translates the latitudes and longitudes into three-dimensional points.
This can be thought of as wrapping the flat map around a sphere. The x-axis comes out at
latitude zero, longitude zero (just off Central Africa), the y-axis comes out also on the equator
at 90 degrees longitude, the z-axis comes out the North Pole:
More trig rotates the sphere around the z-axis (the way the Earth actually rotates) until
Boston's longitude is on the x-axis (ignore Australia - you're seeing it on the other side of
Now we rotate around the y-axis so that Boston is on the z-axis, where the North Pole used to be:
Finally, we do the reverse of the first step to unwrap the map back off the sphere onto a flat
surface and we have the odd projection:
I used Carson Software’s Site Manager to draw the points generated through the Excel
trigonometry in AutoCAD as polylines. Then I just did screen captures of the maps.
And yes, I did this just for the hell of it. It took several hours while watching TV. Now that it’s
all in place, changing the latitude and longitude values in the Excel file will generate any other
Here's the original hand-drawn map:
Using Miltenberg, Germany: