Projecting from WGS84 to WGS84 Polyconic

After being away from this for a while, I had to re-experiment with MAPublisher projections to get a correct projection for a globe gore. It took a while to remember everything, so I thought I’d make some notes this time.

We start by loading one of the Natural Earth shape files into Adobe Illustrator. I picked “ne_10m_graticules_5_line” so I could see that everything was working as expected. Here is the loaded shp file, with me highlighting the 0-degrees longitude and 0-degrees latitude lines. One thing I noticed with version 3.X of Natural Earth, versus version 2.0, is that the canvas size comes in at 25 inches high and 50 inches wide instead of 5.51 x 11.01 inches. Although, since I re-experimented with a new version of Illustrator, MAPublisher, and Natural Earth, it could be the software rather than the data that might explain the size difference:

ne_10m_graticules_5_line
ne_10m_graticules_5_line

I then had to execute the projection. To do this, I brought up the MAP Views view and double-clicked on the map layer. This is the layer with the little globe icon next to it, not the layer with the Capital L icon. It took a while to figure this one out. After double clicking, the Map Editor dialog popped up. From here, I checked “Perform Coordinate System Transformation:” and then clicked the now-unstippled hyperlink called [No Coordinate System Specified].

The destination coordinate system is called WGS84 Polyconic. This is where things get tricky. You can’t just select this projection and expect things to work. You will end up with a small projection which doesn’t shows a vertical meridian right down the center of the projection. Plus, it looks like the left and right hemispheres are not symmetrical. To fix all this, you must modify the definition of the projection. To do this, I selected and copied it (via the dialog options) to a new copy called “Mark WGS84 Polyconic”. This copy, unlike the original, is modifiable. I set the central-meridian from 78 to 0, and set both the false_easting and false_northing to 25,000,000.

That central meridan modification is the part that fixes everything. Having a central meridian set to 0 now results in a projection at the middle of the map area, which also now produces symettric hemipheres and a perfectly verical line at 0 degrees longitude. The false_easting and false_northing would normally be 0, but I wanted to scale the projection so that the meridian at 0 degrees was 47.12390 inches high. This is the height of a gore needed for a 30-inch globe. When scaling, the projection will expand beyond the artboard, including in the negative direction. I don’t know if false_easting and false_northing values are actually required, but google searches say that you use these values to keep the projection calculation from producing negative numbers. So, those values seem to be harmless offsets, that’s all. I made them 25,000,000 by examining the results of the projection (you can mouse over the graticules to see their x and y coordinates) over the course of several projection tries.

One last thing was how to get the meridian at 0 degrees to be exactly 47.12390 inches. This took some trial and error through several projection tries, but after modifying the scale from 31556692.913260 to 16712440.0, I got as close as Illustrator’s precision would allow. The final length was 47.12389 inches, which is only 0.00001 away from perfection.

dialog sequence
dialog sequence
projection details
projection details

After the project, here was the result:

projection results
projection results

I then resized the artboard to include everything, producing the following result:

final result
final result

Mechanics are working, but is the projection accurate? A valuable conversation is now taking place with my Canadian colleague who is also working through the mechanics of gore construction. Stay tuned…

This entry was posted in Cartography. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *