Eggs

Now here is a fantastic projection of the world onto an egg. I have no idea how Peter Bellerby did this, but it demonstrates without a shadow of a doubt his technical and artistic talent.

An egg
An egg

egg2

shading onto water
shading onto water
It is interesting to note the use of shading. For the egg, the shading runs inwards, covering land, rather than outwards covering water. Personally I prefer the latter, but I can’t explain why.

Longitude
Longitude
If I am not mistaken, I think FRGS stands for Fellow, Royal Geographic Society. That is pretty impressive, and it also reminds me of a movie “Longitude” which I just watched latest week for the 3rd time. Here, we get a taste of British accents, British ships, British museums, and all other things British. Of course, most of my Deutsche Bank work buddies are in London office at Finsbury Circus, so it quite easy to pick up the British character. Cheers.

I am a member of the Washington Map Society and the International Coronelli Society, which is nice but likely not as interesting as the Royal Geographic Society. Hopefully, if I can convince my family to embark on an expedition/vacation to London, we can stop by the Royal Geographic Society to check things out.

The Royal Geographic Society
The Royal Geographic Society
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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…

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Maps from 1590 through 1776

The map in progress
A year ago at this time, I wrote about a map I was making for Northumberland county, Virginia. The map has been sitting there, idle, ever since while I’ve been off working. If I didn’t have to work, I sure would like to devote more time to this incredibly interesting subject of cartography and map making.

Anyway, I have recently returned to the map. The problem in completing this map has been, of course, the creative part.

It dawned on me last week that the illustration for the bottom of the map, which, if faithful to my father’s idea before he died in 2005, would have been to place a series of historic homes with a description of each. However, he intended to have a series of the same map which progressed over the years from 1600 through the present time. I, on the other hand, am going to make just one version. So the problem becomes one of representing 400 years of history in one map. I finally decided that a good solution might be to place a series of maps across the bottom, advancing through time, and with some significance to the choice of each map.

Ah, pretty good idea. So here is the bottom of the map:

Four very important maps

These are very important maps, as they served as the prototype for many copies until superceded by the next prototype. The first map is by John White in 1590. The second is by John Smith in 1612, The third is by Augustine Herrman in 1673, and the forth is by Josha Fry and Peter Jefferson in 1753. There have been hundreds of maps published for the Chesapeake Bay region, but it is these four maps which were the foundation for all other maps. As for the main large map, I have not decided on a time, but am leaning towards the early 1900′s. I’d like to capture the time when the local Menhaden fleets where emerging, and sailing ships could still be seen on the water.

If you zoom in to these maps, you will see very many interesting details. Here is an example from the Fry and Jefferson map of 1753:

Details

One last interesting technical point I discovered. I scanned the maps in at 300DPI, which is very acceptable for resolution. The funny thing about Adobe Illustrator is that, when I brought them in for trimming, and then saved them, they got saved at 72 DPI even though I specified “maximum” resolution in my “Save For Web…” dialog box. When I brought the images back in, they were fuzzy, of course, at 72 DPI.

I could not find anything that would let me increase this save DPI setting.

No good at all. It took a while, but the solution turned out to be this. When the original 300DPI image is brought in to Illustrator, immediately scale it by 500% before working on it. Then, when you do your cropping and so on, and then save it at the hardcoded 72DPI value, it goes out to the file as a very large image at 72DPI. When you bring it back it later, to include it in any artwork, if you then scale it back down by 20%, it goes back to 300DPI and returns to its original sharp resolution.

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Size of a gore for a 30-inch globe

Printing the gore, actual size = 47.123890 inches

I printed out a gore last night. Just the vector outline for the continents, so it is very basic in order to get an idea of actual size. And so, just what is the actual size of a gore?

The circumference of a 30-inch globe is 94.24777960769379 inches.

The length of the gore is c/2, which is 47.123890 inches.

The width of a gore spanning 15 degrees longitude is c/(360/15) = 3.926991. The width of a gore spanning 30 degrees longitude is c/(360/30) = 7.853982.

Now, the real question is, have I got enough significant digits? If we take a 15-degree gore whose width has been calculated as 3.926991, and multiply by (360/15), the answer is 94.2477840.

The original circumference was 94.24777960769379, so if we place the 15-degree gores side-by-side at the equator, it looks like we will have an accumulated difference of 94.24777960769379-94.2477840 = -0.00000439230621 inches. Since this is a negative number, we will have a very small overlap.

Hmmm, I wonder if that’s too much of an overlap? I’ll have to get my micrometer and see it looks like in real-life. Standby for further details.

Just outlines, no gradients or artwork yet.
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