Polyconic projection of the Earth centered on meridian 180 degrees west, showing a bowed gap where east meets west.
I did a single polyconic projection of a Blue Marble image of the globe in an earlier article, comparing it to the sample projection in the proj (v.3) documentation. Although seemingly elongated, I called it a success. But when animated by reprojecting 360 times, varying the central meridian from -180° to +180°, I saw that something weird happens where the outside edges meet — there is sometimes, not always, a gap. I don’ t know if this is just an artifact of the projection that is to be expected, or if there’s a problem somewhere in my method or the software. You can see it in the picture at the right and in the animation below.
Sorry, sorta, for subjecting you to this sound track… it seemed to fit the animation given how the image jumps around, another effect of the projection. (My wife doesn’t appreciate the results, but my son does… he’s a good boy!)
The frames for this animation were cropped identically from larger images produced by gdalwarp. The bopping and hopping of the globe results from the image being projected into slightly different locations depending on the central meridian. I haven’t explored the mathematics of the projection to try to explain this and it’s very, very unlikely that I will. Feel free to give it a shot yourself, though, and leave an explanation here if you wish. You can see the formulae for it on its Wikipedia page.
This projection has an interesting history that is not currently mentioned in the Wikipedia article on it. You can read about it in Snyder’s Flattening the Earth*, and perhaps I’ll augment that Wikipedia article with a summary some day. It was developed by Hassler for use in a US coastal survey in the early 1800s. It is undistorted only along its central meridian, so it’s most appropriate for maps with a predominately north-south orientation — much like the Atlantic and Pacific coasts of the U.S. But it was also used extensively by the USGS from its creation in 1875 until the middle of the last century. What I read does not give me the impression that it was really meant to be used to project the whole globe, or hemisphere, like this.
The sound effect is from “AtonalNoise” on The Freesound Project, file “Classic09.wav“, which is licensed with a Creative Commons Sampling+ 1.0 License.
