Random question about Buckminster Fuller's Dymaxion projection


Has anyone worked on making it possible to toggle data between Cesium’s globe and Buckminster Fuller’s Dymaxion projection? I was looking for modern technical approaches to doing this with digital GIS data, and all I have found is this post on how to create Dymaxion maps in Quantum GIS (QGIS) (https://www.reddit.com/r/gis/comments/6t4f88/incorporating_dymaxionfuller_projection_into_qgis/). It references the projection math/code by Dr. R.W. Gray (http://www.rwgrayprojects.com/rbfnotes/maps/graymap6.html) but it cannot be used in any commercial project without his permission. I have an email from him with permission, but then I need to get someone to write a QGIS driver for me that no one else can ever use?! Seems unlikely.

Anyways, has anyone looked in to what it might take to do this?

Thanks in advance for your response.



Hi Chris,

We're working on the ability to project Cesium's 2D and Columbus Views to alternate projections. This feature is going to be backed by the proj4js catalogue but we're also exposing the ability for users to make "custom projection" files available.

This gets tricky when there are an enormous number of cuts in the projection though, such as with the Dymaxion projection or Waterman butterfly. The underlying terrain engine doesn't support cutting terrain tiles into pieces.

It might still be worth investigating, though. My guess is that for the Dymaxion projection, the lack of cutting would manifest as "webbing" between the icosahedron's triangles instead of empty space, since the portions of terrain tiles bridging the cuts would get stretched across the divides. It wouldn't be aesthetically ideal, but it should still be useable for areas inside the triangles. You could also perhaps mask out the "webbed" areas using Entities matched to the background color.

Just keep in mind that this "webbing" effect will also occur for any other Entities added to Cesium, so you may also want to plan any map annotations like polygons or polylines so that they have already been split across any map cuts.

Here's the pull request if you want to check it out: https://github.com/AnalyticalGraphicsInc/cesium/pull/6986

This sounds like a really cool project, keep us posted on your results!


Another thing: the projection will probably have webbing that stretches underneath the icosahedron's faces, which could manifest as Z-fighting or possibly distorted terrain features appearing in unintended places.

Custom projection support includes altitude modification though, so you could work around this by adding a "margin" on the projection's cutting lines, and then dropping positions within this "margin" a thousand kilometers lower than the icosahedron faces to get the webbing out of the way. Visualized, this would end up looking like the map is sitting on top of a mesa whose cross section is the Dymaxion projection. Let me know if you need a diagram.