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I'm trying to create a geodesic dome with the stars of the northern night sky inscribed on the outside. The highest point of the dome would be the celestial north pole. How do I create a map that projects onto the "net" of the geodesic dome, such that when I assemble the dome, the stars are in the correct positions? I have an equirectangular map that I have rotated 90 degrees north so it is centered on the pole.

My existing map is a high-resolution jpeg file in an equirectangular projection. I have some experience creating and manipulating panoramic images, but much less experience converting between map projections! I would like to use a computer program to convert this projection into a printable template if possible.

Glorfindel
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Rúnatál Davino
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  • This is a really interesting and cross-disciplinary question! But you need to explain more exactly what it is you want to do in detail. Is your equirectangular map in a computer file stored as an image, or as a table of coordinates? Will you be projecting with a written computer program (e.g. C++, Python, etc.), or image processing of some kind, or with a real projector? – uhoh Mar 29 '19 at 12:25
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    thank you for your response! I will edit my question to be more clear. – Rúnatál Davino Mar 29 '19 at 12:26
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    I see, great. Now you don't have a spherical printer for spherical paper, so I think you will have to print out each face of the geodetic dome separately. Do you have the coordinates of the vertices of the mesh? Or at least the name of the polyhedron that represents the shape? – uhoh Mar 29 '19 at 12:31
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    It would most likely be a two-frequency geodesic dome based on an icosahedron! – Rúnatál Davino Mar 29 '19 at 12:35
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    I'm voting to close this question as off-topic because it is a question about geometric projection and computer algorithms. – Carl Witthoft Mar 29 '19 at 14:55
  • @CarlWitthoft dang, is there a better place for it, you think? I couldn't really decide where it belonged. I also tried Mathematics. – Rúnatál Davino Mar 29 '19 at 14:57
  • @RúnatálDavino You might try rewording to show you're looking for the algorithm to convert equirectangular to spherical (because your geodesic will be close enough to a sphere that you probably won't care) and posting either to StackOverflow or possibly GeographicInfoSystems.SE . Otherwise, it may be time for a deep Googleification :-( – Carl Witthoft Mar 29 '19 at 15:05
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    This question is on topic. Projecting the celestial sphere on to non-optimal approximations of a hemisphere is planetariums 101. There might be other sites where it is also on topic (thus my earlier comment about it being a cross-disciplinary question). After reading answer(s) here you can always ask a follow-up question on another site, say Mathematics SE if necessary. – uhoh Mar 29 '19 at 23:01

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The mathematically ideal scheme would be a separate gnomonic projection (see Wikipedia or IMO) for each tile of the dome. Many planetarium programs implement this projection as an option. Fortunately, each tile boundary is a straight line on both adjoining maps. Unfortunately, continuity across tile boundaries requires some care in choosing each tile's scale and center of projection.

Mike G
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