I understand next to nothing when I look at a WKT string, but I've copy-pasted and used a few of them for work. However, I came to think of the doughnut shaped world in which my friends and I play Dungeons and Dragons and was wondering if I would be able to build a mapping software that projects that world.

Preferably I'd like to project the world in a Mercator like way, so it's okay for things further north and south to look bigger, as long as the proportions are maintained.

The map would go +/-180° longitude and +/-180° latitude instead of the normal +/-90° latitude. I'd also like the 0° latitude to go along the outside equator and the +/-180° latitude to go along the inside equator.

The circumference of the outer equator is 20 000 km and the circumference of the inner equator is 6 666 km. The circumference along the latitude is also 6 666 km.

The surface areas on the inside of the doughnut are relatively unimportant as travel is extremely restricted by massive mountain chains and thus unexplored. The map would probably mostly say "here be dragons" or something in that area.

My question is threefold (feel free to only answer the parts which you feel reasonably certain about):

  • Is it possible to write a WKT for such a projection?
  • Can Proj4, or whichever library handles projections in GDAL and Sharpmap, handle such a WKT?
  • Idon'tunderstandWKT,couldsomeonewriteitformeprettyplease? >.<
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    Spatial reference WKT is not a magical construction, it's just a text representation to utilize an existing rule-base. You cannot create new rules just by adding to the text. If you take the tour, you'll see, in the section "Get answers to practical, detailed questions", it says "Focus on questions about an actual problem you have faced." I would submit that a fantasy construction does not meet this criteria. – Vince Feb 25 '17 at 12:48
  • So where should I ask this question regarding GIS if not a place focusing on asking and answering questions regarding GIS? If it's not possible to use a WKT to represent the projection of a doughnut shaped world then that would be a valid answer to the question. – Kapten-N Feb 26 '17 at 12:13
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    I voted to close this as too broad becase there were so many incorrect assumptions about GIS and projections, that the reason it's impossible would take too long to explain. The fact that you asked three bulleted questions, in violation of group policy, might have influenced others. If you want to spend years creating the new math theory needed to implement and publish a tortional projection, you can petition to have the question reopened when you have the solution. In the meantime, the answers are, "No," "No," and "No." – Vince Feb 26 '17 at 13:13
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    I don't know of an existing map projection that shows a world as a doughnut. The closest is the Raisz Armadillo or the orthoapsidal. – mkennedy Feb 28 '17 at 23:04
  • Thanks for the tip, but I'm not looking to project a spherical world as a doughnut. I want to take a doughnut shaped world and project it in a way that's visually similar to Mercator. Though, I've been told that this isn't the place to ask about projections of made up worlds... – Kapten-N Mar 2 '17 at 10:53

If you change your world coordinates to match Earth's lat-long (ie halve the actual doughnut "latitude" to get latitude from -90 -> +90) then you can use any projection that works with lat-long.

Note that Mercator projections will put your inner mountains at the top and the bottom, and a player crossing the Dunshire Pass across the range from the top will appear at the bottom.

The properties of projections on the sphere (such as preserving distance, direction, or area) won't be valid when projecting a doughnut.

You might also find https://worldbuilding.stackexchange.com/ useful.

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  • Changing from +/-180° to +/-90° doesn't help if using a spherical projection doesn't give the intended doughnut result. I don't think asking in worldbuilding would help since they likely don't know much about map projections. – Kapten-N Feb 26 '17 at 12:17
  • What does "the intended doughnut result" mean? How do you want to unfold your doughnut into a flat map? That's what projections do. What my suggestion does is to map the doughnut to a flat surface by splitting it and unfolding it, just as a mercator map splits down the 180 line. – Spacedman Feb 26 '17 at 15:07

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