Best Projection for a Ring World
Quite simply, I'm wondering what would be the best projection to use for a map of a Ring World. Distortion would be nonexistent as far as I can tell, and it would only need the left and right edges to match. The map would span 12,742 km from north to south and 940,000,000 km from east to west (approximately). Given the large scales couldn't I use a flat projection for any resonably sized area?
On a side note, does anyone know of an easy way to wrap a fractal terrain around a ring instead of a sphere?
Map projections are used to translate from a sphere to a plane. A ringworld (in the sense of a ribbon around a star) is already planar, just very long and thin. As you surmised, there is no need for a flat projection.
I'm not sure what you mean by wrapping a fractal terrain around a ring. Do you mean in a 3D modeling sense?
Projection wise, perhaps a series of maps, broken up into degree lots, so you'd really be making say, 8 maps of 45 degrees, or 24 maps of 15 degrees. Looks like a massive undertaking.
Well, in Fractal Terrains there is the option to create either a 'planar' world or a synthetic world with the fractal function wrapped around the globe and pinched at the poles. How would I go about setting up a fractal function to wrap around the ring but not pinch the top and bottom edges as they are not poles? Or is this not possible in FT?
Originally Posted by waldronate
A very massive undertaking if I go with a full sized Ring World. Large enough that I'd probably want to break it up into 'equirectangular' sized maps. Looking back at my first post I realise that I may be wrong in opting for a ring with a height equal to the Earth's radius (through the poles). Any (reasonable) arbitrary figure should work - 20,000km (half Earth's circumference). So, simple maths tells me I get (940,000,000/2)/20,000=23,500 map sections, each covering 0°0'55.15'' (I think). That tells me I will NEVER actually be mapping out a Ring World, but it doesn't stop me from having fun playing with the idea. Though I might consider mapping important chunks.
Originally Posted by Ryan K
Now I'm wondering if the ring should be flat or concave to result in varying solar input. If I do go with a concave model, then I would probably go with the same curvature as the Earth (north to south). This would obviously result in a distortion on a flat projection, but due to the scales involved it would be so, so tiny as to be hardly worth taking into account (I'm not 100% sure of this or the maths required).
You'll run out of editing resolution in FT long before you'll be able to get anything particularly useful. Assuming that you get lucky and FT will give you a 6000 resolution editing element, then you'd have 157000km per pixel or roughly 4 times the size of the earth per editing unit. Probably not terribly helpful. FT provides the option for a planar synthetic world, but you're still limited by the editing resolution. It would be a good solution for local areas (a few thousand km on a side).
I recommend a locally flat world. At roughly an earth orbit radius around the sun and with the very small width of the ring then the sun will be pretty much parallel from top to bottom across the width of the ring. Varying the sunlight would defeat the purpose of a ringworld: maximizing habitable area (plus, the angle would be constant - without seasons - so plants would be growing at funny angles from the ground as you neared the "poles"). I'm not sure what you're using for gravity, though, so a concave ring right yield some truly amusing gravity effects (possibly including the atmosphere all lifting off the surface).
I realise FT allows the creation of a planar synthetic world, but I was wondering about a synthetic ring world. I understand what you are saying about resolution limitations, but if I went with a smaller ring world, how would I go about joining up the far left and right edges of the map with no seam?
My purpose for varying the sunlight was to try and force some sort of seasonal variation, but as you pointed out the angle would be constant which would defeat the purpose. I suppose it could have a 'wobble'. Any ideas for forcing seasonal variation?
As far as gravity goes I figure there are two methods I could use. The first would be rotation, however depending upon the rotational speeds required for 1 gravity, I can imagine some fierce winds rushing around the ring. The second option would be some kind of super science/magic artificial gravity system.
Step back for a second. Consider this question:
How big is your ringworld?
If it's got the surface area of more than a dozen earths, here is my advice: Forget mapping it. You surely could automate it and produce a lot of random stuff but that is not compelling, and you will not map that much territory, ever. I have done some prototyping on "small" ringworlds - Banks orbitals - with a surface area of about 1100 earths and once you play around with the scale for even a few minutes you will see what I mean.
Just do regional maps. Honestly, a ringworld is only a gimmick anyway.
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For everything else, just do flat maps and be done with it.
If your ring world is very small, you need to remember that you have issues with either "gravity" - created by centrifugal force - or day length. You'll also have really odd effects if the curvature is very tight. Flight paths of thrown objects, jumping/flying creatures etc.
I have done the math and if I recall correctly, a 1g ringworld with a 24h day/night cycle had a radius of 1.8 mio kilometers, and a surface area of the above-mentioned 1100 earths.
Last edited by bartmoss; 04-09-2011 at 01:32 AM.
I've pretty much come to the same conclusion regarding mapping the whole thing.
Originally Posted by bartmoss
Oddly enough, according to my maths, the ringworld would seem to be flatter than ours, only concaved!
Originally Posted by bartmoss
Projections are mappings from spaces onto lower dimension spaces: Not necessarily just from a planetary surface in ℝ³ onto ℝ². And the surface of a ringworld is not planar, it's cylindrical.
Originally Posted by waldronate
The obvious projection of that cylindrical surface onto a plane (Technically its a form of "Equidistant Cylindrical") is as much a projection as any geographic one. This projection does produce distortion for vertical features: the tops of two mountains on a ringworld are closer together than the points directly beneath them at the vertical datum. There's also a discontinuity where you 'break' the ring in order to 'unroll' it.
The actual amount of distortion is extremely small, but it is there and 'unrolling' it is a projection even if it's much simpler than any we have to deal with on our approximately spherical world.