Any Math Majors in the House? Help Wanted.

[Umbran]

If the land mass is skewed like that, why wouldnt the magnetic field of the planet also be skewed so you get the "same" readings of the direction of north along the skewed meridian.

Honestly? Because to first approximation, the positions of the land masses don't determine the magnetic field.

In any event, we had concepts of north and south long before we used compasses - they were based on the planet's rotation, not the magnetic field. The sun rises in the east and sets in the west. If east is to your right, and west to your left, then north is ahead of you and south behind you. This does depend on the magnetic field.

 

[coce]

removed as i'm not quite as experienced in fields i'm talking about

 

[Flatus Maximus]

So your archipelago is shaped like a loxodrome?

This would mean that on a local scale you could draw them as straight lines at each point of your map. You get problems only if you extend the lines to cover the whole globe.

If the archipelago is in fact shaped like a loxodrome, and if it twists around the globe only once, then ender_wiggin can simplify his life greatly by representing the archipelago as a diagonal line from corner to opposite corner on the map, rather than as a horizontal line.

If it twists around the globe n times, then there will be n diagonal line segments that end on one side of the map and start back up on the other side at the same latitude.

 

[ender_wiggin]

So your archipelago is shaped like a loxodrome?

This would mean that on a local scale you could draw them as straight lines at each point of your map. You get problems only if you extend the lines to cover the whole globe.

Omg thank you so much. This helps tremendously. Although there's still quite a bit of work to do, this is definitely where I want to be starting. Now the much harder part is to determine the latitude/longitude at ANY point on the 2D map, not just the axis (which is the loxodrome).

Of course if anyone else has insight into the mathematics of this project, I could certainly use more help.

 

[ender_wiggin]

If the archipelago is in fact shaped like a loxodrome, and if it twists around the globe only once, then ender_wiggin can simplify his life greatly by representing the archipelago as a diagonal line from corner to opposite corner on the map, rather than as a horizontal line.

If it twists around the globe n times, then there will be n diagonal line segments that end on one side of the map and start back up on the other side at the same latitude.

Although this is true, it's not how I want the map to look. In a map such as the one you're speaking of, all of the distance dilation occurs at the poles. On earth, this is acceptable because not very many people live near there and most of the action is much closer to the equator. In my homebrew, I want the spacial dilation to be away from the axis of the archipelego, instead of at the poles. Thanks for your insight though, it was helpful.

Also, in response to some other posts, the magnetic orientation of the planet is similar to earth, because of the magnetic mass is still under the ocean (presumably). Modern navigators of the archipelego use two sets of directions: N-S-E-W oriented to the cosmic bodies and to magnets, but more frequently Rostral-Caudal-Dorsal-Ventral (analogy of a giant sea beast on its side), to refer to the orientation of the archipelego itself. The two sets of directions have different relations to each other depending on where on the archipelego you are.

 

[Flatus Maximus]

To be clear: You want a rectangular map (not just on a rectangular piece of paper), but you don't want the rectangular grid?

Edit 1: Oh, I think I get it now. You want something like a Mercator, but instead of projecting onto a right cylinder whose tangent curve to the planet is a great circle, you want to project onto a "twisted" cylinder that follows the axis of the archipelago?

Edit 2: If Edit 1 is what you want, then you are no better off projecting onto the "twisted" cylinder since it is not a developable surface.

 

[ender_wiggin]

Correct. And I want to draw the latitude / longitude lines on that map, and perhaps more broadly find a mathematical relationship between any point on my map and the corresponding long/lat.

Also, the map doesn't cover every point of surface area on the planet, like a mercator projection does (since most the ocean is too rough to be sailed). I suspect it will be something like 5000 miles x 30,000 miles (calculations pending).

 

[tuxgeo]

< . . . >
Also, in response to some other posts, the magnetic orientation of the planet is similar to earth, because of the magnetic mass is still under the ocean (presumably). Modern navigators of the archipelego use two sets of directions: N-S-E-W oriented to the cosmic bodies and to magnets, but more frequently Rostral-Caudal-Dorsal-Ventral (analogy of a giant sea beast on its side), to refer to the orientation of the archipelego itself. The two sets of directions have different relations to each other depending on where on the archipelego you are.

So, is the "North Pole" Rostral or Caudal--since you say that the archipelago extends from one pole to the other? (Is the sea-beast's head north or south? Does it make a difference?)
Which way does it helix -- right-handed or left-handed? (Are Dorsal and Ventral NE and SW, or SE and NW?) (Again, does it make a difference?)
[NOT that the answers to these questions will help in your mathematics search; I was merely curious!]

 

[ender_wiggin]

Thanks, and happy to answer.

The "sea-beast" is on its left side with its head as the north pole. So on the map, rostral is to the right, dorsal is up, ventral is down, and caudal is left. At the midline of the archipelego, north is always the same direction, but north changes orientation as one deviates from the midline. I've forgotten how to distinguish left from right handed spirals, but in my mind's eye the archipelego curves to the left as it descends from the north pole.

If it helps here is a regional map. It has the RCDV system emblazoned on it. It is also, of course, lacking proper latitude/longitude lines but for a regional map they don't really matter.

HERE

 

[S'mon]

Longitude is a fairly arbitrary concept which would probably not exist in the world you've created, IMO. Latitude is easy, it's distance from the equator.