Any Math Majors in the House? Help Wanted.

[ender_wiggin]

I want to draw latitude and longitude lines on a map I'm making for my homebrew, but it's a pretty unique map. I suspect I will need the help of a real mathematician.

The sole landmass in my setting is an archipelego that begins at the north pole and runs to the southpole. It does so however, not using the shortest path but one that winds around the globe such that it completes exactly one rotation by the time it reaches the south pole. I want a rectangular map to represent this archipelego such that the left side of the rectangle is one end of the land, the right side is the other end, and the archipelego itself is rendered as a straight line instead of the funny curve that it actually is.

Now, the hard part about this is figuring out where the longitude and latitude lines go. I have an idea in my head but I want to be precise.

I was an engineer in undergrad, so I have the background required to figure this out, but it's been a long time since I've done any of that. I need someone who knows what they're doing to point me in the right direction. It took me about 4 hours just to figure out the length of the archipelego in terms of the planet's radius, so you can see how out of shape I am.

As an aside, I think the solution lies in calculating an equation for x and y of cartesian coordinates as a function of psi & theta of the spherical coordinates of the globe. Then I can use a graphing program to hold either of the angles constant and draw the results. That's pretty much as far as I can surmise.

Advice appreciated.

 

[ArcaneSpringboard]

Just as a practical matter...

Does it really _matter_ if it spirals like that?

 

[WheresMyD20]

Well, I didn't major in Math, I only minored in it. Anyway, I wouldn't bother trying to figure it out mathematically. I'd grab a globe and figure out how the island chain wraps around it. Then, I'd grab a 2-dimensional world map off of the web and erase everything but the latitude and longitude lines. I'd then place the islands on the 2d map using the globe as a reference and the latitude and longitude lines as guides.

 

[jonesy]

Carve it on an apple, use a marker to place the lines, and then carefully carve out the continent part and lay it on the table?

 

[ender_wiggin]

Just as a practical matter...

Does it really _matter_ if it spirals like that?

Practical? No. But we don't play D&D or world build because it's practical. We do it because at the end of the day we have something awesome.

Well, I didn't major in Math, I only minored in it. Anyway, I wouldn't bother trying to figure it out mathematically. I'd grab a globe and figure out how the island chain wraps around it. Then, I'd grab a 2-dimensional world map off of the web and erase everything but the latitude and longitude lines. I'd then place the islands on the 2d map using the globe as a reference and the latitude and longitude lines as guides.

That would work if this map was oriented like a mundane map. But it's not. The map will show a completely linear chain of islands when in reality the chain is curved (mapmakers in my setting did it this way because when they first sailed the archipelego, they didn't know the earth was round, and it required less paper to draw the archipelego as a straight line). I know exactly how the island chain is supposed to curve, I just need help rendering it precisely.

 

[FireLance]

That would work if this map was oriented like a mundane map. But it's not. The map will show a completely linear chain of islands when in reality the chain is curved (mapmakers in my setting did it this way because when they first sailed the archipelego, they didn't know the earth was round, and it required less paper to draw the archipelego as a straight line). I know exactly how the island chain is supposed to curve, I just need help rendering it precisely.

Then just chop off the triangles of water to either side and rotate the map anticlockwise until the land chain is mostly horizontal. It won't be precise, but the latitude and longitude lines would be diagonal, like cross hatching.

 

[Mark CMG]

Have you explored The Cartographers' Guild?

 

[ender_wiggin]

Then just chop off the triangles of water to either side and rotate the map anticlockwise until the land chain is mostly horizontal. It won't be precise, but the latitude and longitude lines would be diagonal, like cross hatching.

Therein lies the issue. I don't need a map imminently (if I did I would just not draw the lines), so I'm not going to compromise. Btw, the lines won't be diagonal; they'll be curves. The ones at the two ends of the map will be circles (due to the poles being on the map), and the equator will have an inflection point.

Have you explored The Cartographers' Guild?

Good point; I have in fact, and its where all my mapping skills come from. I will post there as well.

 

[Jan van Leyden]

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.

 

[coce]

Well, my first thought is that in such a world, you would not have latitude and longitude.

Maybe their "0th meridian" goes along the center of archipelago. 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.

So north would not be "up" but spiraling along your archipelago, and your maps would have a different and unique feel.