Mapping Issues: Curvature, Latitude and Global Projection

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Re: Hollow World: Iciria, 40 miles per hex

Post by Zendrolion » Tue Jun 17, 2008 5:06 pm

Thorf wrote:However, the official maps clearly mark 90 degrees as the beginning of the lip, with the inside of the lip effectively latitude-less. It's not clear where latitude starts to become irregular on the official maps at all, although we can clearly see that the 60-90 part of the world is drawn smaller than 0-30 and 30-40 (which are each about the same size vertically).
IIRC my friends LoZompatore and Zaryck on the Italian MMB determined it between 63,8 and 65 degrees.
P.S.: I don't know if already know, but in another topic LoZompatore demonstrated that the "darklands" between outer and hollow world aren't that "dark" nor so "cold" (most of the area receives light from at least ONE sun, and a small portion of it even light from both suns - I mean, the real sun and HW sun). ;)
Interesting, I'd love to read that. Do you have a link for me?
Here it is!
This excellent work was done months ago by LoZompatore and it's in Italian... You're lucky enough for LoZompatore likes to do his maps in English! ;) Anyway, if something isn't comprehensible at all for you, I can work a translation into English as soon as I have time.
OldDawg wrote:The latitude markers are often in disagreement between HW and PWA (I believe Zendrolion has a good comparison of the maps), so their ultimate fate is open to the community.
Here's another great comparison map made by LoZompatore (yes, he's absolutely the BEST! 8-) ):

http://it.geocities.com/lutetius2/Mappe ... tudini.jpg

LEGEND for sources:
Underlying map: HW/RC Outer World map (section)
Light green: VotPA series
Yellow: PWAI (the northernmost yellow latitude should be 45 degrees)
Red: PWAII
Blue: latitudes extrapolated from tables in TM1 and PWAIII (where the latitudes of three known locations are mentioned)

P.S. @ Zompa: I'm posting all these works of your on your behalf; I hope you've nothing against this. Otherwise, let me know! ;)
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causes of their victories and defeats, so as to avoid the defeats and imitate the victories" N. Machiavelli, The Prince, XIV, 5

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Re: Hollow World: Iciria, 40 miles per hex

Post by Havard » Tue Jun 17, 2008 5:46 pm

Zompatore is a God! :o 8-)

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Re: Hollow World: Iciria, 40 miles per hex

Post by Cthulhudrew » Wed Jun 18, 2008 3:12 am

Holy crap. I used to think I was something of a cartographer, back in the day when I made my Mystara maps, but you guys blow me away with all of this stuff!

The Pentagon/Icosahedron fix for the distortion is brilliant (I'd never even considered that things would distort at the poles), and LoZompatore demonstrates once more that he has a real handle on all things dealing with Mystaran planetary physiology! And of course, Thorf's maps.

Really, all the work you all are doing here is amazing, even when I can't follow it. Awesome!
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Re: Hollow World: Iciria, 40 miles per hex

Post by metal » Wed Jun 18, 2008 3:26 am

My big question (being a pen, pencil, and paper guy) is........."Where can I find this neat hex paper with the pentagons every so often?"
I've got to start redrawing! ;) :)
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Re: Hollow World: Iciria, 40 miles per hex

Post by Thorf » Wed Jun 18, 2008 3:33 am

Something just occurred to me about our icosahedron fix: doesn't this mean that we're going to want to have our hexes with a point to the north, as opposed to with a flat face to the north? Looking at LoZompatore's excellent icosahedron globe, it really seems like there's going to be no way around this, and no way to keep the flat faces to the north.

This is a problem, because almost every map for Mystara is made like this. Do you all remember Shajapur, and my conversion of its map? For those of you who have forgotten, here is what converting maps from one hex orientation to the other entails:

http://mystara.thorf.co.uk/other/the-madness.png

It's not pretty, and the grids don't fit regularly on top of each other. This is not going to be nearly as easy as I thought. :cry:

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Re: Hollow World: Iciria, 40 miles per hex

Post by Ashtagon » Wed Jun 18, 2008 6:25 am

Icosahedron planet mapping in the standard that was used in the Traveller RPG, and later for GURPS:Space. You can find some utility programs for them here: http://www.freelancetraveller.com/infoc ... progs.html.
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Re: Hollow World: Iciria, 40 miles per hex

Post by Cthulhudrew » Wed Jun 18, 2008 7:46 am

I'm not seeing what you're saying about needing to put the point north, Thorf. Looking at the icosahedrons above, if the pentagons are the poles, the flats join up with them? Is it an issue with unfolding it into a 2-dimensional perspective that I'm just not seeing?

[EDIT- All right, I think I see what you're saying, but I'd have to have a more visual representation to be certain...]
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Re: Hollow World: Iciria, 40 miles per hex

Post by LoZompatore » Wed Jun 18, 2008 1:20 pm

P.S. @ Zompa: I'm posting all these works of your on your behalf; I hope you've nothing against this. Otherwise, let me know!
No problem at all: as soon as they are on the web, I consider them as public: feel free to post and use them as you like ;)
...in another topic LoZompatore demonstrated that the "darklands" between outer and hollow world aren't that "dark" nor so "cold" (most of the area receives light from at least ONE sun, and a small portion of it even light from both suns - I mean, the real sun and HW sun)...
The link to the italian topic Zendrolion posted above was an attempt to give a realistic description of what would happen in the polar openings as they are lit by the external sun. Moreover, I tought it was cool to have a very strange habitat in the middle of the stormy/icy area of the opening: the climate would be "interesting" indeed: on some regions in the middle of the opening you'll have 6 months of tropical/equatorial climate (when the emisphere is in summer) and 6 months of polar climate (when the emisphere is in winter).
The ecosystem would be strange indeed (what about this area hosting some altered plants and animals created by the Immortals just after the GRoF, when the climate patterns were so upset that the Immortals had to create special living beings - able to survive to sudden and impredictable cold and hot periods - in order to provide enough food for the starving populations of some areas.

If you like I can translate the whole topic and send it in the Hollow World section. It is not official, but is interesting anyway.

(EDIT: the topic above is done: you'll find it in the Hollow World section of the message board ;) )

Now, about the Pentagon/Hexeagon fix:
The Pentagon/Icosahedron fix for the distortion is brilliant (I'd never even considered that things would distort at the poles)
As you may guess this solution is not mine, but it comes from some mathematic property concerning the geode and the tessellation of a sphere. Moreover, it is also geometrically possible to hexmap the torus (the donut) without distortions so, in principle, we might also have a proper hexagonal mapping for the polar opening area (which is half a torus in shape). This is not an easy task, though.
Something just occurred to me about our icosahedron fix: doesn't this mean that we're going to want to have our hexes with a point to the north, as opposed to with a flat face to the north? Looking at LoZompatore's excellent icosahedron globe, it really seems like there's going to be no way around this, and no way to keep the flat faces to the north.
You are absolutely right. There is no chance to rotate the hexes in such a way you can have the flat side of the hexes in the WE direction instead of having them NS.
The only possible solution I found is described below:
Let's call the hexes of the icosahedron gridding I posted above a "vertical" hex (it has the flat side in the NS direction). The standard Mystara hexes are instead the "horizontal" hexes(the flat side is in the WE direction).

- We may use just the icosahedron frame of "vertical" hexes as a reference for the global map, in order to take in account for latitude distortions and the like. The scale of the "vertical" hexes is not important as they just give the border of the map we want to fill.
- We may fill each "vertical" hex with the standard "horizontal" hexagonal grid of the Mystara's maps we know.

To give you a visual idea of what I'm saying:

Image
http://it.geocities.com/lutetius00/Hexa ... _small.jpg

The bigger hexes give just the frame of the map (the single hex borders dont'even need to be represented in the map, except for the ones composing the side of the icosahedron face), while the smaller hexes represents the standard Mystara map.
Of course you are assuming that the bigger hexes are flat surfaces, and you are introducing an error in area and distance evaluations especially at the center of the bigger hex, but this error is quite small compared to the one we have without taking into acocunt the latitude distortion (that is pretty much avoided with an icosahedral map).
My big question (being a pen, pencil, and paper guy) is........."Where can I find this neat hex paper with the pentagons every so often?"
If you are referring to the blank map I posted above, I made it with some patience. Maybe I have also the hexed verion of it (with hexes inside the blank area, instead of having also the borders), if you are interested I can place it on the web. Unlukily I do not have other bigger/smaller resolution maps.
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Icosahedron planet mapping in the standard that was used in the Traveller RPG, and later for GURPS:Space. You can find some utility programs for them here
Cool! Thank you! I've never heard of them before! 8-)

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Re: Hollow World: Iciria, 40 miles per hex

Post by nerik » Fri Jun 20, 2008 3:37 pm

I've done some tests with icosahedral nets, and it is possible to fit hexagons to the icosahedron's faces with the hexagon oriented such that it has faces facing north and south. You end up with pentagons at the vertices of the icosahedron (as before), but the corners of the pentagons are on the edges of the icosahedron.
To make the hexes fit, the height of each face of the icosahedron needs to be some multiple of 1.5 times the height of each hex.

I hope this is of some use.

Yours,

Charles

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Re: Hollow World: Iciria, 40 miles per hex

Post by JoeNotCharles » Sat Jun 21, 2008 6:49 am

nerik wrote:I've done some tests with icosahedral nets, and it is possible to fit hexagons to the icosahedron's faces with the hexagon oriented such that it has faces facing north and south. You end up with pentagons at the vertices of the icosahedron (as before), but the corners of the pentagons are on the edges of the icosahedron.
To make the hexes fit, the height of each face of the icosahedron needs to be some multiple of 1.5 times the height of each hex.
I'm having trouble visualizing this. Can you post a picture?

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Re: Hollow World: Iciria, 40 miles per hex

Post by nerik » Mon Jun 23, 2008 11:56 am

JoeNotCharles wrote:I'm having trouble visualizing this. Can you post a picture?
Ok, lets see if this works:

One face of an icosahedron mapped with a hex-grid: Image

A net of a whole icosahedron mapped with a hex-grid: Image

In both cases the hex-grids are aligned with top & bottom edges running east-west.

As I mentioned, the limit is doing it this way is that the height of each face of the icosahedron should be some multiple of 1.5 times the height of each hexagon, but as each face of the icosahedron will be thousands of miles high, and our hexes are usually 40 miles or smaller, I don't think this is too much of a problem.

Anyway, I hope this helps.

Charles

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Re: Hollow World: Iciria, 40 miles per hex

Post by Thorf » Mon Jun 23, 2008 2:17 pm

Excellent, Charles! Your diagram makes it really easy to understand. :D

So it looks like we can indeed use this solution without much trouble after all. I'd still like to hear some details of how to adapt the other maps to this sort of projection, though.

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Re: Hollow World: Iciria, 40 miles per hex

Post by LoZompatore » Mon Jun 23, 2008 2:47 pm

Dear Charles, your solution is really brilliant!!! :o 8-)

It is very simple to understand and easy to implement on any existing map: I like a lot what you suggested! :D
I'm still a little worried about the (supposed) 60° rotation you have to apply to a standard map when it meets the border of an icosahedron face, but your grid arrangement solves a lot of problems indeed!

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Thorf » Tue Jul 01, 2008 2:54 am

I split the discussion off to this new thread.

To continue the discussions, can anyone tell me how to go about adapting the maps to the new hexgrid projection? Specifically, how can we warp the northern and southern extremes? Is there a good way to do this, and what programs do you need to do it?

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Gawain_VIII » Tue Jul 01, 2008 2:57 am

Thorf wrote:To continue the discussions, can anyone tell me how to go about adapting the maps to the new hexgrid projection? Specifically, how can we warp the northern and southern extremes? Is there a good way to do this, and what programs do you need to do it?
Not being a cartographer of any talent, this may be totally off the mark, but could you wrap a mercator projection map over a globe, then interpose the icosahedron grid over the top of it to see where everything starts bunching and where?

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by LoZompatore » Thu Jul 03, 2008 9:47 am

To continue the discussions, can anyone tell me how to go about adapting the maps to the new hexgrid projection? Specifically, how can we warp the northern and southern extremes? Is there a good way to do this, and what programs do you need to do it?
I'm currently working on a possible solution. I think I'm close to it, but it needs some more days of work: I'm going to post it here as soon as I have some results.

I'm trying to flesh out a very rough 72mi/hex map of Mystara (actually showing just coastlines taken from the official hexed maps) using Neric (Charles) icosahedron and Mike suggestions about lands subdivision.
In my opinion it is not necessary to warp anything: it should be sufficient to rotate some sections of the larger scale maps (which is almost the same than rotating the compass on the maps we already have) when they cross an icosahedron cutting and we can leave the original hexgridding untouched.
Anyway, I'm still into checking it: more results soon ;)

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Hugin » Thu Jul 03, 2008 2:39 pm

LoZompatore wrote:Anyway, I'm still into checking it: more results soon ;)
I'm really excited to see your results, LoZompatore! It sounds as though we won't have to redraw anything, just shift it around a bit which means less work. I sure am hopeful this works out well.

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Thorf » Mon Jul 07, 2008 3:22 am

I'm looking forward to seeing your results too, LoZompatore! :D

In the meantime I found this interesting page on Wikipedia: Dymaxion map. It has a very nice animation of the globe being made into an icosahedron, and it also shows that you don't necessarily have to arrange the triangles in the pattern we have been talking about.

Another thing I have been thinking about is that we should probably include longitude lines on our maps, to show what directions north and south lie in. Because in the top row of triangles, north is the point at the top of the triangle - not just "up". Longitude lines would make this a lot clearer.

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by LoZompatore » Mon Jul 07, 2008 4:55 pm

Thanks a lot for the link, Thorf! It would be very useful to me. I was thinking about a different disposition of the icosahedron triangles in order to cover the entire surface without having to distort the maps we already have. I made some attempts so far, but some areas always needed major modifications due to the great horizontal extension of the official mapped area (from the Immortal's Arm to Minaea we have almost half of the planet mapped along a thin stripe).

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by LoZompatore » Thu Aug 21, 2008 9:07 am

Just a little update with very good news: I managed to fit the whole official maps in the unfolded icosahedron, without any cutting or distortion. :D
You can cover the whole "official" area with a single, uncut map, from Frosthaven to Davania and from the Immortal's Arm to Minaea. Any hex of this map has the same scale and the same area.

I made a map showing the results, but it still needs some refining: I hope to post it in the following days. ;)

Basically I followed Thorf's suggestion about the Dimaxion map: It was not possible to avoid distortions to the official area by using an icosahedron map that is unfolded starting from the Poles, so I had to make a different folding (something similar to this: http://en.wikipedia.org/wiki/Dymaxion_map) where the Poles are somewhere in the middle of a triangle.

As you can see from the map linked above, parallels and meridians are not very easy to trace (but the task is not impossible at all). Moreover, by now I mapped only the area covered by the official supplements: the lands outside it would be warped and rotated in some odd way and I still have to figure out the changes.
Anyway, from now on, feel confident that the canonical maps as a whole do not need any distortions due to latitude or cutting issues. Of course we are assuming that the hexed maps are the most correct way to represent Mystara: if you assume that planetary maps are the right reference maps instead, then you likely have to introduce scale changes and distortions to the hexed maps.

The regions outside the official maps should be treated very carefully, as they are for sure quite different from what we are accustomed to think. My priority was just to leave the official maps as they are, not to provide an easy way to hexmap the whole Mystara... :(

Anyway, I'm sure you'll better understand what I mean when I'll post the map. ;)

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Thorf » Thu Aug 21, 2008 12:08 pm

I'm very eager to see what you have come up with, but I must admit I have some doubts about placing the poles in the middle of one of the panels. I think it might just make things even more confusing.

Here's some experimentation I've been doing with this whole concept.

First, I started with the Master Set map. The reason for using this map is that it seems to be a "flat" projection, with straight lines of longitude - unlike the Hollow World set maps which have bent longitude lines.

Image

The first job is to define latitude and longitude. For now, I have done this by simply adding a grid based on the borders of the original map, but the resulting map probably won't conform to our needs very well; ideally we want to keep as many of the official references to latitude and longitude intact. Also the extreme northern and southern 30 degrees actually also include the polar openings and the lips of those openings.

Image

Next, I prepared the net of an icosahedron. Eventually we will add hexes, but that can be left until the final stages. For now it remains just a collection of triangles. Note that the layout doesn't have to be like this, although it is nice to have the equator straight along the middle.

Image

Put the two together, and we find that the map is too short.

Image

So I widened the map and added a 10 degree grid to make things clearer. Notice how widening this map makes it strongly resemble the Hollow World set world map; I guess they realised when making that map that the world didn't have enough east-west space - although they still didn't show the great ocean as big as it turns out here.

Image

Put the icosahedral net on top, and we can see it fits rather well. The net doesn't have to be placed in this position; it doesn't correspond exactly with the longitude lines anyway, so there's no problem with moving it east or west to encompass whichever regions we want it to.

Image

The spaces between the triangles now need to be horizontally squashed to fit inside the net. The shaded area in the next image shows the eventual shape of the world map; all the areas outside of that need to be squeezed in.

Image

Lastly, here's an example of what happens during such squeezing. Note how the latitude lines remain constant while the longitude is compressed as it approaches the pole - just as it should be with a sphere.

Image

So far the biggest problem seems to be the position of north on this upper face (and south on the lower faces); north is no longer simply "up" on the map, but rather the point at the top of the triangle. This means that from the bottom left corner, north is up and to the right, while from the bottom right corner it's up and to the left. The longitude lines seem quite necessary for showing this, especially on maps that show large areas of the planet.

Finally, here is the final version with a hex grid added. The size is arbitrary, but given that Alphatia is about 1850 miles from north to south (77 hexes at a quick count), and it's about 5 hexes here, each hex is probably about 370 miles.

Image

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by LoZompatore » Thu Aug 21, 2008 2:03 pm

I agree with you, Thorf: that's the other approach I mentioned in my post above:
Of course we are assuming that the hexed maps are the most correct way to represent Mystara: if you assume that planetary maps are the right reference maps instead, then you likely have to introduce scale changes and distortions to the hexed maps.
I like a lot your very neat work about distortion in icosahedral map. :D While I was drawing my map I noticed that most (if not all) of the hexed map are made by just superposing the hexagonal grid to the Master Set's map. Most of the coastal lines are in perfect agreement with the original Mentzer's map (and I could also spare a lot of work avoiding to redraw the whole coastlines from the official maps, but now it is too late... :oops: )

So, following your results, I guess that we could leave unchanged the hexed maps we have and add to them a longitude reference conversion table.

As an example, from your last picture the hex under the pole covers the same longitude range of the 16 hexes in the bottom line. An hexed map covering the same triangular area, but drawn on a square sheet of paper, would show 16 hexes in the top line and 16 hexes in the bottom line. This means that if the scale is 370 mi/hex at the bottom line, the top line scale would be 1/16 of this - some 23 mi/hex.
The intermediate lines of hexes would have a longitude scale map varying from 370 mi/hex and 23 mi/hex.

I suppose this would be the easiest way to leave unchanged the official maps while keeping to the original latitude and longitude information.

Just to summarize, it seems to me that we are going to have two different options in order to leave the official hexed maps as they are:

- Assume the official maps are undistorted by longitude and so twisting accordingly the parallels, the meridians and other parts of Mystara world's map;

- Assume the parallels and the meridians are correct, draw a simple icosahedral map and then change the longitude scale of the hexes as the latitude increases;

I'll show you my results as soon as possible so we can compare the two methods. ;)

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Hugin » Thu Aug 21, 2008 2:52 pm

Thorf wrote:Put the two together, and we find that the map is too short.
Have you considered extending the map by adding to the Far End Ocean? Or is that not desirable?

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Gawain_VIII » Thu Aug 21, 2008 3:09 pm

Hugin wrote:
Thorf wrote:Put the two together, and we find that the map is too short.
Have you considered extending the map by adding to the Far End Ocean? Or is that not desirable?
If I'm not mistaken, that's exactly how we fixed the Latitude problems when Mystara was superimposed over the Google-Earth globe... IIRC, it was determined that the Width-Height ratio, in order to properly fit on a globe without distorting the latitudes, was 2:1.

It would also be my preference, if at all possible, for two reasons: First, it preserves the shape of the coastlines; second, once again, it would be in agreement with the Earth-sized Mystara suggestion.

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Re: Mapping Issues: Curvature, Latitude and Global Projection

Post by Thorf » Thu Aug 21, 2008 3:29 pm

LoZompatore wrote:I like a lot your very neat work about distortion in icosahedral map. :D While I was drawing my map I noticed that most (if not all) of the hexed map are made by just superposing the hexagonal grid to the Master Set's map. Most of the coastal lines are in perfect agreement with the original Mentzer's map (and I could also spare a lot of work avoiding to redraw the whole coastlines from the official maps, but now it is too late... :oops: )
Yes, I agree mostly about the Master Set map - although of course the actual coastlines on it are no good, due to the total lack of detail. (There are even big mistakes too - look at the northern part of Alphatia: it's all wrong, and some of it seems to be completely missing.) But we can fix that by replacing the outlines in the Master Set map with the detailed ones from the hex maps. This has been my plan for years, regardless of the curvature issues, and I think we have now confirmed that it's a good idea. :)
So, following your results, I guess that we could leave unchanged the hexed maps we have and add to them a longitude reference conversion table.

As an example, from your last picture the hex under the pole covers the same longitude range of the 16 hexes in the bottom line. An hexed map covering the same triangular area, but drawn on a square sheet of paper, would show 16 hexes in the top line and 16 hexes in the bottom line. This means that if the scale is 370 mi/hex at the bottom line, the top line scale would be 1/16 of this - some 23 mi/hex.
The intermediate lines of hexes would have a longitude scale map varying from 370 mi/hex and 23 mi/hex.

I suppose this would be the easiest way to leave unchanged the official maps while keeping to the original latitude and longitude information.
What an excellent idea! It could be confusing for the more northerly maps, and maps with big hex scales, but for detailed maps of small areas it should be no problem.

What all this means is that there is no hurry to make an icosahedron map, because it would be better to spend some time tweaking the Master Set map (a lot) first. Moreover, it brings us to another important conclusion: expanding the current hex maps using the Master Set map will only introduce as much distortion as the current maps already have. 8-) This seems very simple, but it's hugely liberating, because I have been holding back from expanding out from official maps for years due to this issue.
Just to summarize, it seems to me that we are going to have two different options in order to leave the official hexed maps as they are:

- Assume the official maps are undistorted by longitude and so twisting accordingly the parallels, the meridians and other parts of Mystara world's map;

- Assume the parallels and the meridians are correct, draw a simple icosahedral map and then change the longitude scale of the hexes as the latitude increases;

I'll show you my results as soon as possible so we can compare the two methods. ;)
Actually, I think these two ideas combined are the best solution. By which I mean that we should have both! So we keep the traditional hex maps exactly as they are, but we also prepare a companion set of super-accurate maps to go with them. So for example you have Alphatia (hex) and also Alphatia (fixed curvature), and you can compare them to see the true layout.

Incidentally, I made this map as a crazy experiment:

Image

It shows how Alphatia might change. It's very primitive - all I did was use the small image I prepared before as a visual guide. And I'm not sure that it's right at all, because the Master Set version of Alphatia is really weird, as I mentioned above.

Anyway, of course I do not intend to make maps like this, but it's interesting to see the distortion. For me the most interesting thing is that the shape doesn't really seem to have changed that much; neither has the layout of the outlying islands. Perhaps we're just used to seeing distortions like this from real world maps...
Hugin wrote:
Thorf wrote:Put the two together, and we find that the map is too short.
Have you considered extending the map by adding to the Far End Ocean? Or is that not desirable?
I basically already have... The Master Set map has a LOT more ocean than the Hollow World Set map... I think.

Hmm, I just went and tried overlaying my rough Savage Coast/Great Waste/Serpent Peninsula/Known World/Isle of Dawn/Alatians/Pearl Islands/Ochalea/Alphatia coastline on top of the Master Set map, and it seems LoZompatore was right: they are apparently all derived from the Master Set map. They actually don't fit perfectly - it seems like these regions take up too much space, and Davania will be pushed south further.

But I'm not sure about making Far End Ocean so huge - it would be two fifths of the entire world.

It looks like the Master Set map is definitely going to take a lot of tweaking before we fit it to the icosahedron.

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