Mapping Issues: Curvature, Latitude and Global Projection

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Mapping Issues: Curvature, Latitude and Global Projection

Postby Thorf » Fri Jun 06, 2008 6:18 am

I have not yet updated the Iciria maps, but I'm posting them now so that we can discuss an issue that is holding me back with my Hollow World maps, and indeed with my Outer World maps too. The issue is the curvature of the world, and in this case what difference it should make to adding the rest of the Hollow World to this hex map.

It seems to me that so far the issue of curvature and the inherent problems involved with mapping a globe have been almost entirely ignored by most of Mystara's cartographers - myself included. The official maps gave only a cursory nod to the issue with their pseudo-globe-shaped maps.

So the question is: do we need to worry about it?

If we do, the shapes of Aerical, Suridal, etc. will change substantially; the outlying continents will straighten out, and their dimensions may also change. The same is true of the Outer World, with Davania and Skothar, as well as western Brun.

If we don't, we must take it for granted that there is artificial stretching in the far north and south (and probably east and west) of the maps. It seems like this is the route that has so far been taken.

I am leaning towards the latter route, if for no other reason than that I simply don't know how to proceed any other way. I guess I really want to check and see if anyone knows how we could go about taking the world's curvature into account, or for that matter if anyone else is bothered about this issue at all.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Gecko » Fri Jun 06, 2008 7:10 am

I would suggest that as a starting point try to determine what projection method (if any) was used by TSR back when they were creating the original maps that are now your sources, and work backwards from that.

The only world-wide map I have access to is the two in the RC and they look like either an Eckert or a Robinson projection.

Are there any-other world maps in other sources? If so what type of projection do they use?

Also, didn't I see some examples from someone who overlayed Mystara maps into Google Earth? Don't I remember them discussing this issue back on the MMB?

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Re: Hollow World: Iciria, 40 miles per hex

Postby Thorf » Fri Jun 06, 2008 7:31 am

Gecko wrote:I would suggest that as a starting point try to determine what projection method (if any) was used by TSR back when they were creating the original maps that are now your sources, and work backwards from that.

The only world-wide map I have access to is the two in the RC and they look like either an Eckert or a Robinson projection.


Hmm, the Robinson projection looks very similar, indeed.

But assuming that this is indeed a Robinson projection, how do we work backwards from that - and what do we work backwards towards anyway? For years now I've been trying to work out how hex mapping is related to all of this, but I have yet to come up with a satisfying answer. The truth is, I just don't have enough knowledge about geography to resolve this issue by myself. :oops:

Are there any-other world maps in other sources? If so what type of projection do they use?


For the Hollow World, all we have is that one map. Does it being the inside of a sphere make a difference to any of this? We could probably assume that since TSR used the same projection for both inside and out that it doesn't make a difference - or we can safely ignore what difference there may be.

For the Outer World, there have been a number of maps. I'll start a thread about them. :)

Also, didn't I see some examples from someone who overlayed Mystara maps into Google Earth? Don't I remember them discussing this issue back on the MMB?


I seem to remember hearing about the Google Earth project, but I don't know if I had time to check it out back then. And we have definitely talked about this issue at the old MMB before, but it remained an open issue. I hope that with your help we can get it sorted out this time, if only to the extent that I can confidently continue mapping.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Gecko » Fri Jun 06, 2008 8:10 am

Thorf wrote:But assuming that this is indeed a Robinson projection, how do we work backwards from that - and what do we work backwards towards anyway?


Well that would depend on what projection(s) you want to use in your finished maps. You can use Interprolation (like the table at the wikipedia article you linked to) to convert distances from the Robinson into a true sphere calculatons, then You would use whatever interprolation you want to transform your final project into. Set up a few points like this to get an outline and you can get a feel for how little or how much distortion there is. Personally however, if you truely want that level of detail then you are going to be working on it for a very long time. Best thing would probably be to just 'fudge' here and there, since its not like we are going to be guiding any 747s through fog based off these maps or anything!

For years now I've been trying to work out how hex mapping is related to all of this, but I have yet to come up with a satisfying answer. The truth is, I just don't have enough knowledge about geography to resolve this issue by myself. :oops:


hmm, that's an interesting question. Of course the meta answer would be that since the setting, and hence the maps, were created piecemeal, there is no such relationship. Of course if you wanted to develop it further perhaps there is some sort of scaled up version of a trimetric technique (like the Chamberlin trimetric) only using the 6 points of a hex instead of the 3 of a triangle. You'd have to ask a mathmatician (maybe one specilizing in geometry) about that one though...

I wrote:Are there any-other world maps in other sources? If so what type of projection do they use?


For the Hollow World, all we have is that one map. Does it being the inside of a sphere make a difference to any of this? We could probably assume that since TSR used the same projection for both inside and out that it doesn't make a difference - or we can safely ignore what difference there may be.


I wouldn't think there would be any difference. You almost want to intuitively say that there should be a -1 factored into the interprolation, but I don't think there would be. I'm not positive though, that would be a question for a cartographer (or again, a mathmatician specializing in geometry).

Ultimately, I would suggest simply ignoring this issue as much as possible.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Hugin » Fri Jun 06, 2008 2:59 pm

Thorf wrote:I seem to remember hearing about the Google Earth project, but I don't know if I had time to check it out back then. And we have definitely talked about this issue at the old MMB before, but it remained an open issue. I hope that with your help we can get it sorted out this time, if only to the extent that I can confidently continue mapping.

Hey, Thorf. I'm the one who did the Google Mystara experimentations on the MMB. What I found was that we have too much land mapped in the northern hemisphere (which I 'fixed' by saying it wraps around the polar opening), not enough mapped in the southern hemisphere (added more ocean which also means it's not as close to the pole as it looks), and there is not enough area around the east-west circumference ('fixed' by adding to the Far End Ocean). This all makes Mystara something like 96% the size of earth. Northern and Southern regions are also condensed in their east-west profile while north-south profiles are maintained regardless of latitude.

This may be another facet that should be discussed by the community to see which solutions should be used.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Gecko » Fri Jun 06, 2008 3:57 pm

Hugin wrote:Northern and Southern regions are also condensed in their east-west profile


Your saying that when you went from the flat map onto google-earth, the N. & S. regions ended up appearing more condensed on the sphere, right? That would be normal for a Robinson projection and it's cousins.

while north-south profiles are maintained regardless of latitude.


I would think it would still be there, just less pronounced and much less noticable, especially given how you added significantly to the southern ocean as that would further reduce the effect, but there would still have to be some distortion. But for that small a distortion, I'd say "ignore it." ;)
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Re: Hollow World: Iciria, 40 miles per hex

Postby Hugin » Fri Jun 06, 2008 4:31 pm

Gecko wrote:Your saying that when you went from the flat map onto google-earth, the N. & S. regions ended up appearing more condensed on the sphere, right? That would be normal for a Robinson projection and it's cousins.

Exactly. When looking at a flat map, east-west distances on that map will get smaller the further away from the equator you go. For example, one inch along the equator might equal 500 km, while one inch on the tropic might be 400 km, and one inch along the arctic circle might only be 200 km. (numbers for illustrative purposes only).

I would think it would still be there, just less pronounced and much less noticable, especially given how you added significantly to the southern ocean as that would further reduce the effect, but there would still have to be some distortion. But for that small a distortion, I'd say "ignore it." ;)

Nope. The only distortion that would appear would be solely the result of mishandling the image. The reason for this is that the map is at a 2:1 ratio of width to height. At the same instant you have the top of the map on the north pole and the bottom of the map on the south pole you will find the two edges meeting at the exact same longitude. The distance of 1° longitude will remain constant regardless of whether you measure between the equator (0° ) and 1° N or if you measure between 87° N and 88° N.

The reason I added to the southern continent was to make it an equal distance from equator to south pole as there was equator to north pole (i.e. to center the equator along the middle of the map).
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Re: Hollow World: Iciria, 40 miles per hex

Postby Thorf » Fri Jun 06, 2008 5:26 pm

I'm collecting everything into one post to reply to.

Gecko wrote:Well that would depend on what projection(s) you want to use in your finished maps. You can use Interprolation (like the table at the wikipedia article you linked to) to convert distances from the Robinson into a true sphere calculatons, then You would use whatever interprolation you want to transform your final project into. Set up a few points like this to get an outline and you can get a feel for how little or how much distortion there is. Personally however, if you truely want that level of detail then you are going to be working on it for a very long time. Best thing would probably be to just 'fudge' here and there, since its not like we are going to be guiding any 747s through fog based off these maps or anything!


Hehe. To be honest that's basically the answer that I want to hear. It's not as if we're working from mathematically and geographically correct maps. And it's also not as if the original cartographers took this into account at all, because we can be absolutely sure that they didn't; this is the kind of thing that fans worry about, not designers working to a tight schedule. :D

hmm, that's an interesting question. Of course the meta answer would be that since the setting, and hence the maps, were created piecemeal, there is no such relationship. Of course if you wanted to develop it further perhaps there is some sort of scaled up version of a trimetric technique (like the Chamberlin trimetric) only using the 6 points of a hex instead of the 3 of a triangle. You'd have to ask a mathmatician (maybe one specilizing in geometry) about that one though...


Clearly one of the prerequisites for any plan is that we can accomplish it within the Mystara community, and preferably that more than one of us can manage to do it. So we can scratch this level of detail, I think.

For the Hollow World, all we have is that one map. Does it being the inside of a sphere make a difference to any of this? We could probably assume that since TSR used the same projection for both inside and out that it doesn't make a difference - or we can safely ignore what difference there may be.


I wouldn't think there would be any difference. You almost want to intuitively say that there should be a -1 factored into the interprolation, but I don't think there would be. I'm not positive though, that would be a question for a cartographer (or again, a mathmatician specializing in geometry).

Ultimately, I would suggest simply ignoring this issue as much as possible.


Yes, that's what I'm thinking too.

Incidentally, it might be interesting to try mapping the Hollow World map onto Google Earth, just to see how it turns out. Mirror-image the map, and it wouldn't be inaccurate - you just have to imagine looking at the sphere from the outside, like looking through a stained glass window from the outside.

Hugin wrote:Hey, Thorf. I'm the one who did the Google Mystara experimentations on the MMB. What I found was that we have too much land mapped in the northern hemisphere (which I 'fixed' by saying it wraps around the polar opening), not enough mapped in the southern hemisphere (added more ocean which also means it's not as close to the pole as it looks), and there is not enough area around the east-west circumference ('fixed' by adding to the Far End Ocean). This all makes Mystara something like 96% the size of earth. Northern and Southern regions are also condensed in their east-west profile while north-south profiles are maintained regardless of latitude.

This may be another facet that should be discussed by the community to see which solutions should be used.


I thought that it was your project. :) I went and read through your thread earlier, it seems very impressive.

There are a number of points to talk about, however. The main problem is that your results are only as accurate as the original map. As one of the guys making those maps, it's easy for me to see the problems inherent in that scenario. The simple fact is that there are only two official maps to base this on, and the fan maps I have seen so far do not seem to match up with either of them. Specifically, either Davania is too small or Skothar is too big. I have a feeling that this may be the result of working from the official 72 mile per hex maps, which I have so far kept well clear of.

In any case, I'd like to have a go at trying to fit one of the official maps onto the globe, and see what sort of shapes we get out of it.

Hugin wrote:
Gecko wrote:I would think it would still be there, just less pronounced and much less noticable, especially given how you added significantly to the southern ocean as that would further reduce the effect, but there would still have to be some distortion. But for that small a distortion, I'd say "ignore it." ;)

Nope. The only distortion that would appear would be solely the result of mishandling the image. The reason for this is that the map is at a 2:1 ratio of width to height. At the same instant you have the top of the map on the north pole and the bottom of the map on the south pole you will find the two edges meeting at the exact same longitude. The distance of 1° longitude will remain constant regardless of whether you measure between the equator (0° ) and 1° N or if you measure between 87° N and 88° N.


Are you factoring in the fact that the upper and lower 30 degrees of the map are likely compressed north/south compared to the middle parts, from 60N to 60S? Or perhaps more of a point, did Kal figure this in for his map? Or the cartographers whose work Kal used as references?

I hate having to think like this, but unfortunately it's the cost of accuracy.

The reason I added to the southern continent was to make it an equal distance from equator to south pole as there was equator to north pole (i.e. to center the equator along the middle of the map).


This alone suggests that there may be problems with the original map. At the very least it may be a different projection, but it seems more likely that it's just an assemblage of all the hex maps we have been creating over the years. They're great maps, and I have the utmost respect for all the cartographers, many of whom are my friends, but if we want accurate results we have to start from the official maps. There's no two ways about it.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Hugin » Fri Jun 06, 2008 6:09 pm

Thorf wrote:Incidentally, it might be interesting to try mapping the Hollow World map onto Google Earth, just to see how it turns out. Mirror-image the map, and it wouldn't be inaccurate - you just have to imagine looking at the sphere from the outside, like looking through a stained glass window from the outside.

That wouldn't be hard at all, actually. Just need the map!

The main problem is that your results are only as accurate as the original map.

For sure! But which ones are accurate when dealing with Davania and Skothar? Hopefully this will be resolved.

In any case, I'd like to have a go at trying to fit one of the official maps onto the globe, and see what sort of shapes we get out of it.

It's very easy to do. I explain how to do it in the Google Mystara thread over on the MMB. Just remember that the only way to avoid distorting the map is have it at a 2:1 width-height ratio.

Are you factoring in the fact that the upper and lower 30 degrees of the map are likely compressed north/south compared to the middle parts, from 60N to 60S?

Why? If it's because of the smaller circumference around the poles compared to that of the equator, it really is negligible, and can be completely ignored with Mystara. (At least as far as we are concerned; we have larger diseases to cure ;) )

This alone suggests that there may be problems with the original map.

Absolutely. But even the official ones don't necessarily have the equator in the center.

At the very least it may be a different projection, but it seems more likely that it's just an assemblage of all the hex maps we have been creating over the years.

I personally don't think the original maps used any kind of projection at all. I think they just eyeballed it and drew maps. :)
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Re: Hollow World: Iciria, 40 miles per hex

Postby Thorf » Fri Jun 06, 2008 8:43 pm

Hugin wrote:
Thorf wrote:Incidentally, it might be interesting to try mapping the Hollow World map onto Google Earth, just to see how it turns out. Mirror-image the map, and it wouldn't be inaccurate - you just have to imagine looking at the sphere from the outside, like looking through a stained glass window from the outside.

That wouldn't be hard at all, actually. Just need the map!


Well, the only official map of the Hollow World is the one in the Hollow World Set. For the Outer World we have that one plus the original Master Set one. In this case, it's actually more useful for us to have a rectangular "projection", because fitting a Robinson projection (or whatever it is) onto the globe is not easy - we'd first have to make it rectangular, or the distortions of the projection would just be exaggerated.

I had a fiddle using the Master Set map - essentially the same one on my site, but clipped down to the rectangular border. It seems to fit onto the globe rather well, with just the right parts protruding into the polar opening - the bottom tip of Davania, and the double prongs of Hyperborea along with the Nentsun Peninsula. However, as you noted, the latitude markers and the tropics seem to be off.

However... referring to the Hollow World maps, did you notice that the top latitude marker is 90 degrees (in both the outer and inner worlds)? That's fine, except that on earth, 90 is the pole, whereas on Mystara it is apparently the point where the land begins to turn inwards.

What this means is that Mystara still uses 90 degrees to describe its latitudes, but those 90 degrees are not actually the same as the earth's 90 degrees; in fact, they probably correspond to the real world's 80 or perhaps even 70 degrees. This explains why things appear too far north - in fact they're not, it's the latitude markers that are wrong. It's also the only explanation I can think of given that the north and south parts seem to be in the perfect position, as is the equator.

The main problem is that your results are only as accurate as the original map.

For sure! But which ones are accurate when dealing with Davania and Skothar? Hopefully this will be resolved.


The answer is that I have yet to see a hex map that has the continents in the same scale as the official maps. So as of now, only the official maps are accurate in this regard.

Having said that, I really don't mean to be overly critical. Besides, your work in Google Earth is absolutely invaluable! This could solve this whole issue which has been plaguing us for years, and allow us to get a much better idea of the real shapes of the continents.

In any case, I'd like to have a go at trying to fit one of the official maps onto the globe, and see what sort of shapes we get out of it.

It's very easy to do. I explain how to do it in the Google Mystara thread over on the MMB. Just remember that the only way to avoid distorting the map is have it at a 2:1 width-height ratio.


The east-west issue is something I haven't looked into yet, but I totally agree with your method of adding to the sea to fix any inconsistencies. It's always nice to have a big ocean anyway.

Are you factoring in the fact that the upper and lower 30 degrees of the map are likely compressed north/south compared to the middle parts, from 60N to 60S?

Why? If it's because of the smaller circumference around the poles compared to that of the equator, it really is negligible, and can be completely ignored with Mystara. (At least as far as we are concerned; we have larger diseases to cure ;) )


No, it's just because of the way the maps are drawn. Look at the Hollow World Set maps and you'll see that 60-90 degrees is vertically smaller than 0-30 and 30-60. Thus, any hex maps based on that map will also be compressed in those areas. We can't really tell with the Master Set map, since it has no latitudes marked at all, so I guess that the Hollow World maps are the primary source for latitude. The Poor Wizard's Almanacs provide some references too, but I think they agree with the Hollow World maps.

But even the official ones don't necessarily have the equator in the center.


Actually I think they do. :) Lucky for us!

I personally don't think the original maps used any kind of projection at all. I think they just eyeballed it and drew maps. :)


It does seem likely, yes. Based on the revelations (at least for me!) of today, I would theorise that they took a Robinson projection map of the world and redrew the Master Set world map onto it. They seem to have done a pretty good job, although it's also probably not that accurate.

Well, I want to look into this more, but I really must be getting to bed. I'll be back tomorrow (today? :oops: ).
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Re: Hollow World: Iciria, 40 miles per hex

Postby Gecko » Sat Jun 07, 2008 3:25 am

Hugin wrote:
I would think it would still be there, just less pronounced and much less noticable, especially given how you added significantly to the southern ocean as that would further reduce the effect, but there would still have to be some distortion. But for that small a distortion, I'd say "ignore it."

Nope. The only distortion that would appear would be solely the result of mishandling the image. The reason for this is that the map is at a 2:1 ratio of width to height. At the same instant you have the top of the map on the north pole and the bottom of the map on the south pole you will find the two edges meeting at the exact same longitude. The distance of 1° longitude will remain constant regardless of whether you measure between the equator (0° ) and 1° N or if you measure between 87° N and 88° N.

It's hurting my head too much trying to visualize how a 2:1 ratio wold effect it so I'll take your word for it :? But I think were agreed that in either case we can igonre it: either it is not there so we can ignore it, or it is so small that we can ignore it. So, moving on :arrow:

Thorf wrote:Hehe. To be honest that's basically the answer that I want to hear.

8-)
Thorf wrote:It's not as if we're working from mathematically and geographically correct maps. And it's also not as if the original cartographers took this into account at all, because we can be absolutely sure that they didn't; this is the kind of thing that fans worry about, not designers working to a tight schedule.

yep, and a definate double yep.

Thorf wrote:Incidentally, it might be interesting to try mapping the Hollow World map onto Google Earth, just to see how it turns out. Mirror-image the map, and it wouldn't be inaccurate - you just have to imagine looking at the sphere from the outside, like looking through a stained glass window from the outside.

Wow, I was thinking the very same thing just before I read this post. :)

Thorf, replying to Hugin about his Google Mystara project wrote:I went and read through your thread earlier, it seems very impressive.

Indeed, very impressive (I was not a member of the MMB, only a lurker, so I couldn't comment thusly at the time, but here, now, I can).

Thorf wrote:However... referring to the Hollow World maps, did you notice that the top latitude marker is 90 degrees (in both the outer and inner worlds)? That's fine, except that on earth, 90 is the pole, whereas on Mystara it is apparently the point where the land begins to turn inwards.

What this means is that Mystara still uses 90 degrees to describe its latitudes, but those 90 degrees are not actually the same as the earth's 90 degrees; in fact, they probably correspond to the real world's 80 or perhaps even 70 degrees. This explains why things appear too far north - in fact they're not, it's the latitude markers that are wrong. It's also the only explanation I can think of given that the north and south parts seem to be in the perfect position, as is the equator.


:lol: So apparently Mystara's (in Game) philosophers/academics/etc. are not very good at geometry and can't calculate their own planets circumference. hmm... I wonder If I could use that in a game somehow :?: :twisted:

Thorf wrote:
Hugin wrote:I personally don't think the original maps used any kind of projection at all. I think they just eyeballed it and drew maps.

It does seem likely, yes. Based on the revelations (at least for me!) of today, I would theorise that they took a Robinson projection map of the world and redrew the Master Set world map onto it. They seem to have done a pretty good job, although it's also probably not that accurate.


I'd definately say that is the case. Also, isn't it based on a map of Earth in the geologic past (Jurassic period or some such, If I recall correctly?)

Thorf wrote:Well, I want to look into this more, but I really must be getting to bed. I'll be back tomorrow (today? ).

Warning: Think of things and issues such as this just before bedtime can lead to some interesting dreams... :P
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Re: Hollow World: Iciria, 40 miles per hex

Postby Hugin » Sat Jun 07, 2008 4:18 am

Thorf wrote:However... referring to the Hollow World maps, did you notice that the top latitude marker is 90 degrees (in both the outer and inner worlds)? That's fine, except that on earth, 90 is the pole, whereas on Mystara it is apparently the point where the land begins to turn inwards.

What this means is that Mystara still uses 90 degrees to describe its latitudes, but those 90 degrees are not actually the same as the earth's 90 degrees; in fact, they probably correspond to the real world's 80 or perhaps even 70 degrees. This explains why things appear too far north - in fact they're not, it's the latitude markers that are wrong. It's also the only explanation I can think of given that the north and south parts seem to be in the perfect position, as is the equator.

I've always discarded that as nonsensical - on numerous fronts. It makes a circle have more than 360°. Also, the tropics and arctic circles must be located at equal degrees as the tilt of the planet's axis. If the degrees of latitude are measured differently than the planet's axial tilt, we have a problem. I'm of the opinion that if we use that skewed latitude scheme we'll be making things more difficult for ourselves.

Gecko wrote:Also, isn't it based on a map of Earth in the geologic past (Jurassic period or some such, If I recall correctly?)

I believe so. Although, there is no real cultural association to geographic locations (i.e. you generally won't find the RL earth culture and its Mystaran counterpart sharing the same relative regions).
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Re: Hollow World: Iciria, 40 miles per hex

Postby Thorf » Sat Jun 07, 2008 5:48 am

Hugin wrote:
Thorf wrote:However... referring to the Hollow World maps, did you notice that the top latitude marker is 90 degrees (in both the outer and inner worlds)? That's fine, except that on earth, 90 is the pole, whereas on Mystara it is apparently the point where the land begins to turn inwards.

What this means is that Mystara still uses 90 degrees to describe its latitudes, but those 90 degrees are not actually the same as the earth's 90 degrees; in fact, they probably correspond to the real world's 80 or perhaps even 70 degrees. This explains why things appear too far north - in fact they're not, it's the latitude markers that are wrong. It's also the only explanation I can think of given that the north and south parts seem to be in the perfect position, as is the equator.

I've always discarded that as nonsensical - on numerous fronts. It makes a circle have more than 360°. Also, the tropics and arctic circles must be located at equal degrees as the tilt of the planet's axis. If the degrees of latitude are measured differently than the planet's axial tilt, we have a problem. I'm of the opinion that if we use that skewed latitude scheme we'll be making things more difficult for ourselves.


Yes, definitely. 90 degrees simply must be at the poles, even if they don't physically exist.

But what this means is that the official maps are wrong, and consequentially all of our maps are wrong. Since 90 degrees north and south on the Hollow World Set maps represent the start of the lip of the polar openings, we either have to conclude that the latitude markers are different from earth's (and that they do not extend to the poles), or that they are marked wrongly on the maps.

As I see it, there are two possible solutions:

  1. Add some space at the extreme north and south to represent the polar openings. Since the Hollow World Set maps already compress the 60-90 degree ranges, this extra space will resolve the compression, and the 90 degree mark on the map will become more like 80 degrees. The advantage with this method is that it probably allows us to maintain the latitude markings on the official maps as is, or at least close to how they are marked. However, the shapes of the continents will be compressed slightly, and the polar openings will of course be unavoidably different from how they look on the official maps.
  2. Redefine latitude for the globe based on the Master Set map. The equator and the poles seem to align perfectly with the other maps, including the Hollow World polar opening maps. Therefore, the equator and poles will remain the same, but the position of the tropics and the other lines of latitude in between will change slightly. The advantage with this is that the maps will remain visually exactly the same, and we will also have an excellent source for expanding hex maps accurately - the Master Set map. The disadvantage is that the latitude lines as we know them from the Hollow World world maps and the Poor Wizard's Almanac maps will change.
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360 degrees?

Postby Gecko » Sat Jun 07, 2008 8:36 am

Thorf wrote:
Hugin wrote:
Thorf wrote:However... referring to the Hollow World maps, did you notice that the top latitude marker is 90 degrees (in both the outer and inner worlds)? That's fine, except that on earth, 90 is the pole, whereas on Mystara it is apparently the point where the land begins to turn inwards.

What this means is that Mystara still uses 90 degrees to describe its latitudes, but those 90 degrees are not actually the same as the earth's 90 degrees; in fact, they probably correspond to the real world's 80 or perhaps even 70 degrees. This explains why things appear too far north - in fact they're not, it's the latitude markers that are wrong. It's also the only explanation I can think of given that the north and south parts seem to be in the perfect position, as is the equator.

I've always discarded that as nonsensical - on numerous fronts. It makes a circle have more than 360°. Also, the tropics and arctic circles must be located at equal degrees as the tilt of the planet's axis. If the degrees of latitude are measured differently than the planet's axial tilt, we have a problem. I'm of the opinion that if we use that skewed latitude scheme we'll be making things more difficult for ourselves.


Yes, definitely. 90 degrees simply must be at the poles, even if they don't physically exist.


After giving this some more thought I came up with something. I don't think it really helps with mapping or anything but it could perhaps be an in-story resoning: Who say's that Mystaran's divide a circle into 360 degrees? Maybe they divide it into 375 or 400? After all, one of the commonly quoted reasons why we divide a circle into 360 degrees is because that is approximately how many days there are in a year, as noted by the Bablyonians and Egyptians and ancient Indians (and others), but Mystara has 336 days, so why would they pick 360?
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Re: 360 degrees?

Postby Thorf » Sat Jun 07, 2008 12:06 pm

Gecko wrote:After giving this some more thought I came up with something. I don't think it really helps with mapping or anything but it could perhaps be an in-story resoning: Who say's that Mystaran's divide a circle into 360 degrees? Maybe they divide it into 375 or 400? After all, one of the commonly quoted reasons why we divide a circle into 360 degrees is because that is approximately how many days there are in a year, as noted by the Bablyonians and Egyptians and ancient Indians (and others), but Mystara has 336 days, so why would they pick 360?


That's certainly an interesting idea, but it's probably best to leave that sort of stuff alone as much as possible - it just complicates things. ;)

I'm more inclined to go with the second option I listed. I'd rather deal with a slight shift in latitudes (which aren't marked on the vast majority of maps anyway).
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Re: Hollow World: Iciria, 40 miles per hex

Postby Zendrolion » Sat Jun 07, 2008 12:45 pm

We long argued about tropic-polar circles and curvature issues in the Italian MMB long ago... LoZompatore (which also posts on these boards) and Zaryck (another friend from the Italian MMB) did extensive researches and calculations to find a solution to the problem... Which they ultimately didn't found. :cry:

My takes on these issues are:

CURVATURE: I think it'd be difficult (and the result unfamiliar to most of us) to stretch the canon maps to obtain the right curvature of the lands toward the poles. Instead, I think that leaving the maps (with the hex grid) as they are while changing the scale as we approach the poles could be respectful of "real" distances and easier. For example, we can rule that from latitude 50°N each 24-miles hex only measures actually 20-miles across (the number is random), then that scale would reduce at another fixed (and square, say 60°N) latitude, and so on. It'd be a simplification nevertheless, but I think it'd be much more easy to manage - even if the whole latitudes would have to be recalculated.

POLAR CIRCLES & TROPICS: I'd like to keep the positions of tropics and polar circles along the same latitudes as they're on Earth (that is about 23° for tropics and about 67° for polar circles). Do do this, I'd consider Mystara as if it was a sphere (that is, without polar openings which square it at the poles).
This way, we should try to determine at which latitude the beginning of polar curvature (the one that curves toward the HW) begins; on the Italian MMB, LoZompatore and Zaryck determined it at about 65°N, IIRC (but I'll check). This point should be the "90°N" indicated (wrongly) in the HW and RC outer-world map. Beyond it, the crust of Mystara curves toward the HW, until it reaches the "90°N HW" indicated (wrongly, again) in the HW and RC HW-map.
On the Italian MMB we agreed to subdivide the curved area between HW and outer-world in an additional 90°n (outer-world) and 90°s (HW), with "absolute north" in the middle point between them.
This way, you'll have latitudes comparable with Earth's ones until the polar curvature begins. This would require to recalculate the latitudes of HW also, becouse "90°N" both in HW and in the outer world don't mean anything REAL - as you've been saying, they're not REAL degrees.

Anyway, I'll try to have LoZompatore joining discussion here, he's a lot more learned than me on these matters! :ugeek:

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). ;)
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Re: Hollow World: Iciria, 40 miles per hex

Postby OldDawg » Sun Jun 08, 2008 12:18 am

Thorf wrote: Does [the HW] being the inside of a sphere make a difference to any of this?

Being interior to the sphere makes no difference for the purposes of distortion, as HW position is identical to that of the OW spot on the same radial segment. [Thus East-West is reversed in the HW.]

On Hugin’s map: the 2:1 ratio is likely based upon the assumption that the flat map being used is an equi-rectangular map constructed from the equator (which has a perfect 360:180 grid structure). There is still distortion even when your map is 2:1, however. It is an unavoidable mathematical fact that all plane to ellipsoid/toroid mappings have some distortion. It has nothing to do with mishandling the image, but refers to locally variable scrunching or compression of distance, orientation or area.

Gecko wrote:So apparently Mystara's (in Game) philosophers/academics/etc. are not very good at geometry and can't calculate their own planets circumference. hmm... I wonder If I could use that in a game somehow


Well there was radical disagreement over Earth’s circumference for a long while, and trans-oceanic distances were notoriously wrong until the advent of watch technology allowed accurate time keeping for the computation of longitude by position of the sun. Not to mention developing cartesian and then non-cartesian coordinates.

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Re: Hollow World: Iciria, 40 miles per hex

Postby OldDawg » Sun Jun 08, 2008 12:51 am

Thorf wrote:Redefine latitude for the globe based on the Master Set map….

…. In this case, it's actually more useful for us to have a rectangular "projection"


I would suggest that the Master’s Set Map, is an equi-rectangular or Mercator map. 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.

Going by the HW/RC map as a guide, let 66N be just north of the Great Bay, parallel to the bottom of the westernmost mountain hex (24mph) at the mouth of the GB. From there, every 16 24mph hexes equals 6 degrees of latitude. It makes the radius of Mystara much closer to the Earth's (radius= 3667 miles vs ~3950; cf. PWA), but key latitudes fall within the official ranges, and it has a useful working ratio of 64 miles:1 degree.

Thorf wrote:However... referring to the Hollow World maps, did you notice that the top latitude marker is 90 degrees (in both the outer and inner worlds)? That's fine, except that on earth, 90 is the pole, whereas on Mystara it is apparently the point where the land begins to turn inwards.
[other comments about 90 degrees north].


Depends on how you define 90. Normally, latitude is defined as the angle a fixed position (for the RW Polaris) makes off of the horizon. So 90 is correctly marked from an astronomical point of view.

There is a discontinuity in curvature at some point prior to 90 degrees. Latitude changes are more rapid between this curvature jump and Astr. 90. This rate of latitude gradation continues into the aperture (assumed circular and elliptical) until a similar jump at the same latitude is encountered in the HW.


Image

Zendrolion wrote:CURVATURE: Instead, I think that leaving the maps (with the hex grid) as they are while changing the scale as we approach the poles could be respectful of "real" distances and easier.


Do you mean an equidistant scaling where both the latitudinal and longitudinal distances are scaled? Or just the east-west? [I would opt for the latter.]

-OD

PS to Thorf: this seems to be getting a bit off topic to the original thread starter, would you prefer that general mapping discussions be bumped over to another thread, so this one stays centered on Iricia?
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Re: Hollow World: Iciria, 40 miles per hex

Postby Mike » Mon Jun 09, 2008 1:29 am

Thorf wrote:If we do, the shapes of Aerical, Suridal, etc. will change substantially; the outlying continents will straighten out, and their dimensions may also change. The same is true of the Outer World, with Davania and Skothar, as well as western Brun.

If we don't, we must take it for granted that there is artificial stretching in the far north and south (and probably east and west) of the maps. It seems like this is the route that has so far been taken.

I guess I really want to check and see if anyone knows how we could go about taking the world's curvature into account, or for that matter if anyone else is bothered about this issue at all.


There is a way, and that is to map the world to an icosahedron. This is the method used in the real world, for example doing weather simulation, because it allows the entire surface of the world to be represented by a tiling of nearly equal-sized hexagons with fairly low distortion.

(I've actually been working on mapping Mystara to an icosahedron and was planning to post some stuff here this weekend, so your timing is good!)

As an illustration, I loaded a "flat" rectangular hexmap into Google Earth to show the distortion as you approach the poles:

http://members.dsl-only.net/~bing/temp/ ... t-grid.jpg

Next I loaded an icosahedral hexmap:

http://members.dsl-only.net/~bing/temp/ ... s-grid.jpg

You can see the icosahedral map maintains the correct north-south spacing. There is some distortion along the "edges" where the faces meet, but it is IMO minor and the area of each hex remains nearly the same. Also this distortion is only apparent when mapping to a globe, not when laying the map out flat. (Also my map is a quick hack-job and I didn't take time to make the hexes match up perfectly.)

An icosahedron has 20 faces and 12 vertices; a d20 is a familiar example. (Making it all the more fitting for a D&D world!) Each face is an equilateral (60-60-60) triangle which can be mapped perfectly on a flat hexagonal grid. You can view the icosahedron as a three rows of triangular regions:

Northern: between 30N and 60N (five regioins)
Equatorial: between 30N and 30S (ten regions)
Southern: between 30S and 90S (five regions)

The difficulty is to convert the existing Mystaran maps to an icosahedral "projection." When laid flat, it has triangular "cut-outs" in the north and south... so you do still have to adjust things to fit on the map. The important part is that once the adjustments are made, you can work with a flat undistorted hexmap.

The thing to consider is what parts of Mystara have been mapped, and whether those parts can be placed onto a hexmap without distortion or "cutting".

The good news is, I think it is (barely) possible. Almost the entire Known World, from Darokin to Alphatia, can be fit onto a single triangular "face" without modification. The savage coast fits on another face. But in between the two, near the border of Darokin and Sind, there is a triangular "cut" (northward from 30 degrees).

If a little bit of a map crosses the edge of a "cutout" area it's okay, you can continue the hexmap on the other edge for a short distance without distortion. This is necessary for a thin edges of eastern Alphatia, and may also apply to western Glantri and Wendar. You don't want to go too far this way though as now you'll be bending 60 degrees southwards.

Likewise, the corners are impossible to map flatly, so ideally you want to put them in out-of-the-way places... the middle of the ocean, or in the midst of impassable mountains.

To determine whether this idea is feasable for Mystara, I took the "Robinson projection" from the RC and morphed it into a rectangular map.

Then I converted the rectangular map to an icosahedral map. This is the result:

http://members.dsl-only.net/~bing/temp/ ... os-125.jpg

The black rectangle shows the approximate location of the known world. On the map the rectangle is slightly distorted, however you can easily map it directly and ignore the distortion. I doubt anyone is going to care, and it's still way more correct than mapping the entire world as a rectangle.

There is another cut (and vertex) in Belissaria. This is hard to avoid, if you shift the map eastwards to put it in the ocean, it appears to put another vertex in Sind instead.

The next step in making this work is to rough in a 72-mile per hex map of the entire region and see if it will fit, as well as parts of neightboring regions with the Savage Coast and Belissaria.

To check distortion on this map, I added hexes and loaded the icosahedral mapp into Google Earth:

http://members.dsl-only.net/~bing/temp/globe-icos.jpg

For comparison, here is the standard rectangular map (based on the Robinson projection) with a hexmap applied, in Google Earth:

http://members.dsl-only.net/~bing/temp/globe-rect.jpg

As you can see, the landforms have the same overall distortion, but the hexes map much better in the icosahedral verison. (Again my edges didn't like up correctly along the region edges, but that's my own mistake and not related to the mapping.)
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Re: Hollow World: Iciria, 40 miles per hex

Postby Mike » Mon Jun 09, 2008 1:35 am

Thorf wrote:Hmm, the Robinson projection looks very similar, indeed.


It is similar, but not precise. The curved edges are distorted and asymmetrical in both N/S adn E/W directions (making it very difficult to analyze with a computer program). Rather it is a very good imitation of a Robinson projection. I'm guessing created by a very skilled artist without the use of math-based computer tools.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Mike » Mon Jun 09, 2008 2:15 am

OldDawg wrote:Depends on how you define 90. Normally, latitude is defined as the angle a fixed position (for the RW Polaris) makes off of the horizon. So 90 is correctly marked from an astronomical point of view.

There is a discontinuity in curvature at some point prior to 90 degrees. Latitude changes are more rapid between this curvature jump and Astr. 90. This rate of latitude gradation continues into the aperture (assumed circular and elliptical) until a similar jump at the same latitude is encountered in the HW.


This was the same conclusion I came to! I even made up a diagram but you beat me to it. :lol: (Your explanation and artwork is much better through.)

I think Mystara must be a perfect sphere, not distended. This matches the diagram in the HW book, and it is the most intuitive.

The "edge" begins at approx 75 degrees lat (from projecting the diameter of the opening onto a sphere 19440 miles in diameter.) The transition from 75 degrees to 90 degrees occurs in the space of only 146 miles.

Outside the hole, every 54 miles corresponds to one degree latitude. Inside the hole, every 10.5 miles corresponds to one degree latitude: walking through the hole would be an 1884 mile journey from edge to edge.

I think that the "apparent" 90 degrees indicated on the outer world map is actually close to the "midway point" through the holes between the outer and inner world. The land north of 75 degrees is actually inside the hole.

Since everything north of 75 degrees is covered in dense fog, storms, and antimagic, a Mystaran trying to reach the pole would only be able to determine his position by distance walked. In that case he'd get halfway through the hole, determine that this is the correct "location" of the north pole, and turn around and walk south again. He would never notice that he passed the (astronomical) 90 degree point long ago.

In any case I'm not terribly concerned about the latitudes. The maps are clearly omniscient, conveying information unknown to to the inhabitants of Mystara, and are for the GM. The only real reason a GM needs to know latitude is to determine climate. So we can think of the labeled latitudes as "earth-equivalent climate zones" and leave it at that.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Hugin » Mon Jun 09, 2008 3:51 am

Interesting work Mike. Although I can see how it would be very beneficial if we were creating hex maps from scratch, I can't see how it helps fix the existing ex maps we have. (Of course, it may very well help but I just don't understand how. :D )

Mike wrote:I think Mystara must be a perfect sphere, not distended. This matches the diagram in the HW book, and it is the most intuitive.

I tend to share this view. I mean, an extended Mystara is interesting, but canon and intuition say spherical.

The "edge" begins at approx 75 degrees lat (from projecting the diameter of the opening onto a sphere 19440 miles in diameter.) The transition from 75 degrees to 90 degrees occurs in the space of only 146 miles.

I basically came to the same conclusion but at 76° latitude.

Outside the hole, every 54 miles corresponds to one degree latitude

I'm finding we have more like 64 miles to one degree latitude. That may be due to the maps I'm using though (they were done by someone else). However, I'm fairly sure others found roughly the same number.

I think that the "apparent" 90 degrees indicated on the outer world map is actually close to the "midway point" through the holes between the outer and inner world. The land north of 75 degrees is actually inside the hole.

Agreed. I'm of the opinion that some of the extreme north that we see mapped is actually areas that wrap around into the polar open to a significant degree.
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Re: Hollow World: Iciria, 40 miles per hex

Postby Mike » Mon Jun 09, 2008 3:38 pm

Hugin wrote:Interesting work Mike. Although I can see how it would be very beneficial if we were creating hex maps from scratch, I can't see how it helps fix the existing hex maps we have. (Of course, it may very well help but I just don't understand how. :D )


The "fix" (as I see it) is in properly positioning the maps we do have. (I mean the canonical hexmaps, not fan maps that cover entire continents.) Careful positioning will minimize distortion and establish a clear objection location. The continent maps and fan maps can then be re-done around these, but fitted to the icosahedral topography. The end result would be the first and only TSR world with a "globular" map. The maps themselves do not change, instead we embrace the distortion we already have, trying to minimize its impact and noticeability, but moving forward work to ensure there is no distortion for any new maps we create.

The HW maps could receive the same treatment. Map everything to an "inside out" icosahedron. Iciria would be tricky to convert though, I suspect it is too big to pass through unscathed.

Areas without hexmaps, such as the Masters set map, are easy to convert to the new topography. As a side benefit, the icosahedral map provides convenient positioning markers and it is easy to subdivide hexmaps, so any new maps can be quickly and easily located and created without the headache of mismatched boundaries. It would be possible to create an 8-mile trailmap of the entire globe.
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Re: Hollow World: Iciria, 40 miles per hex

Postby LoZompatore » Fri Jun 13, 2008 6:22 pm

Great job, Mike! Very, very impressive. :shock:

I was on the way of doing the same work of you, but you were faster and much more efficient than me. I agree with almost everything you said.
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Just a remark:

Likewise, the corners are impossible to map flatly, so ideally you want to put them in out-of-the-way places... the middle of the ocean, or in the midst of impassable mountains.


Well, actually this is not a problem: you have to place 12 regularly-spaced pentagons at each icosahedron vertex and in such a way you'll get an exact coverage of the sphere without having to distort any of the hexes in the whole grid.
The picture below clarifies the concept: I highlighted in pale green the edges of the triangular sides of the icosahedron:

Image
http://it.geocities.com/lutetius00/Hexed_Sphere.jpg

You may add as much hexes as you like among the 12 pentagons and you'll always get a sphere (you are just better approximating the sphere by reducing the scale of the hexgridding). You never have to add other pentagons.
Notice that if the number of hexes between two pentagons is 1 the geometrical shape you'll have is the well known soccerball.
If the number of hexes between two pentagons is 0 the geometrical shape you'll have is a dodecahedron (the familiar d12 dice).

Notice that the pentagon side is identical to the hex side you are using so, if the scale is small enough, the pentagons become negligible comparing to the rest of the map. You can approximate them with hexes without adding great errors to the map.

An hexed grid suitable for a world coverage would be something similar to this (the scale is 300km(186mi)/hex for Earth, approx 234km(145mi)/hex for Mystara):

http://it.geocities.com/lutetius00/Hexed_Globe_ENG.jpg

Unlukily, as you may notice, the connection between two triangles of the icosahedron implies a 30° rotation of the hexgridding, which is not very consistent with the official hexed map we have. :|
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Re: Hollow World: Iciria, 40 miles per hex

Postby Thorf » Mon Jun 16, 2008 3:46 am

This is going to be a big reply. Sorry it's so late - I've been working on it since last week. I'll try and make it as brief as I can.

Zendrolion wrote:CURVATURE: I think it'd be difficult (and the result unfamiliar to most of us) to stretch the canon maps to obtain the right curvature of the lands toward the poles. Instead, I think that leaving the maps (with the hex grid) as they are while changing the scale as we approach the poles could be respectful of "real" distances and easier.


Agreed. I don't think there's much of a problem with this in the Outer World. In the Hollow World, the slightly more familiar extreme north and south areas of Iciria will actually be a lot smaller than they look, but it can't be helped; the world is not flat.

POLAR CIRCLES & TROPICS: I'd like to keep the positions of tropics and polar circles along the same latitudes as they're on Earth (that is about 23° for tropics and about 67° for polar circles). Do do this, I'd consider Mystara as if it was a sphere (that is, without polar openings which square it at the poles).


Yes, definitely - Mystara is a regular sphere, and we will continue to think of it as such. Doing anything else makes it needlessly more complicated. The polar openings are just big holes in the sphere at either end; we don't need to worry about them much otherwise.

Also, for ease of use of earth-related programs such as Google Earth, it makes sense to keep the world spherical and as similar to earth as possible.

This way, we should try to determine at which latitude the beginning of polar curvature (the one that curves toward the HW) begins; on the Italian MMB, LoZompatore and Zaryck determined it at about 65°N, IIRC (but I'll check). This point should be the "90°N" indicated (wrongly) in the HW and RC outer-world map. Beyond it, the crust of Mystara curves toward the HW, until it reaches the "90°N HW" indicated (wrongly, again) in the HW and RC HW-map.
On the Italian MMB we agreed to subdivide the curved area between HW and outer-world in an additional 90°n (outer-world) and 90°s (HW), with "absolute north" in the middle point between them.
This way, you'll have latitudes comparable with Earth's ones until the polar curvature begins. This would require to recalculate the latitudes of HW also, becouse "90°N" both in HW and in the outer world don't mean anything REAL - as you've been saying, they're not REAL degrees.


That's effectively what I have been proposing, too. We can make some interesting conclusions by looking at the maps of the polar openings, which give a good idea of how much land folds over into the opening on each side.

Further, I have been considering what the effect would be if we keep to earth-style latitudes right up to the beginning of the lip of the polar openings, then assign the rest of the latitude markers (for example from 65, or 70, or whatever it is, until 90) to the inside of the polar openings, with 90 degrees at the centre of the opening, so that 90 degrees Outer World equals 90 degrees Hollow World.

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).

Anyway, I'll try to have LoZompatore joining discussion here, he's a lot more learned than me on these matters! :ugeek:


That would be great!

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?

OldDawg wrote:
Thorf wrote:Redefine latitude for the globe based on the Master Set map….

…. In this case, it's actually more useful for us to have a rectangular "projection"


I would suggest that the Master’s Set Map, is an equi-rectangular or Mercator map. 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.


Yes. The reason for my liking of the Master Set map is that it seems to be the original base for most of the current hex maps. The shapes that we are most familiar with are probably those on that map. The Hollow World set maps are somewhat warped due to the redrawn pseudo-projection, and therefore less easy to use.

On the other hand, as you say, the Master Set map is really a projection too. I will be happy with any solution that lets me map accurately, and leaves me with a master map for reference.

Going by the HW/RC map as a guide, let 66N be just north of the Great Bay, parallel to the bottom of the westernmost mountain hex (24mph) at the mouth of the GB. From there, every 16 24mph hexes equals 6 degrees of latitude. It makes the radius of Mystara much closer to the Earth's (radius= 3667 miles vs ~3950; cf. PWA), but key latitudes fall within the official ranges, and it has a useful working ratio of 64 miles:1 degree.


I'm a little puzzled that you're talking about hexes, because the Hollow World and Rules Cyclopedia world maps don't have any.

Anyway, in regards to world measurements, I don't think we need to try and work those out until later. The fact is, the official figures will probably be wrong however we work it out, because it seems unlikely that they did a lot of complex research in order to figure them out. I'm not worried about that at all. The defining factor in working out the size of the planet, and the overall number of hexes, will be the existing maps, and how they fit with the world maps.

I should probably clearly state my position on this: the only maps that are relevant in this discussion are the official world maps and official hex maps. No fan-made maps of the world up until now have completely taken into account all of the factors that we're talking about, and in any case they are all based on the official maps. If we want maximum accuracy, we have to go back to the primary sources.

There are only two world maps of the Outer World, and only one of the Hollow World. Small scale hex maps exist for a large part of the Hollow World, but they will almost certainly need to be adapted for curvature. Small scale hex maps for the Outer World cover only a reasonably small section of the world, mostly in the lower half of the northern hemisphere.

Depends on how you define 90. Normally, latitude is defined as the angle a fixed position (for the RW Polaris) makes off of the horizon. So 90 is correctly marked from an astronomical point of view.


Perhaps, but I don't think it really matters how we define latitude in the real world. Latitude is just there as a real world analogy. That's why it would be best to keep them the same as earth as much as possible.

I guess it comes down to where we start making latitude different from the earth's. If we want to keep the same tropics and polar circles, we're probably going to have to make some adjustments to the latitudes shown on the official map - whether to the whole map or just the northern and southern regions remains to be seen.

One more thing: looking at the official maps of the openings along with the world maps, it looks very much like they didn't place 90 degrees at the point it should be (scientifically), but rather at the start of the lip.

There is a discontinuity in curvature at some point prior to 90 degrees. Latitude changes are more rapid between this curvature jump and Astr. 90. This rate of latitude gradation continues into the aperture (assumed circular and elliptical) until a similar jump at the same latitude is encountered in the HW.


This analysis is fascinating, but I'm not sure it's going to help us. It seems to me that the start of the lip (where the discontinuity you mention starts) is the place we should concentrate on - either to mark it as the last "stable" latitude, or to mark it as 90 (as the official maps seem to).

PS to Thorf: this seems to be getting a bit off topic to the original thread starter, would you prefer that general mapping discussions be bumped over to another thread, so this one stays centered on Iricia?


Don't worry. I intend to reorganise these posts at some point in the future. For now we can continue to post here.

Mike wrote:There is a way, and that is to map the world to an icosahedron. This is the method used in the real world, for example doing weather simulation, because it allows the entire surface of the world to be represented by a tiling of nearly equal-sized hexagons with fairly low distortion.

(I've actually been working on mapping Mystara to an icosahedron and was planning to post some stuff here this weekend, so your timing is good!)


This idea seems excellent, not to mention uniquely appropriate considering our extensive use of hex maps! I'm extremely interested in exploring it further.

An icosahedron has 20 faces and 12 vertices; a d20 is a familiar example. (Making it all the more fitting for a D&D world!) Each face is an equilateral (60-60-60) triangle which can be mapped perfectly on a flat hexagonal grid. You can view the icosahedron as a three rows of triangular regions:

Northern: between 30N and 60N (five regioins)
Equatorial: between 30N and 30S (ten regions)
Southern: between 30S and 90S (five regions)


Wasn't this the system they had in the World Builder's Handbook? I remember seeing blank grids with this pattern, although without hexes.

The difficulty is to convert the existing Mystaran maps to an icosahedral "projection." When laid flat, it has triangular "cut-outs" in the north and south... so you do still have to adjust things to fit on the map. The important part is that once the adjustments are made, you can work with a flat undistorted hexmap.


It seems that you have a way (a program?) to make this adaptation... Can you explain how?

The thing to consider is what parts of Mystara have been mapped, and whether those parts can be placed onto a hexmap without distortion or "cutting".


I outlined this above, and I think the Outer World will pose very little problem at all. The Hollow World might be another matter, though... I'd love to see a rendition of what it would look like adapted to this format. I am quite willing to change the big map of Iciria to factor in these changes.

The good news is, I think it is (barely) possible. Almost the entire Known World, from Darokin to Alphatia, can be fit onto a single triangular "face" without modification. The savage coast fits on another face. But in between the two, near the border of Darokin and Sind, there is a triangular "cut" (northward from 30 degrees).

If a little bit of a map crosses the edge of a "cutout" area it's okay, you can continue the hexmap on the other edge for a short distance without distortion. This is necessary for a thin edges of eastern Alphatia, and may also apply to western Glantri and Wendar. You don't want to go too far this way though as now you'll be bending 60 degrees southwards.


Sounds like this is going to be fun. :D

To determine whether this idea is feasable for Mystara, I took the "Robinson projection" from the RC and morphed it into a rectangular map.

Then I converted the rectangular map to an icosahedral map. This is the result: http://members.dsl-only.net/~bing/temp/ ... os-125.jpg


Wonderful! This is absolutely what I have been wanting to do all these years. Once again, can you explain how you were able to do this?

The black rectangle shows the approximate location of the known world. On the map the rectangle is slightly distorted, however you can easily map it directly and ignore the distortion. I doubt anyone is going to care, and it's still way more correct than mapping the entire world as a rectangle.


We can worry about these details later. At first glance at least, I don't think it would be too hard to do a little clipping and adapt the official maps to fit the new order. And if it makes the maps more accurate, I say we go for it.

There is another cut (and vertex) in Belissaria. This is hard to avoid, if you shift the map eastwards to put it in the ocean, it appears to put another vertex in Sind instead.


Hmm, I'm not sure about this... I'd have to see the larger scale maps to see how things split. Splitting Sind may end up being inevitable.

The next step in making this work is to rough in a 72-mile per hex map of the entire region and see if it will fit, as well as parts of neightboring regions with the Savage Coast and Belissaria.


Wow, things are going to get a little complicated. For my atlas, I've been working on the assumption that the largest scale maps (generally 8 miles per hex, sometimes 24 mile per hex) are the highest authority. As such, I have been working on creating new 24 and 72 mile per hex maps based on those maps, with a high level of accuracy; official 72 mile per hex maps really leave a lot to be desired when it comes to accuracy.

I would prefer if we could work from these new maps when we do the actual calculations and decide where to split things up, but I'll need to finish making them first.

Mike wrote:
Thorf wrote:Hmm, the Robinson projection looks very similar, indeed.


It is similar, but not precise. The curved edges are distorted and asymmetrical in both N/S adn E/W directions (making it very difficult to analyze with a computer program). Rather it is a very good imitation of a Robinson projection. I'm guessing created by a very skilled artist without the use of math-based computer tools.


Interesting. That is pretty much what I assumed. I also noticed that it's not symmetrical while making my replica of the world map.

Mike wrote:I think Mystara must be a perfect sphere, not distended. This matches the diagram in the HW book, and it is the most intuitive.


Agreed.

The "edge" begins at approx 75 degrees lat (from projecting the diameter of the opening onto a sphere 19440 miles in diameter.) The transition from 75 degrees to 90 degrees occurs in the space of only 146 miles.

Outside the hole, every 54 miles corresponds to one degree latitude. Inside the hole, every 10.5 miles corresponds to one degree latitude: walking through the hole would be an 1884 mile journey from edge to edge.


Where are you taking these measurements from?

I think that the "apparent" 90 degrees indicated on the outer world map is actually close to the "midway point" through the holes between the outer and inner world. The land north of 75 degrees is actually inside the hole.


If you look at the maps of the polar entrances I don't think that's the case. In fact they clearly mark 90 to be the beginning of the lip; inside the polar openings there is no latitude marked at all.

The only real reason a GM needs to know latitude is to determine climate. So we can think of the labeled latitudes as "earth-equivalent climate zones" and leave it at that.


Yes, absolutely agreed.

Hugin wrote:Interesting work Mike. Although I can see how it would be very beneficial if we were creating hex maps from scratch, I can't see how it helps fix the existing ex maps we have. (Of course, it may very well help but I just don't understand how. :D )


I think we can fit the existing hex maps into this scheme - at least that is my hope.

I think that the "apparent" 90 degrees indicated on the outer world map is actually close to the "midway point" through the holes between the outer and inner world. The land north of 75 degrees is actually inside the hole.

Agreed. I'm of the opinion that some of the extreme north that we see mapped is actually areas that wrap around into the polar open to a significant degree.


I'm not convinced of this. Again, see the Hollow World Set maps of the polar openings.

Mike wrote:The "fix" (as I see it) is in properly positioning the maps we do have. (I mean the canonical hexmaps, not fan maps that cover entire continents.) Careful positioning will minimize distortion and establish a clear objection location. The continent maps and fan maps can then be re-done around these, but fitted to the icosahedral topography. The end result would be the first and only TSR world with a "globular" map. The maps themselves do not change, instead we embrace the distortion we already have, trying to minimize its impact and noticeability, but moving forward work to ensure there is no distortion for any new maps we create.


Yes, this is pretty much exactly how I feel too. Consider the existing maps as fixed as much as possible; maps covering a reasonably small area are not problematic for distortion anyway. But to expand the maps to cover the whole world, we really need to take distortion into account, or we'll end up with a very inaccurate world map.

The HW maps could receive the same treatment. Map everything to an "inside out" icosahedron. Iciria would be tricky to convert though, I suspect it is too big to pass through unscathed.


Yes, I think so too - but I'd love to try it and see how it turns out. Remember that the only areas that really matter are Azca, Nithia and Milenia, which have very detailed maps already. Nithia in particular is quite far south, and may pose problems.

Areas without hexmaps, such as the Masters set map, are easy to convert to the new topography. As a side benefit, the icosahedral map provides convenient positioning markers and it is easy to subdivide hexmaps, so any new maps can be quickly and easily located and created without the headache of mismatched boundaries. It would be possible to create an 8-mile trailmap of the entire globe.


:D :D :D
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