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Mapping Issuesby Thorfinn Tait
That's a very fair question. Does the curvature change if we're talking about the inside of a sphere rather than the outside? The official cartographers seem to have taken the position that it doesn't. I can't think how it would be any different, other than that the surface is interior rather than exterior - but it's still the same surface. (Well, for Mystara it's not, but that's only a matter of distance, not proportion.) The polar regions are another matter entirely, but for now I haven't been taking them into account.
Since quite a few people seem to be having a little trouble working out what exactly I'm trying to do, let me summarise the issues we're dealing with here.
One World, Three World Maps, Two Projections and a d20
As we all know, there are three different world maps detailing Mystara: the Master Set Outer World map, the Hollow World Set Outer World map, and the Hollow World Set Hollow World map.
The Master Set map was apparently presented in a latitude/longitude projection (aka equirectangular projection), which is to say that it just maps coordinates onto a grid of squares. It's sometimes called "unprojected", and (for us at least) it's the easiest form of map to convert into others. This is the form of surface map that we are probably most familiar with from working with computers, and with a ratio of 2:1 it is perfect for applying as a texture to a sphere in 3D programs. It has the advantage that direction is always true, but area is not - while the area near the equator is okay, the map gets more and more distorted as you move away from it. The polar regions of the map are especially warped. The only caveat with the Master Set map is that it is not in a ratio of 2:1. But since it was based on maps of the world millions of years ago, we have strong evidence that it should be. For this reason, we seem to have come to a consensus that the Far End Ocean is much larger than we have previously thought.
With the release of the Hollow World Set, the Outer World was redrawn, and we had our first - and only - glimpse of the Hollow World. Both maps are drawn in the same style, in what looks to be a Robinson projection (see also the Wikipedia article). This projection has the advantage that it presents a pleasing view of the world, but the view is pretty warped. Direction is only true along the parallels (latitude lines) and meridians (longitude lines), which means that north only points up in the dead centre of the map; at the outer edges, north points in the direction of the curved of the meridian, so that for example in the extreme west of the map it points up and right. Area is also warped, and again the polar regions suffer the most. The most important thing about this map is the terrain detail it provides, and its topographical labels.
The Hollow World map is the only view we have of the inner world, so we are stuck with it, whether we like it or not. What I have done in my recent posts is change the projection from Robinson to unprojected - the same style as the Master Set map. This allows us to see the map with true directions (north is up, south is down, east and west are left and right - inverted for the Hollow World as usual) for the first time. It doesn't solve the problems with area or scale, but we are now free to change the projection and generate new maps as we need them.
The Outer World map is a different story. It bears a strong resemblance to the Master Set version of the same map, but it introduces numerous problems too. To start with, this map is a proper projection, which means it covers the whole surface of the globe. The Master Set map did not, which means that the continents were stretched to cover this map. The original cartographers may not have realised this. The reason we are going with the Master Set map rather than this stretched map is that it seems the hex maps were all based on the "unprojected" Master Set map.
With our cartography becoming more and more accurate, I have a strong desire to fix these problems. With the Outer World, this means expanding the Far End Ocean on the Master Set map and then projecting it in whatever way we choose. For hex maps, we have chosen to go with an icosahedral projection, which is to say we're treating the world as if it were a d20. It is possible for us to generate other projections too, of course. With the Hollow World map, the first step was unprojecting the map; next we will need to reproject it, presumably using an icosahedral projection to match the Outer World. We may however need to think about how the inverted nature of the Hollow World - being the inside rather than the outside of the sphere - affects projections.
I hope this summary helps everyone understand the somewhat complex topics involved. Please don't hesitate to ask further questions if there's something you don't understand - or to point out mistakes, for that matter!
The next thing I want to talk about is the Master Set map. I'd like to move forward with it, so that we can work towards finalising our view of the world and adapting our maps to take curvature into account.
I can see a number of problems that we're going to have to solve before we can do this.
The state of the polar openings can in some respects be left until later, and adapted to fit the map as necessary. But the 60-90 degree problem and the position of the start of the lip both impact the world maps quite a lot, because they determine the amount of stretching and squashing that is going on in the upper parts of the map. This is relevant to both the Hollow World and the Outer World. I'll try to boil this down into some questions we need to answer.
- The Lip - At what latitude does the lip begin? Is it the same latitude in both the Outer World and the Hollow World?
- The 60-90 Degree Problem - How are we going to handle the degrees for the polar regions? There is less land between 60 and 90 on Mystara than on Earth. Where does 90 fall on Mystara: at the lip of the polar openings; at the central point of the curve between the worlds; or at the top and bottom of the globe where this is no land?
- Mapping the Polar Openings - How are we going to map the polar openings? There is no standard defined way of doing so, since most cartographers don't have to deal with such strangeness.
- Polar Opening Size - How big are the polar openings? I believe that this can be left until later and fit to the size of the world as necessary.
LoZompatore did a great map showing the Latitude Problem with official maps. The official info conflicts in all sorts of ways. Add to this the fact that the Hollow World Set maps are drawings, not accurately-plotted maps. At some point we will have to choose where the latitude lines actually fall - and warp the map accordingly to reflect our decisions. For the Hollow World map, I have gone with the latitudes marked on the map, and extrapolated more lines that fit roughly in between the ones provided on the map.
Outer World Maps
We have concluded that the Master Set map is an unprojected map; that the Gazetteer maps and other hex maps are based on it rather than the Hollow World Set map; that the Master Set map does not cover the whole world, and the Far End Ocean needs to be expanded to compensate; and that the world was stretched for the Hollow World Set map to fit the pseudo-Robinson projection.
Master Set Map Revisions
We need to work out how we want to fix the Master Set map; specifically, we need to create a new view of the world, and place the latitude and longitude lines appropriately. This is not hard, but I think creating a view centred on 0 longitude would be nice. This of course means centring the map on the meridian of Sundsvall.
- Dimensions - Do the borders of the map define the extent of the world? The map border was identical for both appearances of the map, in the Master Set and Dragon 153. We will be expanding it east-west, but are north and south acceptable as they are? Additionally, any land shown in the extreme north/south will need to be folded into the polar opening.
- Scale - What is the scale of the map, and what is the exact size of the world? In answering this question, we need to consider the 60-90 degree problem, and measure the area covered by the official hex maps. We can then extrapolate the size of the whole world using this information.
- Corrections/Updating - The map badly needs to be updated with more detailed coastlines derived from the hex maps. Some parts are way out of date, or just plain wrong - look at Alphatia, for example, the northern part of which is simply not there! This is related to working out the scale, and the precise position of the official hex maps needs to be decided and locked in before any corrections are made.
Hollow World Set Map Revisions
Despite the unhelpful stretching present on this map, we still need to use it. Aside from anything else, it gives development details and place names for many areas of the world, and it is also the key to relating the Outer World to the Hollow World. At the same time, this map suffers from some of the same problems as the Master Set map.
- Projection and Stretching - The map needs to be unprojected to match the Master Set map, and squashed to restore it to the proper aspect ratio to fit with the Master Set map. It may well not match up with it properly, but even a reasonably loose fit will still allow us to make use of the map's details.
- Corrections/Updating - This map may be some help in updating the Master Set map, especially in areas not covered by hex maps.
This map in the Hollow World Set depicting the Outer World before Blackmoor's demise is the only such map published in official sources. It would be nice to keep it in line with the revised official maps, but in order to do this it will need to be processed in the same way as the regular Hollow World Set Outer World map as described above (i.e. unprojected and unstretched).