Mystara

18 February 2016

Lining Up Mystara XIV

Atlas of Mystara, Hollow World, Known World, Mystara 21

First, thank you very much for the wave of feedback since my posts last weekend. I think I have finally caught up with all the messages — apologies if yours slipped through the net. I hope this article answers all of your comments and questions.

I’m going to examine three more placements, all based on your feedback.

Placement 4

Both Paul Dupuis and Michele Carpita advocated a tunnel-shaped polar opening, to solve the problems with Mystara’s size. Here’s what I’ve come up with. First, the latitudes are the same as placement 2:

Placement 3 full world view; the red line shows 66º latitude, where the polar lip begins — Placement 4 full world view; the red line shows 76º latitude, where the polar lip begins

This of course means that the size of the world is the same 31,752 miles as placement 2, too, with 12.25 hexes to every 10º:

Placement 4 close-up showing 10º of latitude

But the polar lip now starts a full 10º higher, at 76º. The Hollow World remains largely the same, with the polar lip starting at 66º, although the curve of course is different.

I used the official figure of 774 miles for the width of the polar openings at their narrowest point. Of course they could be a lot smaller if we wanted them to be, but I think the terrain fits pretty well like this anyway; the land beyond the red lines on the map above will easily fit onto the curve before the tunnel begins.

This seems like the best we can do using the Princess Ark/Hollow World Set equator. But what about that other one — the equator shown on Poor Wizard’s Almanac II‘s map?

Placements 5 & 6

Sheldon Morris proposed that we use the PWA2 equator. Back in 2012, he used it and 72 mile per hex maps to calculate an Outer World circumference of 25,920 miles. That is small enough to solve our problem with polar openings, even using the gradual curve model, I believe. This circumference comes with the bonus of 1º being equal to 72 miles.

However, Sheldon’s calculations were based largely on 72 mile per hex maps, and as we have already seen in this project, those unfortunately are not to be trusted. Our model now is primarily based on 8 and 24 mile per hex maps, with the 72 mile per hex maps filling in just a few gaps with Davania, Skothar and Bellissaria. The main difference is that the 8 and 24 mile per hex maps include more space between the various areas.

Personally, I don’t think the neat mathematics of 1º = 72 miles is as important as getting a good fit with the latitudes, so I’m going to present my own take on this, too.

Placement 5

My take on the PWA2 equator is that it could perhaps work best using the official figure for Farend at 60ºN. Take a look:

Applied to the gradual curve model, this will mean that Frosthaven sits at the top of the world, near or on the point of absolute north. Farend is at 60ºN, Sundsvall 45ºN, Landfall 44ºN, Thyatis 31ºN, and the eastern Thanegioth Archipelago around 18ºN. These numbers are all rather close to the official figures.

The main difference with this model, unsurprisingly, is that a large chunk of Davania will be moved further into the polar opening. It’s actually less of a chunk than it may appear to be, because (due to the shape of the world) southern Davania is nowhere near as large as it looks. But it’s still quite a lot. And of course Davania itself will be smaller, since it straddles the equator less.

It’s still huge, nonetheless.

I reckon that Davania’s southern tip will find its way far into the polar opening.

It’s worth mentioning that a tunnel model could still be used with this, but if a gradual curve model is an option at all, I’d definitely prefer to go with it.

Let’s do some counting:

Placement 5 close-up showing 10º of latitude

This is 10.5 hexes precisely. 10.5 x 72 = 756. 756 / 10 x 360 = 27,216 miles circumference.

We need to see some mock-ups of this on the 3D model, but I think this is the best option so far. Mystara is quite a bit bigger than Earth, but not nearly as much as it was with the other equator. The official latitudes are largely in place. The only potential problem is with how much of Davania and indeed northern Brun and Skothar may fall into the polar openings.

Placement 6

Last for your consideration today is Sheldon’s placement, albeit adapted to the Atlas of Mystara‘s hex map composite.

As you can see, it’s not all that different from placement 5 — just a bit more compact. The main difference is that reducing the length of 1º to 72 miles makes the world a bit smaller. Count the hexes, ten to each 10º:

Placement 6 close-up showing 10º of latitude

Everything is a bit further north: Farend is at 63ºN, Sundsvall 47.5ºN, Landfall 46.5ºN, Thyatis 32ºN, and the eastern Thanegioth Archipelago around 20ºN. Frosthaven looks as if it may be past absolute north, on the inward slope of the polar opening. The gap between the sides of the opening will be around 250 miles.

I prefer placement 5 to this one. The latitudes worked out better, with everything a little further south, and slightly less land in the polar openings. I don’t think it’s worth shrinking things just to make the maths rounder — especially since I believe that 72 miles per hex is an inappropriate scale. Hex maps work better at larger scales such as 8, or 24 at most. Smaller scales should be topographical maps, not hex maps.

In any case, you can all make up your minds for yourselves. I await your feedback. 🙂

14 February 2016

Lining Up Mystara XIII

Atlas of Mystara, Hollow World, Mystara 17

Thanks for the feedback from yesterday’s posts. Today I’m going to concentrate on applying the different placements of Davania and the resulting latitudes to the 3D model.

Size Problems

Unfortunately, it turns out that this is not as easy as I would have liked. Why? Because of the polar openings.

The size of the Hollow World is reasonably fixed. Official sources give a circumference of 11,908 miles, and the full extent of official maps fits quite neatly into this space. The only question for me is how much land to fold into the polar openings; recently I have been thinking that the majority of land shown on the Hollow World poster map should not fold into the openings. Official maps seem to support this.

The problem is, if there is a large difference in size between the inner and outer worlds, the polar openings get smaller and smaller, and eventually disappear. This can be fixed by lowering the latitude of the beginning of the polar lip, but that of course means folding even more land into the openings.

The problem lies in the amount of space the hex mapped areas take up on the Outer World.

Let’s take a look at the placements I proposed yesterday, and see how they do.

Placement 1

Count the hexes between the two horizontal graticule lines here:

I count roughly 12.75 hexes from line to line; this represents 10º of latitude. At 72 miles per hex, we can do a simple calculation to find out how much land 1º of latitude on the Outer World takes up: 12.75 x 72 / 10. 12.75 x 72 = 918. 918 / 10 = 91.8, so that’s 91.8 miles per 1 degree of latitude.

In comparison, earth has roughly 69 miles per degree. So this Mystara is going to be significantly larger than earth. How large? Simply multiply by 360 to get the circumference of the spheroid: 33,048 miles, compared to earth’s 24,860 miles.

Some of you may at this point think, “Wait a minute, isn’t earth an ellipsoid, not a sphere?” Yes, it is, and the circumference I just quoted is the polar circumference (since we’re measuring latitudes). The equatorial circumference is about 24,902 miles. So yes, there’s a difference of around 42 miles — a pretty minor difference, and one that’s not hugely relevant to this discussion. I will likely define Mystara as an ellipsoid later in this project, when I create a coordinate system, complete with its own reference ellipsoid. But note that this minor equatorial increase in circumference is not really enough to help us solve the problems at hand, so let’s ignore it for now.

Getting back to Placement 1, what would this look like on our model, with the polar lip starting at 66º in both the Hollow and Outer worlds?

Oh dear. So there would be no polar openings at all.

In order to fix this, we need to do one or all of the following:

Decrease the size of the Outer World.
Increase the size of the Hollow World.
Move back the lips of the polar openings in one or both worlds.

Placement 2

Happily, we have already done this with Placement 2: by rescaling the latitudes, I shrunk the dimensions of the Outer World. But is it enough? Let’s count the hexes and see.

I count roughly 12.25 hexes. 12.25 x 72 = 882. 882 / 10 x 360 = 31, 752 miles circumference. Radius 5,053 miles, diameter 10,107 miles.

It still seems rather big, but let’s mock it up anyway, just to be sure:

Still no good.

Talk about hitting a brick wall!

Options

I don’t like option 3 (bringing back the polar lips to lower latitudes), which leaves us with just the first two options: further shrink the Outer World, and enlarge the Hollow World. Maybe we can try and make things meet halfway.

We can probably squeeze the Outer World a bit more. These circumference numbers in the thirty thousands were unexpected, because previous fan estimates have been in the twenty thousands, with a Mystara just a little bit bigger than Earth. The true size of the world doesn’t really matter, as long as everything fits, so we can play with this further.

It actually also deals with an issue I had, which is that at 30ºN, the Sea of Dread coast with Karameikos and Thyatis seems awfully tropical. However, shifting latitudes will also result in northern Alphatia and northern Norwold being at a much higher latitude. Perhaps this fits, too, though.

But let’s start with the easier part of this next attempt.

The Hollow World

Back in 2012, there was a great discussion at The Piazza about World Dimensions. We didn’t come to any firm conclusions, due to all of the issues I’ve been working through on this project. But there was a lot of discussion of the Hollow World, which we can draw from here.

Here’s the composite I came up with to measure the extents of the Hollow World’s landmasses:

Hollow World Set Iciria hex map overlaid on the same set's world map, with hexes marked off in fives from the equator for counting — Hollow World Set Iciria hex map overlaid on the same set’s world map, with hexes marked off in fives from the equator for counting

A couple of interesting things to note: the latitudes near the equator are larger north-south than the extremes near the poles; and the map shows 90ºN and S, despite the lack of an actual pole.

Regardless of the marked latitudes, it seems clear from the hex map that all of this terrain is supposed to be on a constant north-south scale. In other words, the closer together lines from 60º outwards can be safely ignored. I’m not at all worried about having to reassign latitudes, either, as it may be a necessary evil in order to get the world working right.

A little hex counting will reveal 62.5 hexes (at 40 miles per hex) from the equator to “90ºN” and 62 from the equator to “60ºS”. The north shows more water, so let’s ignore that and call it 124 hexes. 124 x 40 = 4,960 miles. Or we could think of it as 125 hexes for a nice even 5,000 miles.

At this point in the 2012 map I went on to extrapolate the circumference, assuming these figures stretched from imaginary pole to pole; the “extra” lands could then be folded into the actual polar openings. (Given the above figures, this would be 9,920 or 10,000 miles.)

But that’s not what I’m thinking this time. First, the compressed latitudes are a big clue that these lands are not supposed to extend to the imaginary poles, and therefore are not supposed to fall into the polar openings — at least not very much. Further, my reproduction of the Hollow World map, which “fixed” these squashed latitudes, turning them into regular latitudes, was probably a mistake. I now believe that these regions should be left unstretched.

The biggest point is that I think these lands should largely fit into the unwarped space between the polar lips, i.e. between 66ºN and 66ºS — or at least a smaller area.

We can calculate an ideal area by extrapolating the circumference in the same way we did with the Outer World: by counting hexes and finding out the number of miles per degree. If we do this for the equatorial area, I think we will reach a larger figure than we did before.

I count roughly 8 hexes, so: 8 x 40 = 320. 320 / 10 * 360 = 11,520 miles. (This is also what Hugin came up with in the 2012 thread.)

Unfortunately, this is not helping: the official measurement was 11,908 miles, and our estimate has actually ended up smaller. If that’s the case, we’d be better to go with the official number, because making the Hollow World smaller at this point is simply not an option.

Darn.

Placement 3

So we’re left with shrinking the Outer World. I’m beginning to feel increasingly desperate… Are we going to be able to make this work at all? Keeping Davania in the same Champions of Mystara-based location, I’ve squashed the latitudes as much as I dare to.

Lands past the red line start to fold into the polar openings, but until around 70º it’s not really obvious that this is starting to happen. Nevertheless, Frosthaven will be squarely within the opening.

Ambur, Ar and Frisland now fall between 60 and 63ºN or so, and Alpha is at about 60ºN too. Farend looks to be almost at 65ºN. Take a close look at the map to see all the other latitudes.

So how does this measure up? Time for some more hex counting:

Placement 3 close-up showing 10º of latitude

I count about 10.75 hexes. 10.75 x 72 = 774. 774 / 10 x 360 = 27,864 miles circumference. Better, but is it going to work?

We do at least have polar openings this time, but I don’t know if I’d call this working.

And yet I can’t see shrinking the Outer World any more than this — we’re already going into dangerous territory by shrinking it this much.

What other options could there be?

Should we move the equator north to the PWA2 location? I somehow doubt that would allow us to shrink the world much more, if at all, because southern Davania can’t all be shunted into the polar openings.

But what else is there to do?

Should we enlarge the Hollow World? We may be able to squeeze another thousand miles or two in there, in order to open up the polar openings a bit. That may be the best bet — and I can stretch the northern and southern areas to compensate a little, or rather leave them as they are on my reprojected Hollow World map.

Any thoughts on all of this?

13 February 2016

Lining Up Mystara XII

Atlas of Mystara, Davania, Mystara, Skothar 9

Reconciling the World Map II

Skothar

Let’s start with Mystara’s eastern continent. We actually have most of the western coast of this in hex maps, but the actual continent is huge, so it’s just the tip of the iceberg.

I already established last time that I’d rather not apply a rotation to Skothar’s Master Set outline if at all possible, in order to maintain its latitudes. I’d also rather keep it the same scale as Brun if at all possible. Let’s see how that works out:

Master Set Skothar (same scaling as Brun, no rotation) overlaid on the hex maps — *Master Set* Skothar (same scaling as Brun, no rotation) overlaid on the hex maps

This is not too bad. I based the fit on the Bay of Thorin, lining up the southern coast with the edge of Minaea on the hex maps.

Of course there are numerous problems. First and foremost, the northwestern coast is quite far out from its hex map version. I’m tempted to revise the hex map to go with the world map here, because we haven’t generally been placing a lot of faith in the Dawn of the Emperors 72 mile per hex map. However, the standard up until now has been to go with the hex maps, and this seems to be where community consensus lies every time. So let’s go with the hex coastline and join it to the world map coastline as best we can.

Esterhold is actually the least of our problems, because we have all of it on hex maps. I’m happy with this fit, even it’s a bit loose, because it’s only acting as a placement guide.

Minaea is more problematic, because the coastline is very different. At first I thought perhaps the map needed rescaling, because doing so would surely make the northwestern coastline line up, too. But this would require Skothar to be scaled significantly larger than Brun, which seems rather undesirable. It seems better to preserve the relative sizes of the continents, after all.

Look more closely at the small bay on the world map outline that’s entirely missing from Minaea’s hex map. The coastline after that bay seems to line up pretty well with where the hex maps were going. This leads us to another decision between hex map and world map: do we incorporate this small bay into Minaea’s hex maps, or just ignore it?

Actually, I think we could do both, simply by shifting the bay two hexes to the east. That would allow us to keep the detail while preserving the authenticity of the printed hex map.

Finally, I’m quite happy with the placement of the isles north of Alphatia. This is perhaps the most arbitrary thing about this placement, but I’d rather have them placed relative to Skothar, with no rotation applied, than lump them in with Brun. The distance between the islands and Brun, and indeed Alphatia, seems fine. It should be noted that the hex maps require a placement of Skothar that’s further south than the world map has it, so these islands have also moved south. It seems to make sense to keep them in line with Skothar and especially with the Nentsun Peninsula.

So to conclude, I think this is the best fit we can get for Skothar. We keep it the same scaling as Brun, but without any rotation, and join the world map outlines to the hex maps as best we can.

That just leaves…

Davania

Up until now we’ve been working with areas with the hex maps locked in already, so it has been relatively easy to work out placements.

Unfortunately, Davania’s hex maps are not compatible in this way. In fact, all three of Davania’s appearances on hex maps conflict with each other. Let’s take a look:

(If you can’t see this, the maps are available here and here.)

This comparison shows our base hex maps with the three sources for Davania: Champions of Mystara‘s 24 mile per hex map (the corner of Davania is visible on the Serpent Peninsula map); Dawn of the Emperors‘ 72 mile per hex map (showing the Thyatian Hinterlands); and Poor Wizard’s Almanac II‘s poster map (showing the largest chunk of Davania on any hex map). Since Champions and Dawn‘s maps only barely overlap each other, I put them together.

Note first how both Kastelios and Garganin are one hex to the north in Champions compared with PWA2. The coast itself is about a hex and a half to the north. This location discrepancy aside, these two maps give similar views of this small area. The most important point is that Champions places Davania closer to the Serpent Peninsula.

On the other hand, Dawn‘s map and PWA2 are completely at odds with each other. The really big difference is in the shape of the land itself, and the position of the Thyatian Hinterlands. They both place Davania’s northern tip at roughly the same latitude.

To sum up the problem:

Sources conflict on Davania’s exact position
They also disagree on the shape of the coastline

What to do?

Latitudes and the Equator

My preference is to take a side-route at this point and deal with the issue of latitudes and the equator. Why? Because the position of Davania is inextricably tied up with the position of the equator — which in turn largely dictates where the rest of the latitudes fall.

The equator’s location is another area where official maps disagree. Michele Carpita produced this map which shows the situation quite nicely:

The Latitude Issue by Michele Carpita — *The Latitude Issue* by Michele Carpita

This is the Hollow World Set Outer World map. It’s a very problematic map, as I have already stated, but its latitudes are not necessarily affected by this, so let’s take a look.

The equator on this map is almost the same as that given in The Voyage of the Princess Ark (marked VotPA on this map, in light green). It brushes the northern tip of Izonda, bisects the Adakkian Mounts and the Jungle Coast, passes just north of the Cape Eriadna next to the Pass of Cestia, north of Cestia itself, then under the “hook” of Oceania. Not visible on this map is that it brushes the southernmost tip of Skothar in the far east. I remade the relevant Princess Ark map for reference.

The red line shows PWA2’s equator, which is further north. This one is problematic, and I much prefer the Princess Ark maps as a source for this.

The rest of the latitudes are not quite so important, except that official sources place Thanegioth (presumably the Isle of Dread) at 20ºN, Thyatis at 30ºN, Landfall at 40ºN, and Farend is 60ºN. (These are from TM1’s “Sunrise and Sunset” table, and were repeated in Poor Wizard’s Almanac II.) These are marked on Michele’s map above in blue. Note how the Hollow World Set‘s map has a totally different set of latitudes.

I contacted Bruce Heard about these issues, and he replied that his calculations may have been wonky, and may need updating.

My conclusion is that we should use these numbers as guides, and see how things go. I highly doubt it will be possible to make all of them work, but we can use the most important of them — Thyatis being at 30ºN — together with the equator location to scale the rest of the latitudes properly.

Note also that the locations of the tropics is not relevant, because these are determined by the axial tilt — which we have already arbitrarily set at 24º. Thus, the tropics will appear at 24ºN and 24ºS. These were not consistently placed in official maps, so I am disregarding them.

Davania and the Equator

First, let’s overlay Davania’s Master Set outline with Dragon 155’s map showing the location of the equator. I’ve added in Dragon 158’s map for good measure.

Dragon 155 and 158 maps with Master Set Davania outline overlaid in red — Dragon 155 and 158 maps with *Master Set* Davania outline overlaid in red

I went for a best fit with these rather than lining up the meridians. So far so good. They fit pretty well. The northern tip of Davania seems slightly out of sync, though.

The question is, how does this relate to the rest of the world?

Well, it depends on what we use as a reference point. The Master Set map itself is out of the question, as we’ve already seen that it had to be cut up and spread out in order to match the hex maps. But let’s slot this in anyway just to see how it looks:

Dragon 155 and 158 maps with the full Master Set world map — Dragon 155 and 158 maps with the full *Master Set* world map

It could be better… Ochalea and the Pearl Islands already being out of sync bodes ill for how this will look with the hex maps. The problem is, what do we line it up with?

Let’s explore some possible placements:

Placement 1

Placement 1 is based on Champions of Mystara‘s Serpent Peninsula map, lining up Davania’s outline with the small area showing Kastelios and Garganin. The black outlines over the northern continents and landmasses are the Master Set map’s coasts, in their placement

Pro — the 24 mile per hex map is the largest scale to show Davania on any map, and could therefore be considered to be the most accurate.
Pro — the Master Set outlines of Ochalea and Dwair match hex map Ochalea and Dwair almost perfectly. This means that the relative locations of Ochalea, the closest of the Pearl Islands, and Davania match the Master Set world map.
Con — the Serpent Peninsula is in a totally different position relative to Davania from where it fits on the Master Set map. However, Champions‘ map could be considered to supersede this anyway.
Con — with the equator in this location and Thyatis at 30ºN, the extreme northern and southern areas of the world are devoid of land, meaning that there may be more space between landmasses within the polar openings.

Placement 1 full world view; the red line shows 66º latitude, where the polar lip begins

This placement could be made to work if we revise latitudes so that Thyatis is a bit north of 30ºN.

Placement 2

This is just placement 1 with latitudes redefined so that the landmasses stretch almost to the limits of the world. This should result in a placement similar to the one I modelled back in Lining Up Mystara X.

Specifically, the north polar opening should look something like this:

Mystara's north pole from the outside — Mystara’s north pole from the outside using the preliminary model; this is similar to how it would look using Placement 2

Pro — the polar openings would look more like they do on official maps, with roughly the same amount of landmasses folding into the poles.
Con — Thyatis would be at around 32ºN, and none of the other official latitudes would be quite correct. They would be reasonably close, though.

Other Placements

Other possible placements include lining up Davania with PWA2 or Dawn of the Emperors‘ maps; rethinking the equator and going with PWA2’s location for it; or trying to keep the relative placement between the Thanegioth Peninsula and Davania from the Master Set map (this last would involve Davania bumping into Dwair, unfortunately).

There’s an interesting effect when moving Davania: moving it south moves the equator south, resulting in Brun and Skothar moving north and being shrunk slightly. Moving it north moves Brun and Skothar closer to the equator, and enlarges them slightly. For the same reason, the Princess Ark equator makes Davania slightly bigger, as it straddles the equator more, while the PWA2 equator leaves it slightly smaller — and Brun and Skothar slightly larger.

Conclusions

This isn’t something I can just decide by myself, so I’d love to hear some feedback before continuing. Having said that, I also want to continue with this ASAP, as my mid-February deadline is upon us, and I need to get this done and move on to my next project.