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Yaga

The Wurm Universe - Part 1: Basic Metrics

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This is the first part of a series of articles on the "physics and astronomy" of the universe of Wurm Online, trying to describe the structure, dynamics and "laws of nature" of our in-game world . The information compiled here has been carefully researched and discussed by a small group of players who call themselves "The Wurm Astronomical Society" (Docterchese, McGarnicle, Valdor, WojorowskiPL and Yaga).
 
Part 1 summarizes all we know about the basic dimensions of the Wurm universe: tiles, distances, slopes and heights.

 

Part 2 is here: http://forum.wurmonline.com/index.php?/topic/143679-the-wurm-universe-part-2-time-date-and-calendar/

 



The most basic unit of measurement is defined by the size of a tile. Tiles are the equally sized squares that the landscape of Wurm Online is entirely composed of. In the 3D world of Wurm a tile can be either flat or inclined, so that one or more of its corners can be higher or lower than the others.
 
In all our calculations we used the following fundamental information, given in the Wurmpedia (http://www.wurmpedia.com/index.php/Tile) :

 

Quote

A tile is a 4 meter by 4 meter square.

 

 How can we measure distances and heights in Wurm? Originally we tried to use a spyglass, because it displays the distance between the observer and an object pointed to by the crosshairs:

 

 
BlQD6Jo.png

 
Using a spyglass is sufficient to verify the basic unit of measurement (1 tile = 4m x 4m) and to measure linear distances within a reasonable accuracy. However, when it comes to measuring heights it turned out that a spyglass is not quite accurate enough to yield reliable results.
 
Thus we need to use a more precise method: triangulation! This method uses basic trigonometric functions to determine the height of an object.

 
AN6wZja.png

 
To determine the height H of an object, you define a reference point, take a screenshot (as shown in the example) and measure the angle α between the ground and the top of the object, as seen from the reference point. (As we have no means to measure angles in-game, we need to use a graphics program to determine the angle on the screenshot.) Additionally you need to measure the horizontal distance, which you obtain by counting the number of tiles T (remember: one tile corresponds to a distance of 4 meters). You then get the height H by using this formula:
 

Quote

H = T tan α

 

 
Here is an example: For a distance of 40 tiles (T=160m) we measure an angle of 14°. Thus, our avatar of Magranon would have a height of:

 

 

H = 160m x tan(14°) = 40m

 
(Please note that the result has to be rounded, due to the immanent inaccuracy of this method.)
 
Here is a list of heights for some arbitrary objects, just to give some examples (sorry, this forum doesn't provide tables):

  • Player character: 1.7m
  • House wall (1 floor): 3.0m (note: the ground floor of a house has a height of 3.3m)
  • Pillar: 5.6m
  • Freedom tower (incl. flag): 25m
  • Colossus: 34m
  • Deity avatar 40m

Finally, talking about measuring heights, we must look at another basic unit of measurement used in the Wurm universe: dirts. Whenever we see sloped tiles defining the 3D landscape the elevation of slopes is given in terms of the amount of "dirts dropped". When terraforming the land you use a shovel to dig or drop dirt - you add or subtract one "unit of dirt" with each action of the shovel.
 
Using the method of triangulation described above we can find out how these "units of dirt" correspond to metric units. By dropping dirt we make elevated platforms of various heights, thus creating different slopes. We then position an observer in a pit, so that the eye level is slightly above the ground, and take screenshots:

 
DNu3mBV.jpg   ..   VnNLVqP.jpg
 
EvVyxOw.jpg?1

 
Measuring the angles and using the formula given above, we can triangulate the elevation of the platform:

 
ZGZHvAQ.jpg   ..   2LKCKSz.jpg

 
We obtain the following table (for slopes spanning a single tile):
 
Slope .. Angle .. Elevation (m)
----------------------------------------
10 ...... 14.0 .... 1.0
20 ...... 26.6 .... 2.0
30 ...... 36.9 .... 3.0
40 ...... 45.0 .... 4.0
50 ...... 51.3 .... 5.0
60 ...... 56.3 .... 6.0
70 ...... 60.3 .... 7.0
80 ...... 63.4 .... 8.0
90 ...... 66.0 .... 9.0
100 ..... 68.2 ... 10.0
150 ..... 75.1 ... 15.0
200 ..... 78.7 ... 20.0


 
Thus, there is a simple relation between "dirts" and metric units:

 

Quote

1 meter = 10 dirts.

 

 
Using this method it is also possible to determine the height of a player character with sufficient accuracy:

 


 
57nXESm.jpg

 

 


We plan to continue this series with the following chapters:

 

"Part 2: Time, Date and Calendar"

"Part 3: The planet Wurm  (Basic Physics)"

"Part 4: Sky and Stars (Basic Astronomy)"

"Part 5: Sol and the Moons (Celestial Mechanics of the Solar System)"  .... etc......

 

The articles can also be found in Wurmpedia.

 

Edited by Yaga
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Mmm math porn... yeah trig that angle.

It really helps we are all the same height. B)

Edited by Klaa
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Great stuff Yaga, my engineering mine loves this :)


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Yaga did a ton of great work towards this and got some solid results. In particular, knowing that 1 metre = 10 dirts and that a player is 1.7 metres tall is pretty useful stuff!


 


When I can find the time to spend literally days taking measurements, I'll do a very in-depth study of the moons of Wurm :ph34r:


Edited by Docterchese
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Well done - all of you ! :)


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Would love to see this linked to the wiki somehow.


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Part 2 of the series is here:

 

 

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And assigning different heights to objects within Wurm matters why? You build a house of one or numerous stories and there is some need to break this down into meters? The game assigns certain dimensions to these objects which are not dependent upon anyone making adjustments to make them turn out in an accurate dimension of height; therefore, there is no practical need to know the height of anything within Wurm.

 

The height of dirt dropped is again of no relevance in terms of meters of height that you have described because you just drop the dirt and the slope is then available to see by mousing over it with minimal skill required. All of Wurm is a visual experience in terms of player constructed objects composed of parts which have fixed dimensions, whatever they might be. Building something and then seeing the visual results requires no mathematics to achieve. Those sorts of computations are the Developers concerns and thankfully the player has no need to take them into consideration when constructing anything within the game.

 

To all this Wurm Universe metrics I say: irrelevance! Nicely composed and described yes but needless to consider really, other than for those who think of in-game visual effects in terms of measurements just for the sake of it.

 

=Ayes=

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1 hour ago, Ayes said:

To all this Wurm Universe metrics I say: irrelevance!

 

I disagree! (And to be honest, I don't really get your point.)

 

Why are units of measurement needed? They are essential for comparing the size and dimensions of objects - in the real world as well as in any game that "simulates" a real world! Whenever people are planning things they need to have a scale and units to measure and compare the size of things. Here are some examples of typical questions Wurm players may ask:

 

"How long will it take me to run / ride a certain distance?"

"How many floors do I have to build to get a structure that is as high as a guard tower / a hill?"

"How many dirts will I have to drop in order to hide this colossus?"

"Will this planned slope be too steep for my horse / cart?"

"Will this wall of dirt effectively block the view of characters?"

.....  and many more.

 

It is obvious that answering questions like these would be difficult without having a common system of linear units of measurement. (That's why mankind introduced linear measures a long, long time ago.) They are needed in the real world just as much as in the Wurm world.

 

Of course, it doesn't have to be the "meter" - we could use any other unit of measurement ("Wurm yards", "Rolf leagues", "Wogical miles"... ;)). Only, it seems convenient to use units everyone is familiar with - that's why Wurm devs used the meter, obviously.

 

Most players "live" in the Wurm world very much like they would in the real world. So, why wouldn't they want to measure the size and dimensions of objects and the terrain?

 

----------------------------------------------------------------------------------------------------------------------------------------

EDIT:  Oh - and of course you are welcome just to ignore this article, if metrics are not relevant for you. Nobody will ever expect you to make use of the information given here or blame you for not needing them. :)

 

Edited by Yaga
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Personally, I like having little bits of data like this--it makes the world of Wurm that much more concrete for me. 

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20 hours ago, Yaga said:

Why are units of measurement needed? They are essential for comparing the size and dimensions of objects - in the real world

 

I agree, in the real world measurements are essential in constructing objects and land development; however, within Wurm they are not but are merely *curiosity* aspects since you can build anything within Wurm without knowing any "measurements" involved. In all the examples you have cited, and any I can think of, you just go about building these things and then you find out.

 

This is my point of concluding with "irrelevance!" Nice to know for the mathematical theorists I suppose but other than that totally unnecessary for building and land shaping within Wurm. Also I am just being a contrarian here for the sake of relevance. *winks*

 

=Ayes=

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Confirms I can't fit a colossus in my mine.

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Great job, Yaga - thanks. This really helps me to understand the world of Wurm Online better.

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So I have to ask...

 

When calculating the heights of things and using the H = T tan alpha equation, did you account for the fact that the distance is measured from the perception of the player, i.e. approx. 1.5m high (where the eyes are)?

I appreciate there's an innate [which I believe is the word you're after rather than immanent] inaccuracy in it all anyway so it probably doesn't make much odds, but I know you'd want to have considered it ;)

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On 17.8.2016 at 0:24 AM, Hordern said:

So I have to ask...

 

When calculating the heights of things and using the H = T tan alpha equation, did you account for the fact that the distance is measured from the perception of the player, i.e. approx. 1.5m high (where the eyes are)?

I appreciate there's an innate [which I believe is the word you're after rather than immanent] inaccuracy in it all anyway so it probably doesn't make much odds, but I know you'd want to have considered it ;)

 

You are right that when triangulating using the observer's eye level as a baseline you usually have to take the height of the observer into account:

 

8zQsm.png

 

Or, in a simpler way: Tree height = A + H (where H = height of the observer).

 

However, this is not the method of triangulation described here. In my OP I use the "screenshot" method, because we have no easy way to measure angles in game. That method uses the ground level as a baseline (as can be seen in the second image of the OP), so there is no parallax error. (The method has an inherent inaccuracy though, as you mentioned.)

 

If your question refers to the "dirt height" measurements however (last part of the post), I tried to compensate the height of the player by positioning him in a ditch, so that the eye level more or less corresponds to the ground level (see image in OP). I hope that answers your question.

 


Generally, the relative error made by ignoring the eye-level parallax is getting smaller with the distance and height of the object measured. For example, the error can be ignored when using the simple tangent formula to measure the height of a distant mountain.

 

 

Edited by Yaga

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Aye, I got the dirt one :)

 

I think you're right with inherent too rather than innate which I used (both of which are better than immanent ;) )

As for the first part, I get what you did now. I probably didn't read it properly, I think I assumed a method which you didn't use because otherwise you'd have had other measurements too. The method I thought you might have used was measure T with the spyglass (hence my query above) although you could get around that by counting tiles, and then measure the hypotenuse with the spyglass. You could then work out the angle with some form of equation with cos (something like cos alpha = T/h).

However, it now occurs to me that far easier than that, it's a right angle triangle. To find H, just find the root of h^2/T^2, so rather than taking screenshots, just measure distance to top and bottom of the object with the spyglass, and job done (or tiles if you want to remove parallax). Having said that. due to the inherent inaccuracies you could only use this as a rough guide to things over a reasonable height.

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Yes, that would be the proper ingame method (without the need to take screenshots). However, I tried that with various objects and unfortunately it turned out to be highly inaccurate - as you suspected. The reason probably is the inaccuracy of the spyglass reading.

 

So my final solution was the "screenshot method" :-) .

 

 

Edited by Yaga

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