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PostPosted: Mon Feb 02, 2015 2:52 pm 
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A STUDY OF LOCATE: MAGNITUDE, DIRECTION, AND THE GRID
Researched by: Accepted Thuvia Aldelorna
Assisted by: Accepted Varina do Almany a'Morlin



Introduction
Much progress has been made previously on the subject of Locating, and several useful maps created by Accepted Khahliana and Accepted Aria exist to show the relative locations of Zones to each other. Using these, a channeler who receives a Locate showing a person or item to be "very far north" can usually narrow the location to within a few zones.

This study intends to investigate the meaning of the locate messages given. Terms such as 'far', 'very far', and 'extremely far' will be explained mathematically in relation to the Coordinate Grid in which the zones are actually located. Similarly, the 8 directions of N, S, E, W and NW, SW, SE, NE will also be explained in detail.


Method
Participants
I was assisted at times by Accepted Varina who helped pinpoint certain locates where no unique mobs and items were available.
Weaves Used
Locate Life, Locate Object, and Travel
Procedure
Character level was 39 for the duration of the testing.
Travel was kept at 99% for the duration of the test for safer movement.
The two Locate weaves were gradually levelled up during testing. Different prac% in each was used to test the amount needed to Locate a given point.


Results
The Zones may be thought of as occupying a grid, with Whitebridge occupying the central point. The distance and direction from one Zone to another within the Grid is not always the same as one would expect. Two Zones which, in the game, have a N-S connection may actually be located diagonally from each other, or may not occupy adjacent spots at all.

Magnitude
The magnitude of the distance given by a Locate is a function of the locations of the two Zones within the grid. Two zones which occupy the game grid spot, such as Inner Caemlyn and Outer Caemlyn (zones 010 and 011, see Figure 1), or Far Madding North and Far Madding South (shown as L and M, see Figure 1), will show a distance of "somewhere around here", even though they are technically separate zones. In this case, their distance is 0.

Beyond that, magnitude is related to the shortest distance between two zones, given either by a simple straight line when zones are located along the same horizontal or vertical axis, or by the hypotenuse formed by their (x,y) coordinate separation.

Figure 1. Consider zones 016 (Whitebridge) and 063 (Aringill). From the Grid map, we see they both lie along the same axis, with a separation of 6 grid units along the x-axis and 0 grid units along the y-axis. Their distance is then found to be

10*SQRT(6^2 + 0^2) = 60

Thus, one must have Locate practiced to at least 60% to find an object or life form when Locating in one from the other. Similarly, to avoid misporting one should have Travel to at least 60%.

Figure 1. Now consider zones 016 (Whitebridge) and 025 (Tar Valon). The grid indicates an x-axis distance of 6 units and a y-axis distance of 5 units. Their distance is then found to be

10*SQRT(6^2 + 5^2) = 78.1

As the MUD deals in integer units for such things, the value is rounded up to 79. This value is then the minimum needed to Locate from one to the other. At 78%, one will never succeed in a locate between these two, while 79% and up gaurantees success.

This was initially noticed when attempting to Locate from zone 025 (Tar Valon) to zone 103 (Lugard). Having Locate Life practiced to 86% and Locate Object to 85%, life forms could be found but never objects. Subsequent testing with other distances has verified this.

On this basis, we are able to come up with the following graphic.

Figure 2.

Taking the central point to be the Zone one is Locating from, the required Locate% can be calculated for all possible points according to the rules noted above. As 99% is the maximum amount one can practice in Locate or Travel, so too are the distances limited by them.

From this data and in-game observations, we can now assign boundary values for the magnitude values of "somewhere around here", Direction Only (ie "North"), Far, Very Far, and Extremely Far.
The values contained within each go up in increments of 30. In theory, an 11 Int Channeler with minimum Elements for a Locate weave could practice 1 time and have 9% profficiency. This would enable the character to Locate a life form or object within their current Grid box only. Similarly, practicing up to 29% enables Locating to any point whose distance value on the grid (Figure 2) is less than or equal to 29, and so on all the way to 99%.

Figure 3 provides a graphical view of these limits.


Direction
As the magnitude of the distance between zones depends on their Grid locations, so too does the direction given. The direction of a zone is either given as a Cardinal (N,S,E,W) or Ordinal (NE,NW,SE,SW) term, preceded by a magnitude whose value was described in the section previous.

A direction will be Cardinal if the absolute value of the ratio of its x distance to y distance is either <= 0.4 or >= 2.5.
Similarly, a direction will be Ordinal if the same ratio is > 0.4 and < 2.5.

Figure 4 provides a graphical view of these limits.

As an example, let us consider Locating from Lugard (103) to Tar Valon (025). Located (3,8) from Lugard, Tar Valon will show as "Very Far North", since 3/8 = 0.375, which is less than 0.4 and thus a Cardinal.

If we instead Locate from Lugard to the zone labelled E (Tar Valon-Cairhien Road), it will instead show as "Very Far Northeast", as its distance of (3,7) from Lugard yields a ratio of ~0.429, which is both greater than 0.4 and less than 2.5 and thus an Ordinal.

Figure 5 provides a complete view of all possible Locates from a given zone, with their ranges of magnitude and direction given.


Conclusion
The information gathered in this study can be of use in more than one way. From a Support standpoint, knowing better details of where a zone is and what a locate message means can help to better pinpoints targets. Depending on the level of Locate distance required, one can more accurately tailor practices to achieve this with less waste.

Further research will build upon this. A follow-on paper will be released at a future time, with the aim to completely Map all zones on the Grid. While a previous version of such a map is still available, many zones have been added since, and some existing ones have moved. The mapping project will aim to correct any errors resulting from such accumulated changes over the years, and introduce new zones into their appropriate locations.


Appendix:

Figure 1 - Sample Grid Portion

Figure 2 - Locate Magnitudes

Figure 3 - Locate Magnitude Areas Colored

Figure 4 - Locate Direction Areas Colored

Figure 5 - Locate Directions

See Also:
Locate Zone Maps by Khahliana


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