Tutorials - Ki coordinate to grid conversion
The form below will allow you to convert Ki coordinates into an X/Y/Z grid with one foot as the base unit of measure. Currently, the resulting grid is not "normalized" to a local grid reference; rather, any coordinates entered will be in a shared grid with all other possible coordinates in the D'ni Cavern. A future version of this utility will afford the ability to choose between normalized and shared grids.
In a related work, I have a page which, using the cavern map from the Book of Ti'ana, gives approximate Ki coordinates by clicking on the map. Click here to try the utility. Unfortunately, based on knowledge that we have gathered by exploring Ae'gura, Bevin, and Kirel, this map is highly inaccurate. Until further notice, this utility will only work if the complete image is visible in your browser window.
How it works
A Ki, when activated, shows three numbers. From left to right, the numbers are bearing, distance, and elevation. The bearing is expressed in torans, a D'ni measurement of arc, similar to degrees that we on earth (as opposed to in it (double entendre recognized but not intended)) are familiar with. Distance and elevation are both expressed in spans, a D'ni measurement roughly equivalent to 13 feet.
To convert from torans to degrees, a ratio equality function ( a/b == x/y ) is used. The simplified function looks basically like this:
degrees = 360 x ( torans_on_Ki / 62500 )
62500 is the total number of torans in a full circle, and was obtained using information found in the The Book of Ti'ana. Specifically, it is noted that 3825 torans is equivalent to 22.032 degrees.
To convert from spans to feet is even simpler. Also found in The Book of Ti'ana, 3 spans is "almost" 40 feet. Some other authorities have decided that 3 spans is exactly 40 feet, based on nothing more than speculation and in spite of the information provided. For ease of working this out on paper, I've chosen 39 feet as equivalent to 3 spans, which gives you exactly 13 feet in a span. To calculate feet from spans:
feet = 13 x spans
Once the appropriate conversions are made, some trivial algebra is applied to convert the Ki coordinate to a three-dimensional grid. The X position is determined by multiplying the sine of the bearing (now in degrees) by the distance in feet. The Y position is determined by multiplying the cosine of the bearing by the distance. The Z position, or elevation, is simply carried along.
x_pos = sin( bearing_in_degrees ) x distance_in_feet
y_pos = cos( bearing_in_degrees ) x distance_in_feet
z_pos = elevation_in_feet
There are two problems with using Ki coordinates alone for making maps. First is that the resolution of distance and elevation reported by the Ki is not sufficient - there may be a significant degree of variance. Second is that as you move farther away from Rezeero, the "width" of a bearing increases. Luckily, the super-dense resolution of the toran means that this width, at 10 miles from Rezeero, is a mere 5.3 feet or so. In the 'hoods, the width of the toran is only about 1.3 feet. At the Great Library, it's about 7 inches wide. Everything in D'ni is so big that even the 5.3 feet out at the edge of the cavern doesn't make a lot of difference. The formula for calculating this bearing width looks something like this:
width = distance_from_GZ * 2π * ( 1 / 62500 )
On the other hand, the span gives us a lot of difficulty. Standing right next to GZ, you could get a reading of 0/0/0 on your Ki, and be anywhere within 13 feet of true zero, both along the 0 toran and vertically. This is an error of about 170 cubic feet (though it's a very skinny 170 cubic feet). This is a very difficult error to express as a number without some visualization. Until I get some graphics up, here, you can just pretend from the following description: From any point you stand, face the GZ. Walk backwards 6.5 feet. Mark this position with a cone. Walk forwards 13 feet and mark this position with another cone. Not caring about elevation, you could actually be anywhere between those cones and get the same Ki readout (try it). That same area, between the cones, applies vertically, though. So, you have to multiply the error to be anywhere between those cones, and also anywhere between the top of your hard hat and 6.5 feet underground. Now, if you're at the eastern edge of the cavern, you have to extend your arms out, parallel to the ground, and include all that space in your error factor, as well.
In the following top-down map, you are standing just a few feet from Rezeero. Your Ki tells you that you are exactly at the blue point, but you could be anywhere in the thin yellow rectangle. This error is mostly due to your Ki not reporting increments of spans, only whole spans. This image is not to scale, and should only be used for illustration of this error concept. Click on the image to enlarge.
If you were to draw a map using just these coordinates, it would probably appear to be scrunched up like GZ was some black hole sucking everything in to it. Fortunately, we have some other tricks that we can use in addition to GZ coordinates which will probably make GZ readings pretty valuable, after all. Look into the other tutorials for those answers, but basically we will use GZ coordinates as LOPs.
Without further ado, the converter. Simply enter your coordinates and click Add Point. Elevation is preserved after each addition.