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Moon Hotspot


AirMe

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I suppose we need to make sure that when we post data points (say -71,67) with just integers that you in fact moved it to exactly -71.00000, 67.00000, otherwise we could be getting bad readings and wasting time and money.

On another note, I'll be buying my moon colony tomorrow, any data points to try?

On yet another note, I posted a question about the hotspot precision in the Question Center (http://forums.cybernations.net/index.php?showtopic=70679).

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Are you sure that these are all the points that could fit???

Do you have no problem with that 92% point?

No problem with the 92% or any of the points. Yeah, I'm pretty sure the feasible region is correct. I actually just double checked it via another method:

Instead of just defining one feasible region for the hotspot, we can define a feasible region with respect to any individual datapoint. The feasible region for a datapoint p is the set of points which, if they were the hotspot, would match p. This can be defined as an inequality:

feasible(p) = {x : p.value <= eff(p,x) <= p.value+1}

With this definition, the global feasible region is just the intersection of all the feasible region of each datapoint. The advantage of doing it this way, is we can use powerful existing tools for computing/graphing inequality equations.

Here is a sequence of plots I produced using this method, zooming in closer and closer to the feasible region (in yellow). Each "band" is the feasible region of a single datapoint.

zoom0.png

zoom1.png

zoom2.png

zoom3.png

I suppose we need to make sure that when we post data points (say -71,67) with just integers that you in fact moved it to exactly -71.00000, 67.00000, otherwise we could be getting bad readings and wasting time and money.

On another note, I'll be buying my moon colony tomorrow, any data points to try?

On yet another note, I posted a question about the hotspot precision in the Question Center (http://forums.cybernations.net/index.php?showtopic=70679).

Great idea posting @ the question center.

I don't have any ideas for points right now. If the question gets answered and we find out some information about the number of decimal places, I might be able to do something more; until then I consider the problem solved as far as possible.

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I like your analytic approach :) I am not the grapic type, so I am forced to used boring mathematics.

After analyzing the points we already have, I assumed that the efficiency function is eff(p) = floor(100 - d(p, h) / 50).

This functions "works" for all points of which efficiency > 90% using many points inside the 99% region (see examples below).

Using (-70.9225, 67.01) as the hotspot, I get an efficiency of 93% for the 92% point (-79, 100) and 99% for (-71, 71.5), of which actual efficiency is 98%.

For reference, I am posting my results using the following guesses:

G1 = (-71, 65.1)

G2 = (-71, 66.2)

G3 = (-70.9225, 67.01) (your point)

hotspotsheet.png

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I assumed that the efficiency function is eff(p) = floor(100 - d(p, h) / 50).

That's why you aren't matching the further-out points, the constant 50 isn't quite correct.

The formula I came up with (using line fitting) is: eff(p) = floor(100 - 125*d(p,h)/pi) where d(p,h) is calculated with r = 1. I think it's better to do it this way so we don't need to know the actual number admin used for the moon radius. I quoted this formula in one of my earlier posts btw.

If I work that formula into the same form as yours, it comes out to something like 43.6556 instead of 50, using 1737km for the moon radius.

Edited by Provost Zakharov
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If we are right and the coordinates are not integers, it seems that there is no way to get a perfect mathematical solution (efficiency 100%). Getting close to it, inside the 99% zone, is possible, and I think that the difference is insignificant.

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I was hoping that the points are still distributed on a grid, just with smaller spacing (like 0.01) so that we might still be able to find it. But, now that I think about it, I realize it would never monetarily be worth all the tries it would require to find it at that resolution. So I guess we can call the problem solved at this point. I'm looking forward to using our method to solve for a far away point next month =)

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So I had all of my wonders at 97% (which likely means that it's not profitable to move them), but in the interest of furthering this exploration, I moved them all anyway. So here's what I have to contribute. Hope this helps for those of you trying to run the calculations!

-68,72 ==> 97%

-71,62 ==> 98%

-71,63 ==> 99%

-72,65 ==> 99%

Edit: and yes, those were precise integer coordinates. I'm too lazy to type a bunch of zeros :)

Edited by King Irwin
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Oh good grief. I've tried moving my moon base three times, and I've managed to mess it up every time.

First two times I wasn't paying close enough to the order, then sign, of the recommended coordinates. I guess that sort of thing is bound to happen when you're in a hurry.

This time I had plenty of time, I was being duly cautious. Then, while highlighting the latitude number in the movement link I'd pasted to my address bar, I somehow managed to click and drag the address from the bar, to the bar.

Third attempted move, and still at 50% efficiency! :facepalm:

Next time I'll use notepad. Or maybe I just have to accept the fact that I'm a klutz and hire a team of trained Hotspot Relocation Technicians.

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