Moon Hotspot

Chintan · January 30, 2011

It appears that 100-125/pi*dist is the wrong formula. It gets some of the points wrong.

The actual formula is 100-x*dist, where is x is somewhere betweeen 39.57151035 and 39.60015756. I got those bounds using about 100 different moon wonder location/hotspot combinations entered here.

125/pi is 39.789, which doesn't fall between 39.58324298 and 39.60015756.

I'm just going to use 39.6 until someone comes up with an example for which that doesn't work, or comes up with a more elegant number within those bounds. Why the admin would pick 39.6 I don't know. Maybe I'll start calling 39.6 Kevin's constant. :lol1:

EDIT: I narrowed the bounds a bit more. 39.6 still falls within the bounds.

Edited January 30, 2011 by Chintan

Provost Zakharov · January 30, 2011

Cool, so you are going to try to automate the process even more?

If you're interested in reducing the complexity of the search from 360*180 evaluations down to a much smaller number, you can compute a continuous approximation to the discrete problem as your initial guess, then just examine a small number of points around that. Of course it's not really necessary with fast computers, but perhaps you find it mathematically interesting.

Also, for the record, I was aware that the formula [url="http://forums.cybernations.net/index.php?showtopic=71214&view=findpost&p=2152464"]isn't exact[/url]

Chintan · January 30, 2011

[quote name='Provost Zakharov' timestamp='1296388773' post='2611028']
Cool, so you are going to try to automate the process even more?

If you're interested in reducing the complexity of the search from 360*180 evaluations down to a much smaller number, you can compute a continuous approximation to the discrete problem as your initial guess, then just examine a small number of points around that. Of course it's not really necessary with fast computers, but perhaps you find it mathematically interesting.

Also, for the record, I was aware that the formula [url="http://forums.cybernations.net/index.php?showtopic=71214&view=findpost&p=2152464"]isn't exact[/url]
[/quote]

Mostly automated at least for now. I still have to copy the coords from the forums into MATLAB, and then copy the plots and priority points back. Also, I sometimes manually edit the priority points to pick ones that will narrow down the possibilities better. For example, if there's just one 50% point, the best one to pick next is the one directly opposite the known 50% point, because that's least likely to be 50%, so it will narrow down the number of choice most. Right now my program will just pick a few arbitrary red points to be priority points though, so I still have to figure out a good way to pick those well automatically.

It would be cool to have this as a website which is fully automated, where people enter there coords into the website and it automatically updates the map and suggests what to try next.

Narrowing down your guess initially using a continuous approximation works well if you have 3 non-50% points spaced far apart, but otherwise there might be problems with having 2 possible regions, or a really long arc of possible locations.

Edited January 30, 2011 by Chintan

Chintan · January 30, 2011

[quote name='Chintan' timestamp='1296391695' post='2611051']
Narrowing down your guess initially using a continuous approximation works well if you have 3 non-50% points spaced far apart, but otherwise there might be problems with having 2 possible regions, or a really long arc of possible locations.
[/quote]

For example: This is what you get using the first 2 points from the Dec 2010 moon hotspot: (-13, -168): 64% and
(-15, -169): 65%.

Even though there are only 2 points, and they're really close to each other, they narrow down the possibilities for where the hotspot could be quite a bit, especially if you only consider the red points.

[img]http://lh6.ggpht.com/_aIYowgo2fqo/TUVfz82JnII/AAAAAAAAAKI/xZFMO191F9Y/s0/Screen%20shot%202011-01-30%20at%204.53.02%20AM.png[/img]

Coffee Shock · January 30, 2011

[quote name='Provost Zakharov' timestamp='1296388773' post='2611028']
If you're interested in reducing the complexity of the search from 360*180 evaluations down to a much smaller number, you can compute a continuous approximation to the discrete problem as your initial guess, then just examine a small number of points around that. Of course it's not really necessary with fast computers, but perhaps you find it mathematically interesting.
[/quote]
There is a much easier way to reduce the number of possible hotspot locations as they aren’t as random as you may think.
Hint: Plot all hotspots found so far.

My hotspot finding code, maybe it’s of some use to someone.

[code]
struct pos_t {
double lat;
double lng;
int efficacy;
} static const pos_data[] = {

//Moon 2010-11
{70.00000002, 7, 50},

{19.31114335506464, -81.5625, 50},
{-37.16031654673676, -101.25, 55},
{17.978733095556155, 113.5546875, 50},

{30.14512718337613, 146.953125, 58},

{-9, -161, 93},
{-34, 145, 67},
{-12, -19, 50},
{-17, -173, 96},
{37.71859032558813, -129.375, 56},
};

static int calc_efficacy(double h_lat, double h_lng, double base_lat, double base_lng){
const double pi = 3.14159265358979323846264338327950288;
const double deg2rad = pi / 180;
const double magic_constant = 39.5856603902019127; //pi*12.6 ???

double h_lat_rad = h_lat * deg2rad;
double h_long_rad = h_lng * deg2rad;
double base_lat_rad = base_lat * deg2rad;
double base_long_rad = base_lng * deg2rad;
double distance = acos(sin(base_lat_rad) * sin(h_lat_rad) + cos(base_lat_rad) * cos(h_lat_rad) * cos(h_long_rad - base_long_rad));
return std::max(int(100 - distance * magic_constant), 50);
}

void moon_mars_find_hotspot(){
const int num_data_points = sizeof(pos_data) / sizeof(pos_data[0]);

std::vector<pos_t> scores;
for(int lat = -85; lat <= 85; lat++){
for(int lng = -180; lng <= 180; lng++){
int diff_sum = 0;
for(int i = 0; i < num_data_points; i++){
int efficacy = calc_efficacy(lat, lng, pos_data[i].lat, pos_data[i].lng);
diff_sum += std::abs(efficacy - pos_data[i].efficacy);
}
pos_t tmp_pos = {lat, lng, diff_sum};
scores.push_back(tmp_pos);
}
}

int num_to_print = 30;
int num_possible_hotspots = 0;
std::vector<pos_t>::iterator it = scores.begin();
for(; it != scores.end(); ++it){
if(it->efficacy == 0){
num_possible_hotspots++;
if(num_to_print >= num_possible_hotspots){
bool tilt = calc_efficacy(it->lat, it->lng, it->lat, it->lng) != 100;
std::cout<<"lat="<<std::setw(5)<<it->lat<<(tilt ? "*" : " ")<<" lng="<<std::setw(5)<<it->lng<<std::endl;
}
}
}
std::cout<<"Possible hotspots: "<<num_possible_hotspots<<std::endl;
}
[/code]

Provost Zakharov · January 31, 2011

[quote name='Chintan' timestamp='1296391695' post='2611051']
It would be cool to have this as a website which is fully automated, where people enter there coords into the website and it automatically updates the map and suggests what to try next.[/quote]

Yeah that would be pretty neato. One thing to be careful about though, is you'll want to avoid recommending the same guess to more than one person, which would be a waste.

[quote]Narrowing down your guess initially using a continuous approximation works well if you have 3 non-50% points spaced far apart, but otherwise there might be problems with having 2 possible regions, or a really long arc of possible locations.
[/quote]

Actually it works well with 2 points as well. If there are two possible regions you want to guess inbetween them to get the average (avoid a chance of getting 50%) and that's exactly what the continuous approx will do.

[quote name='Coffee Shock' timestamp='1296427931' post='2611631']
There is a much easier way to reduce the number of possible hotspot locations as they aren’t as random as you may think.
Hint: Plot all hotspots found so far. [/quote]

I'm talking about reducing the number of evaluations of the efficiency function, not the number of possible hot spots.

I never said anything about hotspot locations being "random", so I'm not sure where that's coming from.

Also, FYI, giving out "Hints" with winky emoticons comes across somewhat condescending :rolleyes:

Chintan · January 31, 2011

[quote name='Coffee Shock' timestamp='1296427931' post='2611631']
There is a much easier way to reduce the number of possible hotspot locations as they aren’t as random as you may think.
Hint: Plot all hotspots found so far.
[/quote]

Wow.

Now why does mars have 2 outliers? :huh:

[img]http://lh4.ggpht.com/_aIYowgo2fqo/TUaS0PeBLOI/AAAAAAAAAKc/a4BfnhuiSmE/s800/Screen%20shot%202011-01-31%20at%202.43.51%20AM.png[/img]

Edited January 31, 2011 by Chintan

Chintan · February 1, 2011

Ok, here we go. Someone post the efficiency at last month's hotspot to begin, and I'll figure out the best place to test next.

I'm going to be logged on for a while, and can calculate the best location to try next, so if you have multiple moon wonders, wait for me to suggest a location, then move 1 wonder, wait for me to suggest another location, then move the next one, etc. That way you get the most out of your moves.