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How can i calculate the angle between 2 vectors lat long?

Posted on 2006-05-02
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How can i calculate the angle between 2 vectors lat long?

x: lat, long
a: -95.77071229704562,34.9343240443434
b: -95.76835645203101,34.9339768366878
c: -95.774587384548,34.9259077248493

vector A is ba
vector B is bc

I have the distance in km of both vectors

A 0.218 km
B 1.062 km


thanks

Richard
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Question by:verintsupport
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Expert Comment

by:WelkinMaze
ID: 16589592
the angle is arcos((v1.v2)/(|v1||v2|))
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Author Comment

by:verintsupport
ID: 16589612
Thank you

Now how do you get v1.v2 and |v1||v2| with simple math.
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Accepted Solution

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WelkinMaze earned 2000 total points
ID: 16589690
And
A.B = Ax * Bx + Ay * By
You have the lat and long of the points so you can calculate Ax, Ay, Bx, By by subtracting the lats and longs of the corresponding points (assume A and B are v1 and v2).
So you have the way to calculate v1.v2

You have the magnitudes of v1 and v2 which are 0.218 km and 1.062 km
So by multiplying them you have |v1||v2|
And that's all you need.
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LVL 27

Expert Comment

by:d-glitch
ID: 16589810
a     -95.770712     34.934324      
b     -95.768356     34.933977      
c     -95.774587     34.925908      

Subtract the b coordinates to redefine the origin:

a'      -0.002356      0.000347     171.62 deg      use atan2(long, lat) to find the heading
b'       0.000000      0.000000      
c'      -0.006231     -0.008069     232.32 deg

                                                 60.71 deg      the difference between the headings.

All this is a planar approximation to a sphere,
which should be okay considering the small distances involved.
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Expert Comment

by:WelkinMaze
ID: 16589814
The lag and long values are in degrees I suppose, so you have to convert them in km.
The difference between lats of the two points for A is (-95.77071229704562  -  (-95.76835645203101))
The diff between longs of the two points for A is (34.9343240443434 - 34.9339768366878)
If these two values are named x and y, you can calculate the hypotenuse as sqrt(x*x+y*y)
Let's name this value z
Let X is the corresponding value for x in km
So you have X/x = 0.218/z
you already know x and y, thus you find the X
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Expert Comment

by:d-glitch
ID: 16589853
Ignore my answer, it is very wrong.
Degrees of long and lat are not the same size at (-95, 34).
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Expert Comment

by:WelkinMaze
ID: 16589908
You may read here about vectors if you needed further knowledge.
http://www.euclideanspace.com/maths/algebra/vectors/index.htm
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Expert Comment

by:d-glitch
ID: 16590300
At the equator, degrees of long and lat are the same size:   ~70 miles/deg
As you move north or south, deg lat stay the same, but deg long shrink by cos(lat)

So it is not correct to treat the long and lat coordinates as distances.


a    -95.770712    34.934324            
b    -95.768356    34.933977            
c    -95.774587    34.925908            


a'    -0.002356     0.000347            
b'     0.000000     0.000000            
c'    -0.006231    -0.008069            
                        
Correcting for the latitude:
            
a"    -0.001932     0.000347        169.82 deg
b"     0.000000     0.000000
c"    -0.005109    -0.008069        237.66 deg
--------------------------------------------------------
                                                 67.84 deg
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Author Comment

by:verintsupport
ID: 16591346
d-glitch,

please view question http://www.experts-exchange.com/Miscellaneous/Math_Science/Q_21835596.html for you.

Thanks

Richard
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