How can I get then angle between a line connecting two points in the plot and a vector (with only direction specified)?

As you can see above, I have x and y co-ordinates for n number of Wind Turbines in a wind farm. Suppose there is a vector (wind speed direction) with direction in degrees, how do i find the angle between the line connecting all the other points to any point i,j in the x-y plane and the direction vector (whose onlyu data known is the direction?

xy=[0 0

0 800

0 1600

0 2400

500 0

500 800

500 1600

500 2400

1000 0

1000 800

1000 1600

1000 2400

1500 0

1500 800

1500 1600

1500 2400

2000 0

2000 800

2000 1600

2000 2400];

The above matrix shows the x-y coordiantes of 20 points in the x-y plane.

I need the angle between the line connecting point 1 to all other 19 points and a vector with a direction (say 45 degrees).

Answer 1

[Ruben Costa]

Hi, my aproach is here!

xy=[0	0
0	800
0	1600
0	2400
500	0
500	800
500	1600
500	2400
1000	0
1000	800
1000	1600
1000	2400
1500	0
1500	800
1500	1600
1500	2400
2000	0
2000	800
2000	1600
2000	2400];    %This is your matrix with the points

angle=[];       %this is where the angles will be stored

for i=2:size(xy,1)   
    
    nline=i-1;        
    
   angle(nline) = (atan((xy(i,2)-xy(1,2))/(xy(i,1)-xy(1,1))) - atan((2-0)/(2-0))) * 180/pi;
   
end

- (xy(i,2)-xy(1,2))/(xy(i,1)-xy(1,1)) ---> this is the value of the tangent of the line created with the point (0,0) and other point of the matrix xy

- (2-0)/(2-0)) ---> this is the value of the tangent of the line created with the point (0,0) and point (2,2) because i knew that this line would have 45º

Then I calculated the arctan( the angles) of both and subtracted to know the angle between them. Then I only made the conversion from radians to degrees!

Hope it helps!

Answer 2

[Bjorn Gustavsson]

Best way to go about this is to convert the "wind"-direction to a wind-vector, then use:

w_angle = atan2(norm(cross(wv,b)), dot(wv,b));

Where b is the vector between your points.

HTH

[Sooraj Narayan]

Thanks for the answer.

Just to continue on your comment, what do you mean by converrting the 'direction' to a 'vector'? What would be the vector corresponding to the direction, say 45 degrees?

[Bjorn Gustavsson]

It would depend on the convention for your wind-direction, lets say we use the mathematical notation with phi_w counterclockwise from East, then, with x-component in the Easterly direction, y towards north:

wv = [cos(phi_w), sin(phi_w) 0];