Find angle between dots

Hi all,

I need to calculate the angle between (imaginary lines) connecting dots on an image.

Below is an example of the bw image that I have:

And I want to calculate the angle as shown below:

Thank you

Answer 1

[Image Analyst]

How about using atan(), atand(), or atan2d()?

Answer 2

[Roger Stafford]

The matlab function 'atan2' can be used to accomplish this. It is more accurate for this purpose than 'acos'. Let P0 = [x0;y0] be a vector of x,y coordinates for the vertex of the angle to be measured and P1 = [x1;y1] and P2 = [x2;y2] be vectors for points on the two lines connecting them to P0.

 x10 = x1-x0;
 y10 = y1-y0;
 x20 = x2-x0;
 y20 = y2-y0; 
 ang = atan2(abs(x10*y20-x20*y10),x10*y10+x20*y20);

The angle 'ang' will be in radians.

Answer 3

[Youssef Khmou]

hi, Computing the angle require the scalar product between the points, so you need to know the coordinate of the white dots, here is an example

the image above is generated by :

T=zeros(200);
T(10,10)=1;
T(40,50)=1;
T(60,30)=1;
imshow(T)

Let us compute the Euclidean norm of the vectors :

 ab=sqrt((50-10)^2+(40-10)^2)
ac=sqrt((30-10)^2+(60-10)^2)

You can obtain the angle by :

 acos(dot([10 60],[10 40])/(ac*ab))*180/pi

[Walter Roberson]

TAEYUN commented

if i want to find angle of btween kneejoint and hipjoint, how can i do? just i knew only x,y,z values of joints... help me plz..