How to create for loop for calculating angle between 3 3D points?

Hi there!

I want to create a for loop that calculates the angle between three 3D points. I have a double called 'data3D' that contains 1 row with several points in 3D space. col 1 = pt1_x, col 2 = pt1_y, col 3 = pt1_z, col 4 = pt2_x ..... For this calculation I only need the xyz coordinates for pt1.

data3D =  
-.3      .2     -.3   -.5   .6    -.3

I have a double called 'Coordinates' that contains a varying number of rows, and constant number of columns. col 1 = x, col 2 = y, col 3 = z. The number of rows varies based on how many events occur in a single observation, but columns are consistent throughout.

Coordinates =
-.6    .5    -4.1
-.9    .4    -4.1
-1.1   .2    -4.2

I want my for loop to calculate the angle between my contact point (pt 1, data3D) and each subsequent point in Coordinates. i.e. I want to first calculate the angle between the vector (pt1 -> Coordinates(row1)) and the vector (pt1 -> Coordinates(row2)). The next calcuation should be the angle between vector (pt1 -> Coordinates(row2)) and the vector (pt1 -> Coordinates(row3)) and so forth.

For now, my for loop is structured like this, how would I structure the calculation formula?

nobservations1 = size(Coordinates,1);
icoordinates1 = nobservations1 - 1; %creates a variable that consists of number of observations -1 
scanAngles = []; % create empty vector to store angles
for i_coord1 = 1:icoordinates1 %for each observation
    
    curangle = 
    
    scanAngles = [scanAngles curangle];
    
end

Any help with this would be greatly appreciated, I'm a MATLAB novice and would love to learn!

Answer 1

[Voss]

p = data3D(1:3); % pt1
q = Coordinates;

v = q-p; % vectors from pt1 to each point in Coordinates
N = size(q,1);
angles = zeros(1,N-1);
for ii = 1:N-1
    a = v(ii,:);
    b = v(ii+1,:);
    angles(ii) = acos(sum(a.*b)/(norm(a)*norm(b)));
end

Those angles are in radians; if you want angles in degrees, use acosd instead of acos.

[Jade]

This worked beautifully, thank you!

[Voss]

You're welcome!