MATLAB: What is the best way to find angles between these two lines

anglesMATLAB

I have a file (closest_central_points.m) that has a group of 10 closets central points. I have another file (fpep.mat) that has a group of 950+ central points and endpoints triplets. I have third file (closest_central_points_chords.m) that has a line (chord) created from one central point to another. I need an efficient way to find and store the angles between these chords and the lines made between the central points and the endpoints (see attached pic). I have also attached related files. Thanks in advance for your help!

Best Answer

The angle between vectors is determined using the vector dot product.
Calculate the unit vectors and angles as follows:
v1x = cp_x2 - cp_x1;    % vector 1 components
v1y = cp_y2 - cp_y1;
d1 = sqrt(v1x^2 + v1y^2); % magnitude of vector 1
u1 = [(v1x/d1,  v1y/d1)]; % unit vector 1
v2x = ep_x1 - cp_x1;   % vector 2 components
v2y = ep_y1 - cp_y1;
d2 = sqrt(v2x^2 + v2y^2);  % magnitude of vector 2
u2 = [v2x/d2,  v2y/d2];    % inut vector 2
v3x = cp_x1 - cp_x2;    % vector 3 components
v3y = cp_y1 - cp_y2;
d3 = sqrt(v3x^2 + v3y^2); % Vector 3 magnitude
u3 = [v3x/d3, v3y/d3];    % Unit vector 3
v4x = ep_x2 - cp_x2;    % vector 4 components
v4y = ep_y2 - cp_y2;
d4 = sqrt(v4x^2 + v4y^2); % vector 4 magnitude
u4 = [v4x/d4, v4y/d4];    % unit vector 4
a1 = acos(dot(u1,u2));     % angle between vector 1 and vector 2
a2 = acos(dot(u3,u4));     % angle between vector 3 and vector 4
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