# What is the best way to find angles between these two lines?

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Steve on 10 Oct 2019
Commented: Steve on 12 Oct 2019
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!

Jim Riggs on 10 Oct 2019
Edited: Jim Riggs on 10 Oct 2019
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
Steve on 12 Oct 2019
Thank you for all your help Jim! You really know your stuff.

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