How can I calculate the angles between a polygons vertices?

Due to my lack of MATLAB code knowledge, I am lost as to how I can calculate the angles between vertices of a random polygon.

Below I load and plot a polygon using the polyshape() function in which the x and y values are loaded from a txt file.

My goal is to calculate the angles shown with the red marker any suggestions how this can be acheived.

Answer 1

[Star Strider]

Try this —

X_Y_Val = [0.29218, 0.17609
           0.56518, 0.27635
           0.69555, 0.16324
           0.83819, 0.49486
           0.62653, 0.63882
           0.27684, 0.49743];

X_Val = X_Y_Val(:,1);
Y_Val = X_Y_Val(:,2);
polygon = polyshape(X_Val, Y_Val);

V = [X_Y_Val(end,:); X_Y_Val; X_Y_Val(1,:)];                                                                % Augmented Matrix For Angle Calculations
for k = 2:size(V,1)-1
    anglr(:,k-1) = [(atan2(V(k-1,2)-V(k,2), V(k-1,1)-V(k,1))); (atan2(V(k+1,2)-V(k,2), V(k+1,1)-V(k,1)))];  % Calculate Radian Angles
    angld(:,k-1) = rad2deg(anglr(:,k-1));                                                                   % Convert To Degrees
    anglrinc(k-1) = mod(2*pi-diff(anglr(:,k-1)),2*pi);                                                      % Reduce Radian Angles
    angldinc(k-1) = mod(360-diff(angld(:,k-1)),360);                                                        % Reduce Degree Angles
end
% A = [anglr; angld];                                                                                         % Display Interim Results (Optional)
% Ainc =[anglrinc; angldinc];                                                                                 % Display Final Results (Optional)
 
figure
plot(polygon)
hold on
% plot(X_Val, Y_Val, 'p')
hold off
grid
axis('equal')
text(X_Val, Y_Val, compose('\\angle%d = %.1f°',[1:size(X_Y_Val,1); angldinc].'))

The code is comment-documented and is relatively self-explanatory. The angles appear to be correct (although I did not measure them by hand).

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