Angles at concave polygon

Hello, I have a concave polygon you can see in the picture attached. I need to compute all angles between two consecutive vectors. I tried following:

for k = 1 : size(ps, 1) - 2;
    point1 = ps(k, :);
    vertex = ps(k+1, :);
    point2 = ps(k+2, :);
    v1 = point1 - vertex;
    v2 = point2 - vertex;      
    theta(k) = dot(v1, v2)/(norm(v1)*norm(v2));
    angle(k) = (acos(theta))*180/pi;
end

ps is nx2 matrix containing coordinates of polygon vertices.

In the output angle(k) there are angles allways smaller then 180, but obviously there angles more then 180. I need to somehow distinct which angles are >180 and <180. What do I do wrong? Thank you in advance for your reply

Answer 1

[Image Analyst]

Try atan2d().

Answer 2

[信实 郑]

Use function convex to identify convex and concave parts of polygon.As following:

% ps is nx2 matrix containing coordinates of polygon vertices.
c = convex(ps); % Identify convex and concave parts of polygon

for k = 1 : size(ps, 1)-2
    point1 = ps(k, :);
    vertex = ps(k+1, :);
    point2 = ps(k+2, :);
    v1 = point1 - vertex;
    v2 = point2 - vertex;   
    theta(k) = dot(v1, v2)/(norm(v1)*norm(v2)); 
    if c(k)>0  
        angle(k) = (acos(theta(k)))*180/pi;
    else
        angle(k) = 360 - (acos(theta(k)))*180/pi;
    end
end