Get angle between two lines of a time series in Matlab

Question

How can I calculate angle in degrees between lines AB and BC in Matlab?

Time-series

Answer 1

It's a little bit of an unusual request, but the code below should do the trick :).

% X and Y coordinates of your time series
X = (1:9)';
Y = [-3;-1;-1.2;-4.5;-5.5;.2;-2;-.5;-.4];

angle_rad = zeros(size(X,1)-2,1);         % Preallocate the angle vector
for i = 1:(size(Y,1)-2)                 % Loop over all vector pairs

    % Vectors:
    a = [X(i+1)-X(i);Y(i+1)-Y(i)];      % first vector
    b = [X(i+2)-X(i+1);Y(i+2)-Y(i+1)];  % second vector

    % Vector properties:
    dot_prod = a'*b;
    l_a = norm(a);                      % length of first vector
    l_b = norm(b);                      % length of second vector

    % Angle:
    angle_rad(i) = pi - acos(dot_prod/(l_a*l_b));  % [rad]
end
angle_deg = angle_rad.*180./pi; % [degrees]

See if this works, but this code is a little clumsy, maybe if we knew what you were using this for, there could be a better option?