calculating zig zags from simple path analysis with XY input data

Hello, I was looking for code that, given X and Y coordinate vectors would be able to calculate:

speed (euclidean distance between 2 points over time - this part is easy),

directionality (e.g., number of turns greater than 90 degrees).

The code I started with is below, but I don't think it is accurate.

% X = x-axis data
%Y = y-axis data

t=length(X)-1;
c=zeros(t,1);
D=zeros(t,1);
E=zeros(t,1);
for i=1:t
    c(i)=dot(X(i:i+1),Y(i:i+1))/norm(X(i:i+1))*norm(Y(i:i+1));
    c(i)=acos(c(i))*180/pi;
    c(i)=imag(c(i));
end

c=c-360;

for i=2:t
    D(i-1)= c(i)-c(i-1);
    if D(i-1)>0.5
        E(i-1)=1;
    end
end

with this, E gives the number of turns that are greeater than 180 degrees. I am not sure if this is the best approach, any thoughts would be most welcome.

Answer 1

[David Young]

I believe this does what you are asking, but you should check it against some trial data. It counts turns which exceed 90 degrees.

directions = atan2(diff(Y), diff(X)); % direction of each leg
ddiff = diff(directions);             % angle at each corner 
angle = mod(ddiff+pi, 2*pi) - pi;     % ... in range -pi to pi
E = abs(angle) > pi/2;                % turns exceeding 90 degrees
nturns = sum(E)

You should find the code straightforward to follow, except for the third line, which is a little more subtle. It deals with the fact that a direction of -179 degrees is close to a direction of +179 degrees. If you experiment you should see that this manipulation deals correctly with such cases, and small changes in direction get mapped to small numbers.