How to detect rotation in a trajectory?

I have to write an algorithm to detect rotation in the trajectory. Basically, I have to detect the red zone in the trajectory. Currently I have the time and coordinate data.

How do I approach it?

[DGM]

How is the trajectory defined?

What criteria are used to determine whether a change in direction constitutes "rotation"?

[Struggling in MATLAB]

I think within a defined window of time if the change in direction is ~360 degrees we can define that as rotation.

[Riccardo Scorretti]

You are working in a 2D or 3D space?

[Struggling in MATLAB]

2-D space.

Answer 1

[Star Strider]

I would use the gradient function to calculate the numerical derivative.

For example:

dydx = gradient(y) ./ gradient(x);

Plot that as a function of ‘x’ as well, and it may provide some clues on how to define that region of the curve.

.

[Struggling in MATLAB]

Thanks for your input. I think this will work.

[Star Strider]

As always, my pleasure!

Answer 2

[Sulaymon Eshkabilov]

One way of detecting the region of values is using logical indexing, e.g.:

t = ...
x = ...
y = ...
    % Way 1
Ind = t>=0 &  t<=5;  % Select the region according to the time data
Xs = x(Ind);
Ys = y(Ind);

% Way 2
Ind = x>=0 &  x<=5;  % Select the region according to x data
Xs = x(Ind);
Ys = y(Ind);

[Struggling in MATLAB]

Thanks for your comment.