Vector loop angle and direction

I am working with a 2D array that forms an XY loop and I am trying to get the dominant angle and direction of the loop. I have used principal component analysis (PCA) and obtained the maximum norm of each pair of points but it is not a robust method.... It works correctly for a loop as seen in the first image (fig1.png), however, the second image (fig2.png) should give a similar result and it is detected backwards. Is there any methodology or algorithm that provides a good result?

[Mathieu NOE]

hello

seems to me it would be quite simple to convert your x, y data into polar coordinates (with cart2pol) and find the point of maximum radius ?

[Izan Segarra]

Hello!

Yes, but if the maximum radius is not in the same direction (as in fig2.png) I will detect the wrong angle. I think it is necessary to complement that technique with something that can discriminate false maximum radius.

Thank you for your response.

[Mathieu NOE]

seems the side where the arrow should point to is always the "smooth" side that ressemble to a half elipse

am I wrong ?

maybe we could discriminate the quadrant based on data smoothness or a R² coefficient if we wanted to fit a parabola

[Izan Segarra]

Sometimes, the direction is marked by abrupt data... ( As you can see in the image below) I think that it's necesary to combine different methods to detect the direction correctly.