What type of rotational invariance information can I get from interest points (coordinates) of corners from an image?

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Assume that you are using the FAST algoritm for corner/feature detection. You pick an image and run the FAST algorithm.

enter image description here

Question:

All these green dots are actully coordinates in x and y direction. What type of rotational invariance information can I get from only knowing the coordinates that are created by the geometical shapes inside the image?

For example: If we measure the angles between every point, the angles are going to be the same, no matter how we rotates the image.

NOTE

This is a feature detection algorithm, sometimes one or more coordinates can flicker e.g some green dots disapear and appears few milliseconds after.