Physics Engine Question

hi there! its me again!

i want to try to code a small physics engine. but i need to know the following.
lets use a shape of a box for this example.

for the movement, do i need to work with the centroid of all the corners?
Or do i need to work with the X and Y axis of the box, and use the corners as sensors?

i hope you know what i mean...

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Live for nothing, OR CODE FOR SOMETHING!