The absolute coordinate function returns the absolute values of the position of an object in world space. If you link an object to another object in the project window of Animator the position channels will be reset to 0,0,0 which is the relative offset of the child to the parent object. If you move the parent object around the position of the child object - if you have not animatd it - will still be 0, 0, 0 eventhough it has also shifted in world space.
You may want to know the position of the child object in world space though to be able to attach an object which is outside of the hierarchy or to do dynamic calculations which will need the offset of the child objects position from one frame to the next. You can use the absolute coordinates function for this:
coordinates = coord( child.Position );
Since you may need the absolute coordinates of an object on a frame other than the current frame you can index a frame with using a second argument:
coordinates = coord( child.Position, 5 ); //
If you need to calculate an offset between the current frame and the last frame your statement will look like this:
delta_of_coordinates = coord( child.Position ) - coord( child.Position, frame - 1 );
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