Coordinates x and y in respect to the boundaries of a surface - Action Space RL

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I have been reading a research paper about placing an item in a constrained area like the surface of a box or a pallet and I found equations about the coordinates x and y that I didn't understand.

The document says:

The action space will be defined as a 2-dimensional matrix of size X x Y, where X denotes the length and Y its widht. Each matrix field is then enumerated with i and represents an action a_i = "place item at (x_i, y_i) and rotate item depending on rotate-flag rot_i around upper left corner by 90°"

surface

Coordinates equations

These definitions result in a total action space |A|=2(XY). i can be enumerated as follows, using above equations:

i equation

Could you please explain me what means those equations (x_i, y_i and i)?

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