title: Coordinates x and y in respect to the boundaries of a surface - Action Space RL
body: <p>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.</p>
  <p>The document says:</p>
  <p>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 = &quot;place item at (x_i, y_i) and rotate item depending on rotate-flag rot_i around upper left corner by 90°&quot;</p>
  <p><a href="https://i.stack.imgur.com/m8A3Y.png" rel="nofollow noreferrer">surface</a></p>
  <p><a href="https://i.stack.imgur.com/10AiF.png" rel="nofollow noreferrer">Coordinates equations</a></p>
  <p>These definitions result in a total action space |A|=2(XY). i can be enumerated as follows, using above equations:</p>
  <p><a href="https://i.stack.imgur.com/GIauI.png" rel="nofollow noreferrer">i equation</a></p>
  <p>Could you please explain me what means those equations (x_i, y_i and i)?</p>