title: How do I detect bounded regions of closed-loop polygons?
body: <p>I am given an ordered set of points in 2D space as an output of a previous process. Coordinate points will be given in the form ((x0,y0),(x1,y1),...,(xn,yn)), where the very last coordinate pair will be a repetition of the first pair (i.e x0 = xn and y0 = yn). In this way, I know that when I re-encounter the same coordinate, I have made a closed loop. I would like to be able to detect the enclosed area by the polygon. If a single closed loop is given, the output should be the enclosed area of that closed loop. Now say I have a separate set of points, similar to to the first set. If a set of many closed looped polygons is given, then if each polygon is separated in space from each other, the output should be each enclosed area. However, if some of the polygons enclose each other, it should be the area bounded between both of them. For example, if I have one closed loop polygon inside another, the output area should between both of them (or in other words, the area enclosed by the larger one minus the area enclosed by the smaller one). If I have more than one closed loop polygon inside of a single larger one, it should be the area enclosed by the larger one minus all the areas enclosed by the smaller ones).</p>
  
  <p>For a case where I have a region A enclosed by a region B, where B is enclosed by a region C, there are three distinct regions.</p>
  
  <ol>
  <li>Region C minus region B (bounded on the outside by polygon 1)</li>
  <li>Region B minus region A (bounded on the outside by polygon 2)</li>
  <li>Region A (bounded on the outside by polygon 3)</li>
  </ol>
  
  <p>Of the three regions, I only want region 1) and region 3). The reason I do not take region 2) is because for all the bounded areas on my 2D plane, the outermost polygons always represent the boundaries of a relevant region, and the input that produced my sets of coordinates representing my closed loop polygons would never have given me the points for polygon 2 if in the end region 1) and region 2) were meant to be combined. It instead would have given me only polygon 1 and polygon 3, similar to the case I described above.</p>
  
  <p><a href="https://i.stack.imgur.com/z5EbY.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/z5EbY.png" alt="nested polygons"></a></p>
  
  <p>In summary,
   - I am given enough information to know all the coordinate points for a set of closed loop polygons on a 2D plane and they are distinguishable from each other.
   - I need to develop an algorithm that will take in the entire set of closed loops polygons and return enough information to describe a bounded area. In thinking about the problem, I think the output that I would want is to know whether for a each and every line segment of the a closed loop polygon, on which side of that line segment is inside and outside of the polygon.
   - It should be able to resolve the case where I have polygons inside of polygons.
   - Closed loop polygons will never share any points. Each set of coordinate points will be unique to a polygon.</p>
  
  <p>My initial thoughts were calculate the centroid of the polygon and then compare all line segments to the centroid, but I don't think this would work for all cases. </p>