I'm developing a building editor. Users can draw rooms by adding angles (vertices of the room) with a left click. Clicking on an existing angle closes the room and fills the floor by using the PointInPolygon algorithm. Let me illustrate the problem. I have this room.

    #-----------#
    |           |
    |           |
    |     #-----#
    |     |
    |     |
    |     |
    #-----#

 
Now I want to create another room by connecting two of the vertices like this:

    #-----------#
    |           |
    |           |
    |     V--e--X < first click
    |     |     |
    |     e     | <--new room
    |     |     |
    #-----Y-----#
          ^
    second click
 
I need to detect the vertex V and the edges <i>e</i>. I tried to implement the convex hull algorithm to find the external walls, but there are degenerated cases where those edges are interior walls... I even tried the Dijstra's algorithm to find the shortest path between X and Y, but again there are degenerated cases like this:

     first click
          v
          X----------# < second click
          |          |
    #-----V--e--V    |
    |     |     |    | 
    |     |     e    | <--new room
    |     |     |    |
    #-----V--e--V    |
          |          |
          Y----------# < third click
          ^
     fourth click
 
I think the answer is in some graph algorithm (which I'm not really in). How should I approach this problem?