Adding Buildings after Drawing Roads using L Systems - java

I'm creating a procedurally generated city and I'm having trouble with the logic behind adding buildings after the L System has added all of the roads.
I've done a lot of research as this is my final year project but unfortunately can't find a lot on adding buildings in, but more about adding roads.
My program uses L Systems to draw each road and when intersecting another road or changes direction it adds the road to an undirected planar graph. The roads added are just lines at the moment and don't have width yet as I would like to get the underlying logic of adding buildings sorted before adding this in. Roads drawn by the L System will be at randomised angles, not right angles.
My original method to find where to place the buildings was to rotate clockwise around the graph to find the polygons within the roads, then add the buildings inside the polygons found. I currently can't seem to get this working due to roads that are dead ends and moving around a graph clockwise doesn't seem to produce correct results.
The main problem is that a building placed at the intersection of a road could overlap the road. I would like the buildings to be placed somewhat similar to the game Subversion.
If there are any other methods to what I have tried I would love to hear your ideas.
Any help will be much appreciated.

Your problem is located at
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then add the buildings inside the polygons found. I currently can't seem to get this working and it also has issues with if the road is a dead end.
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Geometrically speaking yu should be able to define a polygon and see if the base of the building fits into that polygon.
Either using the java polygons or do it yourself
Specifically what goes wrong will get you specific answers

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I can think about taking the first tile that is the 97 by knowing that is the one with the lowest X position but from there what?
I think you're formatting your information in a strange way to solve this problem. If your units are starting at tile 58, then somewhere you're telling them to start at the first drawn tile? Optimally, if you want to have different maps, wouldn't you want to be able to define a particular point on the grid and tell them to start from there?
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I'm current working on a pet project that allows a user to create a graph (vertices/edges) on screen in Java. I have the vertices implemented as JComponents but I have the edges implemented as Line2D's. When a user is moving the mouse across the canvas, if it is within a certain threshold of proximity to one of the edges (or Line2D's) that edge (the closest to the mouse) is highlighted.
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Adding the cubes to BranchGroups and dynamically updating them or managing multiple groups sounds complicated.
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