从边缘形成多边形

Question

I am currently working with a graph, modeling a.network of streets. The graph consists of an array of edges, marking that two streets are connected. The edges are a simple data structure containing an array of two streets.

Using this, I am hoping to find a way to locate cycles within the map. Specifically, I am looking to create "lots" in areas completely surrounded by roads.

So far, I have found a lot of information regarding finding cycles in graphs, but nothing specific to my problem. Can I use a cyclical graph to solve my problem? If not, how should this problem be solved? Thank you!

Edit: Additional information about source data

The data consists of a custom class called RoadSegment, shown below.

Each RoadSegment consists of a start position, an end position, and a list of all of the other RoadSegments it is connected to. (The other variables are irrelevant for this task)

Every place in which two RoadSegments are connected is defined in a class called RoadEdge.

The program contains a list of all RoadEdges.

Answer 1

This is more of a computational geometry problem than graph theory. I would tackle it with this algorithm.

 Calculate position of all intersections
 LOOP over intersections
    Select line segment starting at intersection and heading most closely east to west
    Follow line segment to next intersection ( if none continue to next intersection )
    Turn right
    Follow line segment to next intersection ( if none continue to next intersection )
    ...
    IF reached starting intersection then add to plot list

I have not received any response from you, so I have implemented this using some simplifying assumptions - that all valid plots have 4 sides and the roads are approximately orthogonal to each other.

Here is the C++ code

std::vector<std::vector<cxy>> cCity::plotfinder()
{
    // vector of plots
    std::vector<std::vector<cxy>> vplot;

    // loop over intersections
    for (auto &inter : myIntersection)
    {
        // check if this is the north east corner of a quadrilateral plot

        std::vector<cxy> plot;
        plot.push_back(inter.myLocation);

        // find road from intersection going in approx east west direction
        auto road = inter.EastToWest();

        // find next intersection on road
        cIntersection next1;
        if (!nextIntersection(next1, inter, road))
            continue;   // intersection does not exist, so this is not a plot

        // add to plot
        plot.push_back(next1.myLocation);

        // continue to check the remaining two plot edges, if they exist

        road = next1.NorthToSouth();
        cIntersection next2;
        if (!nextIntersection(next2, next1, road))
            continue;
        plot.push_back(next2.myLocation);

        road = next2.WestToEast();
        cIntersection next3;
        if (!nextIntersection(next3, next2, road))
            continue;
        plot.push_back(next3.myLocation);

        // found a good plot, add to list
        vplot.push_back(plot);
    }

    return vplot;
}

You can find this code and a complete test application at https://github.com/JamesBremner/CityPlotter

Output from a sample run

road from -100, 0 to 100, 0
road from -100, 10 to 100, 10
road from 0, 100 to 0, -100
road from 10, 100 to 10, -100

1 plots found
0 10, 10 10, 10 0, 0 0,