Question

The Requirements
I’m not sure how to describe this so I’ll give an example that should be easier to explain.

I have a small (maximum 50×50 pixels) 1bit/pixel bitmap (black and white).
Only one pixel is added at a time.
Find the largest (by area) polygon that exists using the black pixels as the edges.

The actual scenario isn’t actually graphics related and uses a 2D Boolean array but the logic would be the same I imagine.

The Desired Behavior

The problem
I am not sure how to get the largest polygon when it is completed. I can do the filling if I can just get the polygon. In the above image I have highlighted the polygon that should be selected.

Answer 1

It turns out it was much more simple than I was expecting. I guess I was trying to make things overcomplicated. Because of the small dimensions and the fact that it will not run that frequently, speed is not a really an issue.

I don’t have access to exactly how I did it right now but this is the general idea.

Each pixel is stored as an instance of SomePixelType.
There is a Stack<SomePixelType> of pixels called visitedPixels.
A pixel is considered a possible polygon edge if:

• It has between 2 and 7 (both inclusive) black neighbouring pixels.
• It is not in the visitedPixels collection.

SomePixelType has a method named GetNextPixel.

When GetNextPixel is called it will search neighbouring pixels (starting directly up and going clockwise) for a possible polygon edge and return it. Calling it again will continue searching from the last match. Once all neighbouring pixels have been checked it will return null.

When a pixel is set this method would be called.

public Stack<SomePixelType> GetPolygonEdges(SomePixelType justSetPixel)
{
    visitedPixels.Clear();

    if(!justSetPixel.IsPossiblePolygon)
        return null; // Not a possible edge. No closed polygon could of been completed.

    visitedPixels.Push(justSetPixel);

    SomePixelType currentPixel = justSetPixel;
    while(visitedPixels.Count > 0)
    {
        currentPixel  = currentPixel.GetNextPixel();
        if(currentPixel == null) // No possible neighbouring polygon edges.
        {
            currentPixel = visitedPixels.Pop(); // Backtrack
            continue;
        }
        if(currentPixel == justSetPixel)
            return visitedPixels;

        visitedPixels.Push(currentPixel);
    }
    return null; // Not closed.
}

From here on it is fairly easy to fill in. As the question was about finding the polygon I will stop at this step.