How to merge an arbitrary set of polygons?

Question

Algorithms

There are several polygons that can be combined into one.
They look something like this:

Polygons are selected by the operator, so that the polygons are selected in random order - my main problem is the problem of determining the next section when merging

For two polygons I wrote the following code

public List<Point2d> CombinePolylinePoints(List<Point2d> points1, List<Point2d> points2)
{
  var borderPoints = new List<Point2d>();
  for (int i = 0; i < points1.Count; i++)
  {
    if (points2.Contains(points1[i]))
    {
      Debug.WriteLine("Точка с индексом " + i + " - граничная");
      borderPoints.Add(points1[i]);
    }
  }
  if (borderPoints.Count < 2)
    return new List<Point2d>();
  // проходим по первому полигону?
  var goingFirstParcel = true;
  int iFirst = 0;
  int iSecond = 0;
  Point2d nextPoint = default(Point2d);
  var points = new List<Point2d>();
  while (nextPoint != points1[0])
  {

    if (goingFirstParcel)
    {
      Debug.WriteLine("Идем по первому участку..");
      var currPoint = points1[iFirst];
      points.Add(currPoint);
      if (borderPoints.Any(p => p.IsEqualTo(currPoint, Tolerance.Global)))
      {
        Debug.WriteLine("Текущая точка - граничная. Переходим на второй участок");
        goingFirstParcel = false;

        iSecond = points2.IndexOf(currPoint);
        if (iSecond == -1)
        {
          MessageBox.Show("IndexOf returned 0");
          return null;
        }
        iSecond++;
        if (iSecond >= points2.Count)
          iSecond = 0;
        Debug.WriteLine("iSecond = " + iSecond);
        nextPoint = points2[iSecond];
        continue;
      }
      iFirst++;
      if (iFirst >= points1.Count) iFirst = 0;
      nextPoint = points1[iFirst];
    }
    else if (!goingFirstParcel)
    {
      Debug.WriteLine("Идем по второму участку..");
      var currPoint = points2[iSecond];
      points.Add(currPoint);
      if (borderPoints.Any(p => p.IsEqualTo(currPoint, Tolerance.Global)))
      {
        Debug.WriteLine("Текущая точка - граничная. Переходим на первый участок");
        goingFirstParcel = true;
        iFirst = points1.IndexOf(currPoint);
        if (iFirst == -1)
        {
          MessageBox.Show("IndexOf iFirst returned 0");
          return null;
        }
        iFirst++;
        if (iFirst >= points1.Count)
          iFirst = 0;
        Debug.WriteLine("iFirst = " + iFirst);
        nextPoint = points1[iFirst];
        continue;
      }
      iSecond++;
      if (iSecond >= points2.Count) iSecond = 0;
      nextPoint = points2[iSecond];
    }
  }
  return points;
}

In short:

1. looking for boundary points
2. we go along the first section, adding all the points to the list
3. if the current point is a boundary point, go to the next point of the second section
4. go to step 2 until the next point becomes the first point of the first section

But for an arbitrary set of polygons, it is impossible to write - on some test data, reaching a fork (a point common to 3 or more sections), the algorithm takes the wrong path and loops on it.

Question: how to choose which polygon to go to at the fork?

Answer 1

Recursively won't work?
We take an arbitrary polygon and any that is adjacent to it. We combine them according to the above algorithm.
We repeat.