How to define self-intersection of polygon in google maps (flutter)

I am making an application in which the user can draw a polygon on a map by points. I need to somehow make sure that the polygon does not have self-intersections. I know it is possible to manually check each line. There are various methods for this. But I noticed that Google Maps automatically fills polygons that do not have self-intersections. Is it possible to get this value from the plugin somehow?

i am using google_maps_flutter

without self-intersection

with self-intersection

Perhaps this will be useful to someone. I did not find a built-in function in the plugins listed in the question. So I wrote my own function:

true - there are self-intersections

bool isNotSimplePolygon(List<LatLng> polygon){
  if(polygon.length <= 3)
    return false;

  for(int i = 0; i < polygon.length - 2; i++){
    double x1 = polygon[i].latitude;
    double y1 = polygon[i].longitude;
    double x2 = polygon[i + 1].latitude;
    double y2 = polygon[i + 1].longitude;

    double maxx1 = max(x1, x2), maxy1 = max(y1, y2);
    double minx1 = min(x1, x2), miny1 = min(y1, y2);

    for (int j = i + 2; j < polygon.length; j++) {
      double x21 = polygon[j].latitude;
      double y21 = polygon[j].longitude;
      double x22 = polygon[(j + 1) == polygon.length ? 0 : (j + 1)].latitude;
      double y22 = polygon[(j + 1) == polygon.length ? 0 : (j + 1)].longitude;

      double maxx2 = max(x21, x22), maxy2 = max(y21, y22);
      double minx2 = min(x21, x22), miny2 = min(y21, y22);

      if ((x1 == x21 && y1 == y21) || (x2 == x22 && y2 == y22) || (x1 == x22 && y1 == y22) || (x2 == x21 && y2 == y21))
        continue;

      if (minx1 > maxx2 || maxx1 < minx2 || miny1 > maxy2 || maxy1 < miny2)
        continue;  // The moment when the lines have one common vertex...


      double dx1 = x2-x1, dy1 = y2-y1; // The length of the projections of the first line on the x and y axes
      double dx2 = x22-x21, dy2 = y22-y21; // The length of the projections of the second line on the x and y axes
      double dxx = x1-x21, dyy = y1-y21;

      double div = dy2 * dx1 - dx2 * dy1;
      double mul1 = dx1 * dyy - dy1 * dxx;
      double mul2 = dx2 * dyy - dy2 * dxx;

      if (div == 0)
        continue; // Lines are parallel...

      if (div > 0) {
        if (mul1 < 0 || mul1 > div)
          continue; // The first segment intersects beyond its boundaries...
        if (mul2 < 0 || mul2 > div)
          continue; // // The second segment intersects beyond its borders...
      }
      else{
        if (-mul1 < 0 || -mul1 > -div)
          continue; // The first segment intersects beyond its boundaries...
        if (-mul2 < 0 || -mul2 > -div)
          continue; // The second segment intersects beyond its borders...
      }
      return true;
    }
  }
  return false;
}