Improve logic to compute center of a polygon

Author: uditswaroopa

lib/src/layer/polygon_layer/label.dart

@@ -81,10 +81,65 @@ LatLng _computeLabelPosition(
 
 /// Calculate the centroid of a given list of [LatLng] points.
 LatLng _computeCentroid(List<LatLng> points) {
-  return LatLng(
-    points.map((e) => e.latitude).average,
-    points.map((e) => e.longitude).average,
-  );
+  if (points.isEmpty) {
+    throw ArgumentError('Polygon must contain at least one point');
+  }
+  
+  if (points.length == 1) {
+    return points[0];
+  }
+  
+  double signedArea = 0;
+  double centroidX = 0;
+  double centroidY = 0;
+  
+  // For all vertices except last
+  for (int i = 0; i < points.length - 1; i++) {
+    final double x0 = points[i].longitude;
+    final double y0 = points[i].latitude;
+    final double x1 = points[i + 1].longitude;
+    final double y1 = points[i + 1].latitude;
+    
+    // Calculate signed area contribution of current vertex
+    final double a = x0 * y1 - x1 * y0;
+    signedArea += a;
+    
+    // Accumulate centroid components weighted by signed area
+    centroidX += (x0 + x1) * a;
+    centroidY += (y0 + y1) * a;
+  }
+  
+  // Close the polygon by connecting last vertex to first
+  final double x0 = points.last.longitude;
+  final double y0 = points.last.latitude;
+  final double x1 = points.first.longitude;
+  final double y1 = points.first.latitude;
+  final double a = x0 * y1 - x1 * y0;
+  signedArea += a;
+  centroidX += (x0 + x1) * a;
+  centroidY += (y0 + y1) * a;
+  
+  // Complete the signed area calculation
+  signedArea *= 0.5;
+  
+  // Calculate centroid coordinates
+  centroidX /= 6 * signedArea;
+  centroidY /= 6 * signedArea;
+  
+  // Handle special case of zero area (collinear points)
+  if (signedArea == 0) {
+    // Default to average of all points
+    double sumX = 0;
+    double sumY = 0;
+    for (final point in points) {
+      sumX += point.longitude;
+      sumY += point.latitude;
+    }
+    return LatLng(sumY / points.length, sumX / points.length);
+  }
+  
+  return LatLng(centroidY, centroidX);
+  
 }
 
 /// Calculate the centroid of a given list of [LatLng] points with multiple worlds.