How to count the number of tiles in a map region with min/max zoom level

countTilesInRegion.m

- (NSUInteger)countTilesInRegionSouthWest:(CLLocationCoordinate2D)southWest
                                northEast:(CLLocationCoordinate2D)northEast
                                  minZoom:(int)minZoom
                                  maxZoom:(int)maxZoom
{
  double minLat = southWest.latitude;
  double maxLat = northEast.latitude;
  double minLon = southWest.longitude;
  double maxLon = northEast.longitude;
  
  if (minZoom > maxZoom || maxLat <= minLat || maxLon <= minLon) {
    return 0;
  }
  
  int n, xMin, yMax, xMax, yMin;
  
  NSUInteger totalTiles = 0;
  
  for (int zoom = minZoom; zoom <= maxZoom; zoom++) {
    n = pow(2.0, zoom);
    xMin = floor(((minLon + 180.0) / 360.0) * n);
    yMax = floor((1.0 - (log(tan(minLat * M_PI / 180.0) + 1.0 / cos(minLat * M_PI / 180.0)) / M_PI)) / 2.0 * n);
    xMax = floor(((maxLon + 180.0) / 360.0) * n);
    yMin = floor((1.0 - (log(tan(maxLat * M_PI / 180.0) + 1.0 / cos(maxLat * M_PI / 180.0)) / M_PI)) / 2.0 * n);
    
    totalTiles += (xMax + 1 - xMin) * (yMax + 1 - yMin);
  }
  
  return totalTiles;
}