To get a unique merged bounding box (bbox) from multiple relations returned by your Overpass QL query, you need to:

1. Extract the bbox of each relation from the response.
2. Merge all bboxes into a single bbox that encompasses all individual bboxes.

How to do it:

1. Extract bboxes from the Overpass response

The Overpass API returns each relation with a bounds field if you use out bb;. The bounds field contains the min/max latitude and longitude for that relation.

Example of a relation with a bbox:

{
  "type": "relation",
  "id": 12345,
  "bounds": {
    "minlat": 48.8566,
    "minlon": 2.3522,
    "maxlat": 48.8606,
    "maxlon": 2.3582
  }
}

2. Merge all bboxes

To merge all bboxes into one, you need to find the minimum and maximum latitude and longitude across all relations.

• minlat: The smallest minlat among all relations.
• minlon: The smallest minlon among all relations.
• maxlat: The largest maxlat among all relations.
• maxlon: The largest maxlon among all relations.

Example in Python

If you want to do this programmatically (e.g., in Python):

import json

# Example Overpass response (replace with your actual response)
response = {
  "elements": [
    {
      "type": "relation",
      "id": 1,
      "bounds": {"minlat": 48.8566, "minlon": 2.3522, "maxlat": 48.8606, "maxlon": 2.3582}
    },
    {
      "type": "relation",
      "id": 2,
      "bounds": {"minlat": 48.8556, "minlon": 2.3512, "maxlat": 48.8616, "maxlon": 2.3592}
    }
  ]
}

# Initialize variables
minlat = minlon = float('inf')
maxlat = maxlon = float('-inf')

# Iterate over all relations and update the merged bbox
for element in response["elements"]:
    if "bounds" in element:
        minlat = min(minlat, element["bounds"]["minlat"])
        minlon = min(minlon, element["bounds"]["minlon"])
        maxlat = max(maxlat, element["bounds"]["maxlat"])
        maxlon = max(maxlon, element["bounds"]["maxlon"])

# Resulting merged bbox
merged_bbox = (minlat, minlon, maxlat, maxlon)
print(merged_bbox)

Output

The output will be a tuple like: (48.8556, 2.3512, 48.8616, 2.3592)

This is your merged bbox.

Alternative: Use Overpass QL to get the union of all bboxes

If you want to do this directly in Overpass QL, you can use the union statement and then request the bbox of the union:

[out:json][timeout:25];
{{geocodeArea:Marseille}}->.searchArea;
(
  relation["route"="subway"](area.searchArea);
);
out bb;
>;
out bb;

This will return a single bbox for the union of all relations and their members.

Summary:

• Extract all bboxes from the response.
• Merge them by finding the min/max lat/lon.
• Or use Overpass QL to get the union bbox directly.