Determine/create a geofence/bounding box on the fly - mysql

Question

I have a MySQL table of lat/lon (think of a school campus or shopping mall).
Each location (school/mall) can have dozens of GPS positions stored in the table. All locations are captured using a mobile app and these locations can represent everything from entrances to specific rooms (conference) to easily identifiable locations such as elevators.
A user submits a request (i.e. janitor cleanup on isle 6) and I need to make sure the request (cleanup) being submitted is within the geofence established by finding the 4 points furthest away from each other for that location.
Currently we're using a Haversine search but we want to convert this to a fenced in system. What we can't do is build a separate geofence table.
I've googled around and not found anything (I'm probably not using the correct terms). How do I build that query?

Answer 1

At the first level of approximation, you can scan for a bounding box.
Say you have a loc table with loc_id, lat, lng columns.
And say your candidate point has the position #ptLat, #ptLng.
Compute the bounding boxes for each location. This works fine with latitude and longitude unless you're within a few degrees of the north or south pole or near 180° longitude.
SELECT loc_id, MAX(lat) north, MAX(lng) east, MIN(lat) south, MIN(lng) west
FROM loc
GROUP BY loc_id
This is fast if you have an index on (loc_id, lat, lng). It's also fast because you can avoid all the trig functions in the Great Circle calculation.
Once you have the bounding box, you can decide whether your candidate point is inside it.
Then you can do
SELECT loc_id
FROM (
SELECT loc_id, MAX(lat) north, MAX(lng) east, MIN(lat) south, MIN(lng) west
FROM loc
GROUP BY loc_id
) box
JOIN ( SELECT #ptLat ptLat, #ptLon, ptLon ) pt
ON ptLat <= north
AND ptLat >= south
AND ptLon <= east
AHD ptLon >= west
This gets you a result set with the loc_id values matching your candidate point.
If your lat,lng data is messy--if it has lots of outlier points--this won't work very well. It's sensitive to errors. For example, if a location in Iceland has lots of points right near it, but one point in Greenland miscoded, the bounding box will be absurdly large.
If it isn't accurate enough for you, you should research convex hull algorithms. But that will take you outside pure SQL, most likely.