MySQL geospacial search using haversine formula returns null on same point

Question

I'm trying to implement a geospacial search in a php application. Currently, I'm using the following query to find points within 10km of a given latitude and longitude:

SELECT * FROM (
      SELECT *,
             (6378.1 * ACOS(
                  COS(RADIANS(48.856614)) * COS(RADIANS(latitude))
                * COS(RADIANS(2.3522219) - RADIANS(longitude))
                + SIN(RADIANS(48.856614))
                * SIN(RADIANS(latitude)))
             ) AS distance
      FROM `destinations_info`
      WHERE latitude BETWEEN 48.856614  - (10 / 69)
               AND 48.856614  + (10 / 69)
        AND longitude BETWEEN 2.3522219 - (10 / (69 * COS(RADIANS(48.856614))))
               AND 2.3522219 + (10 / (69 * COS(RADIANS(48.856614))))
      ) d
WHERE distance <= 10
LIMIT 1

This works fine as long I don't search for the exact latitude and longitude that is stored into the POI's table.

So for example if I have in my poi table the following entry

id     name     latitude    longitude
1      Paris    48.856614   2.3522219000000177

And I call the query with lat = 48.856614 and long = 2.3522219000000177 I won't get any results. As far as I see this happens because the following operation returns NULL and not 0 in mysql:

SELECT (6378.1 * acos(cos(radians(48.856614)) * cos(radians(48.856614)) * cos( radians(2.3522219) - radians(2.3522219)) + sin(radians(48.856614)) * sin(radians(48.856614)))) 

Running the same in Chrome Calculator I get 0 rad.

Is there something wrong in the query or do I need to include the NULL results as well using "OR IS NULL"

Answer 1

IFNULL( ... ),0) AS Distance will also help you to get around the error.

Answer 2

The problem is that acos is invoked with a value which is not in the range of -1 and 1, so it returns null.

SELECT cos(radians(48.856614)) * cos(radians(48.856614)) * cos( radians(2.3522219) - radians(2.3522219)) + sin(radians(48.856614)) * sin(radians(48.856614))

1.0000000000000002

It seems to be some sort of rounding issue.

Since, arc cos is defined only between -1 and 1, you probably should pre-check its parameter or be prepared that it can return null if something is wrong with the calculation.