Missing results due to geo proximity formula (store locator)

Question

OK - I\'ve been wrestling with this for about 3 months on and off and since I\'ve exhausted every geo proximity formula out there that I\'ve come across and I\'m no closer to ge

Answer 1

EDIT This location-finder comes up often enough that I've written an article on it.

http://www.plumislandmedia.net/mysql/haversine-mysql-nearest-loc/

Original Post

Let's start by dealing with the haversine formula once for all, by putting it into a stored function so we can forget about its gnarly details. NOTE: This whole solution is in statute miles.

DELIMITER $$

CREATE
    FUNCTION distance(lat1 FLOAT, long1 FLOAT, lat2 FLOAT, long2 FLOAT)
    RETURNS FLOAT
    DETERMINISTIC NO SQL
    BEGIN
    RETURN (3959 * ACOS(COS(RADIANS(lat1)) 
                 * COS(RADIANS(lat2)) 
                 * COS(RADIANS(long1) - RADIANS(long2)) 
                 + SIN(RADIANS(lat1)) 
                 * SIN(RADIANS(lat2)) 
                )); 
    END$$

DELIMITER ;

Now let's put together a query that searches on the bounding box, and then refines the search with our distance function and orders by distance

Based on the PHP code in the your question:

Assume $radius is your radius, $center_lat, $center_lng is your reference point.

$sqlsquareradius = "
SELECT post_id, lat, lng
  FROM
(
    SELECT post_id, lat, lng,
           distance(lat, lng, " . $center_lat . "," . $center_lng . ") AS distance
      FROM wp_geodatastore
     WHERE lat >=  " . $center_lat . " -(" . $radius . "/69)
       AND lat <=  " . $center_lat . " +(" . $radius . "/69)
       AND lng >=  " . $center_lng . " -(" . $radius . "/69)
       AND lng <=  " . $center_lng . " +(" . $radius . "/69)
)a
WHERE distance <= " . $radius . "
ORDER BY distance
";

Notice a few things about this.

First, it does the bounding box computation in SQL rather than in PHP. There's no good reason for that, except keeping all the computation in one environment. (radius / 69) is the number of degrees in radius statute miles.

Second, it doesn't fiddle with the size of the longitudinal bounding box based on latitude. Instead it uses a simpler, but slightly too large, bounding box. This bounding box catches a few extra records, but the distance measurement gets rid of them. For your typical postcode / store finder app the performance difference is negligible. If you were searching many more records (e.g. a database of all utility poles) it might not be so trivial.

Third, it uses a nested query to do the distance elimination, to avoid having to run the distance function more than once for each item.

Fourth, it orders by distance ASCENDING. This means your zero-distance results should show up first in the result set. It usually makes sense to list nearest things first.

Fifth, it uses FLOAT rather than DOUBLE throughout. There's a good reason for that. The haversine distance formula is not perfect, because it makes the approximation that the earth is a perfect sphere. That approximation happens to break down at roughly the same level of accuracy as the epsilon for FLOAT numbers. So DOUBLE is deceptive numerical overkill for this problem. (Don't use this haversine formula to do civil engineering work like parking lot drainage, or you will get big puddles a couple of epsilon, a few inches, deep, I promise.) It's fine for store-finder applications.

Sixth, you are definitely going to want to create an index for your lat column. If your table of locations doesn't change very often, it will help to create an index for your lng column as well. But your lat index will give you most of your query performance gain.

Lastly, I tested the stored procedure and the SQL, but not the PHP.

Reference: http://www.scribd.com/doc/2569355/Geo-Distance-Search-with-MySQL Also my experience with a bunch of proximity finders for health care facilities.

--------------- EDIT --------------------

If you don't have a user interface that lets you define a stored procedure, that's a nuisance. At any rate, PHP lets you use numbered parameters in the sprintf call, so you can generate the whole nested statement like this. NOTE: You might need %$1f etc. You'll need to experiment with this.

$sql_stmt = sprintf ("
  SELECT post_id, lat, lng
    FROM
  (
    SELECT post_id, lat, lng,
           (3959 * ACOS(COS(RADIANS(lat)) 
                 * COS(RADIANS(%$1s)) 
                 * COS(RADIANS(lng) - RADIANS(%$2s)) 
                 + SIN(RADIANS(lat)) 
                 * SIN(RADIANS(%$1s)) 
            ))
           AS distance
      FROM wp_geodatastore
     WHERE lat >=  %$1s -(%$3s/69)
       AND lat <=  %$1s +(%$3s/69)
       AND lng >=  %$2s -(%$3s/69)
       AND lng <=  %$2s +(%$3s/69)
  )a
   WHERE distance <= %$3s
   ORDER BY distance
",$center_lat,$center_lng, $radius);