Great circle distance

Find the distance in kilometres between two points on the surface of the earth. This is just the sort of problem stored functions were made for. For a first order approximation, ignore deviations of the earth's surface from the perfectly spherical. Then the distance in radians is given by a number of trigonometric formulas. ACOS and COS behave reasonably:



             COS(lat1-lat2)*(1+COS(lon1-lon2)) - COS(lat1+lat2)*(1-COS(lon1-lon2))

rads = ACOS( --------------------------------------------------------------------- )

                                              2

We need to convert degrees latitude and longitude to radians, and we need to know the length in km of one radian on the earth's surface, which is 6378.388. The function:



set log_bin_trust_function_creators=TRUE;



DROP FUNCTION IF EXISTS GeoDistKM;

DELIMITER |

CREATE FUNCTION GeoDistKM( lat1 FLOAT, lon1 FLOAT, lat2 FLOAT, lon2 FLOAT ) RETURNS float

BEGIN

  DECLARE pi, q1, q2, q3 FLOAT;

  DECLARE rads FLOAT DEFAULT 0;

  SET pi = PI();

  SET lat1 = lat1 * pi / 180;

  SET lon1 = lon1 * pi / 180;

  SET lat2 = lat2 * pi / 180;

  SET lon2 = lon2 * pi / 180;

  SET q1 = COS(lon1-lon2);

  SET q2 = COS(lat1-lat2);

  SET q3 = COS(lat1+lat2);

  SET rads = ACOS( 0.5*((1.0+q1)*q2 - (1.0-q1)*q3) ); 

  RETURN 6378.388 * rads;

END;

|

DELIMITER ;



-- toronto to montreal (505km):

select geodistkm(43.6667,-79.4167,45.5000,-73.5833);

+----------------------------------------------+

| geodistkm(43.6667,-79.4167,45.5000,-73.5833) |

+----------------------------------------------+

|                           505.38836669921875 |

+----------------------------------------------+

(Setting log_bin_trust_function_creators is the most convenient way to step round determinacy conventions implemented since 5.0.6.)