What is the units of measure used in this MySQL geo query that finds all the points having a specific distance from a center point?

I am working on a MySQL geographical query.

So, following this tutorial: http://howto-use-mysql-spatial-ext.blogspot.it/2007/11/using-circular-area-selection.html

I have implemented this query that finds all the points having a specific distance from a specified point:

SET @center = GeomFromText('POINT(10 10)');
SET @radius = 30;
SET @bbox = CONCAT('POLYGON((',
X(@center) - @radius, ' ', Y(@center) - @radius, ',',
X(@center) + @radius, ' ', Y(@center) - @radius, ',',
X(@center) + @radius, ' ', Y(@center) + @radius, ',',
X(@center) - @radius, ' ', Y(@center) + @radius, ',',
X(@center) - @radius, ' ', Y(@center) - @radius, '))'
);

By this code I am defining the center point and the radious.

Finnally I perform the query that finds all the points having the distance reprensented by the radius from this setted center point:

SELECT name, AsText(location)
FROM Points
WHERE Intersects( location, GeomFromText(@bbox) )
AND SQRT(POW( ABS( X(location) - X(@center)), 2) + POW( ABS(Y(location) - Y(@center)), 2 )) < @radius;

It seems to works fine.

My doubt is: what is the units of measure of the @radius? Are km or what?

In this example @radius is setted with the value of 30. But what exactly represent this value?

Solution

There are no default unit of measure for distances. Actually coordinates in MySQL are are dimensionless. But for the Cartesian coordinates you may pretend, that all distances have the same base unit of measure. It will work properly until all data is interpreted using the same unit.

For example, you may choose meters as the unit distance. In this case, GeomFromText('POINT(10 10)') is 14.14m away from the origin. When you need to provide the radius, just remember, that all distances are measured in meters, so @radius = 30 means that radius is 30m.

For other types of the coordinates, the required unit measure will depend on the used formula for distance calculation. For example, if you are using spherical coordinates (longitude and latitude) the distance formula from the Wikipedia, will give you a distance on the unit sphere. So the @radius should be measured in Earth radii. Therefore the unit for @radius will be 6371km.