Another possibility for creating polygons from points is to compute a convex or concave hull. A convex hull is a polygon containing all input points. It's often described as a rubber band.

PostGIS has an ST_ConvexHull function. It takes one argument - an input geometry. It's not an aggregate function, so in order to supply a set of points, the ST_Collect aggregate has to be used first.

The convex hull of all mineshafts is written as follows:

SELECT ST_ConvexHull( 
    ST_Collect(wkb_geometry) 
) FROM points WHERE man_made = 'mineshaft' 

The convex hull is cheaply computed, but it's rarely a good approximation. Distant and isolated features extend the hull, covering areas where the phenomenon isn't present. To address this problem, another algorithm, called a concave hull, was created.

In PostGIS, the implementation is provided by the ST_ConcaveHull function. Apart from the geometry, it takes two additional parameters: the concavity factor (between 0 and 1) controlling the maximal fraction of the convex hull's area that the concave hull can have, and a Boolean (TRUE or FALSE, default FALSE) controlling whether the output polygon can have holes:

SELECT ST_ConcaveHull( 
    ST_Collect(wkb_geometry), 
    0.5, 
    TRUE 
) FROM points WHERE man_made = 'mineshaft'