ST_ClosestPointOfApproach
Name
ST_ClosestPointOfApproach — Returns a measure at the closest point of approach of two trajectories.
Synopsis
    
     float8
     
      ST_ClosestPointOfApproach
     
     (
    
    geometry
    
     track1
    
    , geometry
    
     track2
    
    
     )
    
    ;
   
Description
Returns the smallest measure at which points interpolated along the given trajectories are at the smallest distance.
Inputs must be valid trajectories as checked by ST_IsValidTrajectory . Null is returned if the trajectories do not overlap in their M ranges.
See ST_LocateAlong for getting the actual points at the given measure.
Availability: 2.2.0
   
    
   
   This function supports 3d and will not drop the z-index.
  
Examples
-- Return the time in which two objects moving between 10:00 and 11:00
-- are closest to each other and their distance at that point
WITH inp AS ( SELECT
  ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,
    extract(epoch from '2015-05-26 10:00'::timestamptz),
    extract(epoch from '2015-05-26 11:00'::timestamptz)
  ) a,
  ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,
    extract(epoch from '2015-05-26 10:00'::timestamptz),
    extract(epoch from '2015-05-26 11:00'::timestamptz)
  ) b
), cpa AS (
  SELECT ST_ClosestPointOfApproach(a,b) m FROM inp
), points AS (
  SELECT ST_Force3DZ(ST_GeometryN(ST_LocateAlong(a,m),1)) pa,
         ST_Force3DZ(ST_GeometryN(ST_LocateAlong(b,m),1)) pb
  FROM inp, cpa
)
SELECT to_timestamp(m) t,
       ST_Distance(pa,pb) distance
FROM points, cpa;
               t               |     distance
-------------------------------+------------------
 2015-05-26 10:45:31.034483+02 | 1.96036833151395