TODO Return the instant of the first temporal circular buffer at which the two arguments are at the nearest distance

nearestApproachInstant({geo,cbuffer,tpoint},{geo,cbuffer,tpoint}) → tpoint

SELECT nearestApproachInstant(tcbuffer '[Cbuffer(Point(2 2), 0.3)@2001-01-01,
  Cbuffer(Point(2 2), 0.7)@2001-01-02]', geometry 'Linestring(50 50,55 55)');
-- Cbuffer(Point(2 2),0.349928)@2001-01-01 02:59:44.402905+01
SELECT nearestApproachInstant(tcbuffer '[Cbuffer(Point(2 2), 0.3)@2001-01-01,
  Cbuffer(Point(2 2), 0.7)@2001-01-02]', cbuffer 'Cbuffer(Point(1 1), 0.5)');
-- Cbuffer(Point(2 2),0.592181)@2001-01-01 17:31:51.080405+01

TODO Return the smallest distance ever between the two arguments

nearestApproachDistance({geo,cbuffer,tpoint},{geo,cbuffer,tpoint}) → float

SELECT nearestApproachDistance(tcbuffer '[Cbuffer(Point(2 2), 0.3)@2001-01-01,
  Cbuffer(Point(2 2), 0.7)@2001-01-02]', geometry 'Linestring(50 50,55 55)');
-- 1.41793220500979
SELECT nearestApproachDistance(tcbuffer '[Cbuffer(Point(2 2), 0.3)@2001-01-01,
  Cbuffer(Point(2 2), 0.7)@2001-01-02]', cbuffer 'Cbuffer(Point(1 1), 0.5)');
-- Cbuffer(Point(2 2),0.592181)@2001-01-01 17:31:51.080405+01

Function nearestApproachDistance has an associated operator |=| that can be used for doing nearest neightbor searches using a GiST index (see the section called “Indexing”).

TODO Return the line connecting the nearest approach point between the two arguments

shortestLine({geo,cbuffer,tpoint},{geo,cbuffer,tpoint}) → geometry

The function will only return the first line that it finds if there are more than one

SELECT ST_AsText(shortestLine(tcbuffer '[Cbuffer(Point(2 2), 0.3)@2001-01-01,
  Cbuffer(Point(2 2), 0.7)@2001-01-02]', geometry 'Linestring(50 50,55 55)'));
-- LINESTRING(50.7960725266492 48.8266286733015,50 50)
SELECT ST_AsText(shortestLine(tcbuffer '[Cbuffer(Point(2 2), 0.3)@2001-01-01,
  Cbuffer(Point(2 2), 0.7)@2001-01-02]', cbuffer 'Cbuffer(Point(1 1), 0.5)'));
-- LINESTRING(77.0902838115125 66.6659083092593,90.8134936900394 46.4385792121146)

TODO Return the smallest distance ever between the two arguments

tgeompoint |=| tcbuffer → float

SELECT tcbuffer '[Cbuffer(Point(1 1), 0.3)@2001-01-01, 
  Cbuffer(Point(1 1), 0.5)@2001-01-03]' |=| cbuffer 'Cbuffer(Point(1 1), 0.2)';
-- 2.34988300875063
SELECT tcbuffer '[Cbuffer(Point(1 1), 0.3)@2001-01-01, 
  Cbuffer(Point(1 1), 0.5)@2001-01-03]' |=| geometry 'Linestring(2 2,2 1,3 1)';
-- 82.2059262761477

TODO Return the temporal distance

tgeompoint <-> tcbuffer → tfloat

SELECT tcbuffer '[Cbuffer(Point(1 1), 0.3)@2001-01-01, 
  Cbuffer(Point(1 1), 0.5)@2001-01-03]' <-> cbuffer 'Cbuffer(Point(1 1), 0.2)';
-- [2.34988300875063@2001-01-02 00:00:00+01, 2.34988300875063@2001-01-03 00:00:00+01]
SELECT tcbuffer '[Cbuffer(Point(1 1), 0.3)@2001-01-01, 
  Cbuffer(Point(1 1), 0.5)@2001-01-03]' <-> geometry 'Point(50 50)';
-- [25.0496666945044@2001-01-01 00:00:00+01, 26.4085688426232@2001-01-03 00:00:00+01]
SELECT tcbuffer '[Cbuffer(Point(1 1), 0.3)@2001-01-01, 
  Cbuffer(Point(1 1), 0.5)@2001-01-03]' <->
  tcbuffer '[Cbuffer(Point(1 1), 0.3)@2001-01-02, Cbuffer(Point(1 1), 0.5)@2001-01-04]'
-- [2.34988300875063@2001-01-02 00:00:00+01, 2.34988300875063@2001-01-03 00:00:00+01]