Return the smallest distance ever

{geo,pose,tpose} |=| {geo,pose,tpose} → float

SELECT tpose '[Pose(Point(2 2), 0.3)@2001-01-01, Pose(Point(2 2), 0.7)@2001-01-02]' |=|
  geometry 'Linestring(50 50,55 55)';
-- 67.88225099390856
SELECT tpose '[Pose(Point(2 2), 0.3)@2001-01-01, Pose(Point(2 2), 0.7)@2001-01-02]' |=|
  pose 'Pose(Point(1 1), 0.5)';
-- 1.4142135623730951
SELECT tpose '[Pose(Point(1 1), 0.3)@2001-01-01, 
  Pose(Point(1 1), 0.5)@2001-01-03]' |=| pose 'Pose(Point(2 2), 0.2)';
-- 1.4142135623730951
SELECT tpose '[Pose(Point(1 1), 0.3)@2001-01-01, 
  Pose(Point(1 1), 0.5)@2001-01-03]' |=| geometry 'Linestring(2 2,2 1,3 1)';
-- 1

The operator |=| can be used for doing nearest neightbor searches using GiST or SP-GiST indexes (see the section called “Indexing”).

Return the instant of the first temporal pose at which the two arguments are at the nearest distance

SELECT asText(nearestApproachInstant(tpose '[Pose(Point(2 2), 0.3)@2001-01-01,
  Pose(Point(2 2), 0.7)@2001-01-02]', geometry 'Linestring(50 50,55 55)'));
-- Pose(POINT(2 2),0.3)@2001-01-01
SELECT asText(nearestApproachInstant(tpose '[Pose(Point(2 2), 0.3)@2001-01-01,
  Pose(Point(2 2), 0.7)@2001-01-02]', pose 'Pose(Point(1 1), 0.5)'));
-- Pose(POINT(2 2),0.3)@2001-01-01

Return the line connecting the nearest approach point

shortestLine({geo,pose,tpose},{geo,pose,tpose}) → geometry

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

SELECT ST_AsText(shortestLine(tpose '[Pose(Point(2 2), 0.3)@2001-01-01,
  Pose(Point(2 2), 0.7)@2001-01-02]', geometry 'Linestring(50 50,55 55)'));
-- LINESTRING(2 2,50 50)
SELECT ST_AsText(shortestLine(tpose '[Pose(Point(2 2), 0.3)@2001-01-01,
  Pose(Point(2 2), 0.7)@2001-01-02]', pose 'Pose(Point(1 1), 0.5)'));
-- LINESTRING(2 2,1 1)

Return the temporal distance

tpose <-> tpose → tfloat

SELECT round(tpose '[Pose(Point(1 1), 0.3)@2001-01-01, 
  Pose(Point(1 1), 0.5)@2001-01-03]' <-> pose 'Pose(Point(2 2), 0.2)', 6);
-- [1.414214@2001-01-01, 1.414214@2001-01-03]
SELECT round(tpose '[Pose(Point(1 1), 0.3)@2001-01-01, 
  Pose(Point(1 1), 0.5)@2001-01-03]' <-> geometry 'Point(50 50)', 6);
-- [69.296465@2001-01-01, 69.296465@2001-01-03]
SELECT round(tpose '[Pose(Point(1 1), 0.3)@2001-01-01, 
  Pose(Point(2 2), 0.5)@2001-01-03]' <->
  tpose '[Pose(Point(1 2), 0.3)@2001-01-02, Pose(Point(2 1), 0.5)@2001-01-04]', 6);
-- [0.707107@2001-01-02, 0.5@2001-01-02 12:00:00+01, 0.707107@2001-01-03]