Temporal contains

tContains(geometry,tgeom) → tbool

SELECT tContains(geometry 'Linestring(1 1,3 3)',
  tgeompoint '[Point(4 2)@2001-01-01, Point(2 4)@2001-01-02]');
-- {[f@2001-01-01, f@2001-01-02]}
SELECT tContains(geometry 'Linestring(1 1,3 3,1 1)',
  tgeompoint '[Point(4 2)@2001-01-01, Point(2 4)@2001-01-03]');
-- {[f@2001-01-01, t@2001-01-02], (f@2001-01-02, f@2001-01-03]}
SELECT tContains(geometry 'Polygon((1 1,1 3,3 3,3 1,1 1))',
  tgeompoint '[Point(0 1)@2001-01-01, Point(4 1)@2001-01-02]');
-- {[f@2001-01-01, f@2001-01-02]}
SELECT tContains(geometry 'Polygon((1 1,1 3,3 3,3 1,1 1))',
  tgeompoint '[Point(1 4)@2001-01-01, Point(4 1)@2001-01-04]');
-- {[f@2001-01-01, f@2001-01-02], (t@2001-01-02, f@2001-01-03, f@2001-01-04]}

Temporal disjoint

tDisjoint({geo,tgeo},{geo,tgeo}) → tbool

The function only supports 3D or geographies for two temporal points

SELECT tDisjoint(geometry 'Polygon((1 1,1 2,2 2,2 1,1 1))',
  tgeompoint '[Point(0 0)@2001-01-01, Point(3 3)@2001-01-04)');
-- {[t@2001-01-01, f@2001-01-02, f@2001-01-03], (t@2001-01-03, t@2001-01-04]}
SELECT tDisjoint(tgeompoint '[Point(0 3)@2001-01-01, Point(3 0)@2001-01-05)',
  tgeompoint '[Point(0 0)@2001-01-01, Point(3 3)@2001-01-05)');
-- {[t@2001-01-01, f@2001-01-03], (t@2001-01-03, t@2001-01-05)}

Temporal distance within

tDwithin({geo,tgeo},{geo,tgeo},float) → tbool
tDwithin({geography,tgeogpoint},{geography,tgeogpoint},float,spheroid boolean=true) → tbool

For temporal geography points, the other argument is a geography point or a temporal geography point. The distance is measured on the WGS 84 spheroid by default. If the last argument is false, it is measured on the sphere. A segment of a temporal geography point moves along a great circle, and the result changes its value at every instant at which the geodetic distance crosses the given distance, which a segment may cross several times.

SELECT tDwithin(geometry 'Point(1 1)',
  tgeompoint '[Point(0 0)@2001-01-01, Point(2 2)@2001-01-03)', sqrt(2));
--  {[t@2001-01-01, t@2001-01-03)}
SELECT tDwithin(tgeompoint '[Point(1 0)@2001-01-01, Point(1 4)@2001-01-05]',
  tgeompoint 'Interp=Step;[Point(1 2)@2001-01-01, Point(1 3)@2001-01-05]', 1);
-- {[f@2001-01-01, t@2001-01-02, t@2001-01-04], (f@2001-01-04, t@2001-01-05]}
SELECT tDwithin(geography 'Point(1 0.1)',
  tgeogpoint '[Point(0 0)@2001-01-01, Point(2 0)@2001-01-03]', 15000);
/* {[f@2001-01-01, t@2001-01-01 21:48:53.195554, t@2001-01-02 02:11:06.804445],
   (f@2001-01-02 02:11:06.804445, f@2001-01-03]} */
SELECT tDwithin(tgeogpoint '[Point(0 0)@2001-01-01, Point(2 0)@2001-01-03]',
  tgeogpoint '[Point(1 1)@2001-01-01, Point(1 -1)@2001-01-03]', 20000, false);
/* {[f@2001-01-01, t@2001-01-01 20:56:51.37512, t@2001-01-02 03:03:08.624879],
   (f@2001-01-02 03:03:08.624879, f@2001-01-03]} */

Temporal intersects

tIntersects({geo,tgeo},{geo,tgeo}) → tbool

The function only supports 3D or geographies for two temporal points

SELECT tIntersects(geometry 'MultiPoint(1 1,2 2)',
  tgeompoint '[Point(0 0)@2001-01-01, Point(3 3)@2001-01-04)');
/* {[f@2001-01-01, t@2001-01-02], (f@2001-01-02, t@2001-01-03],
   (f@2001-01-03, f@2001-01-04]} */
SELECT tIntersects(tgeompoint '[Point(0 3)@2001-01-01, Point(3 0)@2001-01-05)',
  tgeompoint '[Point(0 0)@2001-01-01, Point(3 3)@2001-01-05)');
-- {[f@2001-01-01, t@2001-01-03], (f@2001-01-03, f@2001-01-05)}

Temporal touches

tTouches({geometry,tgeom},{geometry,tgeom}) → tbool

SELECT tTouches(geometry 'Polygon((1 0,1 2,2 2,2 0,1 0))',
  tgeompoint '[Point(0 0)@2001-01-01, Point(3 0)@2001-01-04)');
-- {[f@2001-01-01, t@2001-01-02, t@2001-01-03], (f@2001-01-03, f@2001-01-04]}