These functions support working with trajectories. A trajectory is a linear geometry with increasing measures (M value) on each coordinate. Spatio-temporal data can be modeled by using relative times (such as the epoch) as the measure values.

# Trajectory Functions

ST_IsValidTrajectory

Tests if the geometry is a valid trajectory.

    				boolean ST_IsValidTrajectory
    				geometry  line

### Description

Tests if a geometry encodes a valid trajectory. A valid trajectory is represented as a `LINESTRING` with measures (M values). The measure values must increase from each vertex to the next.

Valid trajectories are expected as input to spatio-temporal functions like ST_ClosestPointOfApproach

Availability: 2.2.0

&Z_support;

### Examples

    -- A valid trajectory
    SELECT ST_IsValidTrajectory(ST_MakeLine(
      ST_MakePointM(0,0,1),
      ST_MakePointM(0,1,2))
    );
     t

    -- An invalid trajectory
    SELECT ST_IsValidTrajectory(ST_MakeLine(ST_MakePointM(0,0,1), ST_MakePointM(0,1,0)));
    NOTICE:  Measure of vertex 1 (0) not bigger than measure of vertex 0 (1)
     st_isvalidtrajectory
    ----------------------
     f

### See Also

ST_ClosestPointOfApproach

ST_ClosestPointOfApproach

Returns a measure at the closest point of approach of two trajectories.

    				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

&Z_support;

### 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

### See Also

ST_IsValidTrajectory, ST_DistanceCPA, ST_LocateAlong, ST_AddMeasure

ST_DistanceCPA

Returns the distance between the closest point of approach of two trajectories.

    				float8 ST_DistanceCPA
    				geometry  track1
    				geometry  track2

### Description

Returns the minimum distance two moving objects have ever been each other.

Inputs must be valid trajectories as checked by ST_IsValidTrajectory. Null is returned if the trajectories do not overlap in their M ranges.

Availability: 2.2.0

&Z_support;

### Examples

    -- Return the minimum distance of two objects moving between 10:00 and 11:00
    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
    )
    SELECT ST_DistanceCPA(a,b) distance FROM inp;

         distance
    ------------------
     1.96036833151395

### See Also

ST_IsValidTrajectory, ST_ClosestPointOfApproach, ST_AddMeasure, geometry_distance_cpa

ST_CPAWithin

Tests if the closest point of approach of two trajectories is within the specified distance.

    				boolean ST_CPAWithin
    				geometry  track1
    				geometry  track2
    				float8  dist

### Description

Tests whether two moving objects have ever been closer than the specified distance.

Inputs must be valid trajectories as checked by ST_IsValidTrajectory. False is returned if the trajectories do not overlap in their M ranges.

Availability: 2.2.0

&Z_support;

### Examples

    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
    )
    SELECT ST_CPAWithin(a,b,2), ST_DistanceCPA(a,b) distance FROM inp;

     st_cpawithin |     distance
    --------------+------------------
     t            | 1.96521473776207

### See Also

ST_IsValidTrajectory, ST_ClosestPointOfApproach, ST_DistanceCPA, geometry_distance_cpa