PostGIS: How to find Nearest Neighbour but only within a direction range?

A positional geometric predicate check is nothing but a 2D cross product. The issue here is that it has to be applied to geometric primitives, i.e. an actual two-vertex vector representation, of which a LineString may have plenty (each segment between two consecutive vertices). In effect, for each closest Point candidate you'd need to find the closest segment on the given LineString, then check for the positional predicate between their vector representations.

This could potentially be implemented in the core math of, say, ST_DWithin, and maybe even the index lookup of the (K)NN operator <->, since somewhere in their algorithms they have to include these per-segment operations already.

But it isn't, yet, and in SQL this is bound to be somewhat dirty and inefficient...

---

...but not entirely useless; tailor yourself some handy functions, and use a classic (K)NN query:

1. Create a set of functions to loop over a given LineString vertices, find the closest two-vertex segment to a given point, and check if it is left or right of it:

   -- Utility function; returns the cross product of three Points
   -- if cp < 0 the point is to the right, cp > 0 to the left, cp = 0 on the line
   CREATE OR REPLACE FUNCTION _ST_DeterminantSign (
     IN  pt GEOMETRY(POINT),
     IN  v1 GEOMETRY(POINT),
     IN  v2 GEOMETRY(POINT),
     OUT FLOAT
   ) LANGUAGE SQL AS
     $BODY$
       SELECT ( ST_X($3)-ST_X($2) ) * ( ST_Y($1)-ST_Y($2) ) - ( ST_Y($3)-ST_Y($2) ) * ( ST_X($1)-ST_X($2) );
     $BODY$
   ;
   
   -- loop over line segments of a given LineString, find its closest segment to a given point and check if it is to the right
   CREATE OR REPLACE FUNCTION ST_IsRightOf (
     IN  pt GEOMETRY(POINT),
     IN  ln GEOMETRY(LINESTRING),
     OUT BOOLEAN
   ) LANGUAGE SQL AS
     $BODY$
       SELECT _ST_DeterminantSign($1, ST_PointN($2, n), ST_PointN($2, n+1)) < 0
       FROM   GENERATE_SERIES(1, ST_NPoints($2)-1) AS n
       ORDER BY
              ST_MakeLine(ST_PointN($2, n), ST_PointN($2, n+1)) <-> $1
       LIMIT  1;
     $BODY$
   ;
   
   -- loop over line segments of a given LineString, find its closest segment to a given point and check if it is to the left
   CREATE OR REPLACE FUNCTION ST_IsLeftOf (
     IN  pt GEOMETRY(POINT),
     IN  ln GEOMETRY(LINESTRING),
     OUT BOOLEAN
   ) LANGUAGE SQL AS
     $BODY$
       SELECT _ST_DeterminantSign($1, ST_PointN($2, n), ST_PointN($2, n+1)) > 0
       FROM   GENERATE_SERIES(1, ST_NPoints($2)-1) AS n
       ORDER BY
              ST_MakeLine(ST_PointN($2, n), ST_PointN($2, n+1)) <-> $1
       LIMIT  1;
     $BODY$
   ;
   

   These functions here only work on LineString and Point geometries!
2. Run

   SELECT t.id, t.geom
   FROM   <table1> AS t1
   CROSS JOIN LATERAL (
     SELECT t2.id, t2.geom
     FROM   <table2> AS t2
     WHERE  ST_IsRightOf(ST_EndPoint(ST_ShortestLine(t1.geom, t2.geom)), t1.geom)
     ORDER BY
            t1.geom <-> t2.geom
     LIMIT  1
   ) AS t
   ;
   

   to get the t2.id & t2.geom that is the closest to the right of each line in t1.

The core operation is fully index driven (ordering by distance via <->); the function execution time increases linearly with the amount of vertices in the given LineString.

---

Related:

• Order matched geometries on line by distance in PostGIS
• Efficient way to find nearest feature between huge postgres tables
• Is the Geometry(4326) an alias for Geography datatype?