If you skip the part where it is highly ambiguous to determine a positional geometric predicate on anything but an infinite line, that check itself 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, it might never be due to ambiguity and lack of usefulness, and in SQL this is bound to be somewhat dirty and inefficient...
...but not entirely useless - and rather surprisingly performant; tailor yourself some handy functions, and use a classic (K)NN query
- 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!
- 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 <->) and the filter applied only on the NN index subset returned by the <-> operation; the function execution time itself increases linearly with the amount of vertices in the given LineString.
Related:
