Detecting if point is on left or right side of line in PostGIS?

I have a linestring table and a point table in postgis.

I know the closest line to any given point. What I need to know is on which "side" of that line is the point. I guess I have to do that by creating a perpendicular line from given point to the line (closest point on the line) and then compare the coordinates, but I don't know exactly how to do that, and if it's the proper way, since line changes it's direction.

I've made a picture to illustrate my task.

The line itself is black, its direction is shown with green arrows. I need to add a "side" column to the point table, so that red points should have value "right" and blue points should have value "left".

Can someone give an SQL code example of calculating a "side" value of a point?

Answer

select (ST_Azimuth(h.vec) - ST_Azimuth(h.seg))
from (
    select 
        ST_MakeLine(cp.p, point.geom) vec,
        ST_MakeLine(cp.p, 
            ST_LineInterpolatePoint(
                line.geom, 
                ST_LineLocatePoint(line.geom, cp.p) * 1.01)
        ) seg
        from (

            select 
                ST_ClosestPoint(line.geom, point.geom)
        ) p as cp
    ) as h

So the idea is to calculate angle between closest line segment, and vector from closest point on the line to your point.

get a closest point on a line

select ST_ClosestPoint(line.geom, point.geom)

create the vector from closest point to your point

ST_MakeLine(cp.p, point.geom) vec

create a vector among your line

ST_MakeLine(
    --original point
    cp.p, 
    --find a point next to the closest point on line
    ST_LineInterpolatePoint(line.geom, 
         ST_LineLocatePoint(line.geom, cp.p) * 1.01)) seg

get the difference between directions

ST_Azimuth(h.vec) - ST_Azimuth(h.seg)

So right and left will be greater than zero and lower than zero.