Intersection between line & polygon in PostGIS?

I have a linestrings consist of 2 vertices. I want to get all lines that don't intersects with any polygons on the way. In my example: blue line Not intersects - only touches some polygons, but black line although touches with some polygon, it also intersects another. So in conclusion the result is only blue line.

What I did:

 SELECT lines.geom
 FROM lines, polygons
 WHERE ST_Intersects(lines.geom, polygons.geom) = false 
       AND
       ST_Touches(lines.geom, polygons.geom) = true;

The ST_Touches seems to work - I guess because the representation of the line-string consist of the vertex that really touches the polygon.

The ST_Intersects not working - The result is that there is no even 1 line that intersect any polygon.

So what I started to thinking: Maybe because in the space where the line intersect polygon - ain't any 'real' representation of the line-string: Because what is line-string? 2 vertices both outside the polygon...

Whats going on? I thought that GEO-DB should deal exactly with this kind of challenges and 'knows' what spatially intersection is...

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Altough I don't know how to do this (because ST_Segmentize not worked for me from some reason) I prefer not to overcome this issue with just 'breaking' the line-string to more elements such that with high probability some vertex would be inside the polygon.

Answer

As user30184 noted, you have to use ST_Crosses() instead of ST_Intersects().

Additional, your expression works on one line compared to one polygon only: The black line touches Polygon 1 and doesn't cross Polygon 1. In more detail:

SELECT x FROM line, polygons WHERE ...

means: Build a case from every pair of a line and a polygon, so number of cases is n_lines x n_polygons. Do the WHERE clause for every case and keep cases where it is true. Result: blue line, P1: false, blue line, P2: true, black line, P1: true, black line, P2: false.

Maybe you want something like this:

SELECT lines.geom

 FROM lines, polygons
 WHERE ST_Touches(lines.geom, polygons.geom) AND
                 NOT EXISTS (SELECT 1 FROM polygons p2 WHERE ST_Crosses(lines.geom, p2.geom));