ST_Intersects returns FALSE while ST_Intersection returns a geometry.

[olehz]

For example:

SELECT ST_Disjoint(a, b), ST_Intersects(a, b), ST_AsText(ST_Intersection(a, b)) FROM ST_GeomFromText('LINESTRING(-57.2696825964778 7.15879416404005,-57 6.93901666666667)', 4326) a, ST_GeomFrom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b

[Algunenano]

I can confirm this is happening in the current development version:

POSTGIS="3.1.0dev r17985" [EXTENSION] PGSQL="120" GEOS="3.9.0dev-CAPI-1.14.0 " PROJ="6.2.0" GDAL="GDAL 3.1.0dev-503585c5ab-dirty, released 2019/10/07" LIBXML="2.9.9" LIBJSON="0.13.1" LIBPROTOBUF="1.3.1" WAGYU="0.4.3 (Internal)" TOPOLOGY
 RASTER

It's most likely an issue to be minimized and reported to GEOS.

[mdavis]

This is a classic case caused by numeric precision issues. The JTS FAQ has an [explanation](​https://locationtech.github.io/jts/jts-faq.html#D8) of why this happens. JTS produces the same result.

This case is particularly interesting/egregious, because it can be reduced to the following:

  A: LINESTRING (-57 6.939016666666666, -57.001016666666665 7.935202777777778)

  B: LINESTRING (-57.2696825964778 7.15879416404005, -57 6.93901666666667)

By inspection these two lines do intersect. So the line segment intersection computation is computing an incorrect answer. Much work has been done to try and make this computation robust, but clearly there is more work to do.