ST_Difference(g1,g2) throws lwgeom_difference: GEOS Error: TopologyException: found non-noded intersection

[Lars Aksel Opsahl]

Hi On this config I get this error with the input below. Both input geos are valid.

POSTGIS="2.5.3 r17699" [EXTENSION] PGSQL="110" GEOS="3.8.0dev-CAPI-1.12.0 " SFCGAL="1.3.7" PROJ="Rel. 6.2.0, September 1st, 2019" GDAL="GDAL 3.1.0dev-7a9a0f4-dirty, released 2019/99/99" LIBXML="2.9.1" TOPOLOGY RASTER

(1 row)

select ST_Difference(
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
);

It works ok on

• POSTGIS="2.5.0beta2 r16690" [EXTENSION] PGSQL="100" GEOS="3.6.2-CAPI-1.10.2 4d2925d6" SFCGAL="1.2.2" PROJ="Rel. 4.9.3, 15 August 2016" GDAL="GDAL 1.11.4, released 2016/01/25" LIBXML="2.9.1" LIBJSON="0.11" TOPOLOGY RASTER
• POSTGIS="2.5.3dev r17437" [EXTENSION] PGSQL="110" GEOS="3.7.2-CAPI-1.11.2 b55d2125" SFCGAL="1.3.6" PROJ="Rel. 6.2.0, September 1st, 2019" GDAL="GDAL 2.4.1, released 2019/03/15" LIBXML="2.9.4" LIBJSON="0.13.1" LIBPROTOBUF="1.3.1" (core procs from "2.5.2 r17328" need upgrade) TOPOLOGY (topology procs from "2.5.2 r17328" need upgrade) RASTER (raster procs from "2.5.2 r17328" need upgrade) (sfcgal procs from "2.5.2 r17328" need upgrade)
• POSTGIS="2.2.2 r14797" GEOS="3.5.0-CAPI-1.9.0 r4084" PROJ="Rel. 4.8.0, 6 March 2012" GDAL="GDAL 1.9.2, released 2012/10/08" LIBXML="2.7.6" LIBJSON="0.11" TOPOLOGY RASTER

[Lars Aksel Opsahl]

It looks like ST_Intersection is also more unstable on later geos

POSTGIS="2.5.3 r17699" [EXTENSION] PGSQL="110" GEOS="3.8.0dev-CAPI-1.12.0 " SFCGAL="1.3.7" PROJ="Rel. 6.2.0, September 1st, 2019" GDAL="GDAL 3.1.0dev-7a9a0f4-dirty, released 2019/99/99" LIBXML="2.9.1" TOPOLOGY RASTER

select ST_Intersection(
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);

ERROR:  XX000: lwgeom_intersection: GEOS Error: TopologyException: found non-noded intersection between LINESTRING (303308 6.79186e+06, 303314 6.79186e+06) and LINESTRING (303309 6.79186e+06, 303314 6.79186e+06) at 303310.45266244782 6791856.911225128
CONTEXT:  SQL function "st_intersection" statement 1
LOCATION:  pg_error, lwgeom_pg.c:247

[mdavis]

This a classic case where nearly co-incident segments produce a robustness issue during overlay. The first one fails in JTS too.

There was some work done on numerical robustness in 3.8, but it clearly was not a general solution to the robustness problem.

There is a new approach to overlay in the works which handles cases like this (and this is a very good test example). Until that lands, the only options is the usual one of reducing precision by snapping to a grid.

[Lars Aksel Opsahl]

Thanks, I did a test now using ST_Snap and with the code in ​https://github.com/larsop/esri_union/blob/handle_topo_errors/src/main/sql/function_01_esri_union_intersection.sql

I managed to run esri_union on two tables that failed before. I got about 2000 topo errors and all of them was resolved by using ST_snap and some other utils.

I added some more test cases is you need in the of this file ​https://github.com/larsop/esri_union/blob/handle_topo_errors/src/test/sql/regress/esri_union.sql .

[pramsey]

Fixed with GEOS 3.9+