Intersection tests with curved polygons

Tue Jan 7 11:19:35 PST 2025

Why isn’t ST_DWithin being used here?

I thought we had native curve distance checking with ST_DWithin as well.

From: Paul Ramsey <pramsey at cleverelephant.ca> 
Sent: Tuesday, January 7, 2025 1:37 PM
To: Andrea Aime <andrea.aime at geosolutionsgroup.com>
Cc: PostGIS Users Discussion <postgis-users at lists.osgeo.org>
Subject: Re: Intersection tests with curved polygons

I’m not 100% sure this is apples and apples?

On Jan 7, 2025, at 2:55 AM, Andrea Aime <andrea.aime at geosolutionsgroup.com <mailto:andrea.aime at geosolutionsgroup.com> > wrote:

 testing 3 scenarios:

*	The current query using ST_Intersection as is (returns 2 polygons, wrong result but I'm treating it as the baseline)

ST_Intersection() is an expensive operation, constructing new geometry. ST_Intersects() is a cheaper operation, returning true/false.

*	Using && + ST_Distance

ST_Distance() is cheaper than ST_Intersection(), and similar to ST_Intersects() in how it calculates an answer.

*	Using && + linearized intersection, with a precision good enough to get the correct result (0.01 meters)

Still using Intersection() so on an expensive path.

Some things to note in general:

- ST_Intersection() will always delegate to GEOS and if handed curves will linearize them first. Delegating to GEOS does have some fixed overheads, a full copy of the geometry is made, and GEOS set up.

- ST_Intersects() will sometimes delegate to GEOS, one of those cases being handed a curve polygon. Which will again coast you linearization and a full copy.

- Finer linearization will naturally result in more segments and more processing cost.

- ST_Distance() with native curve support trades the expense of some extra trig doing edge/arc calculations for avoiding the trip to GEOS and processing a much smaller number of edges than the linearized path.

I find the results surprsing:

> pgbench -U cite helsinki -f baseline.sql  -c 32 -t 2000
tps = 10227.810087 ((without initial connection time)

> pgbench -U cite helsinki -f distance.sql  -c 32 -t 2000
tps = 19989.627257 (without initial connection time)

> pgbench -U cite helsinki -f linearized.sql  -c 32 -t 2000
tps = 8984.594159 (without initial connection time)

So... testing with the distance is twice as fast as the other options? Wow, have we been doing intersection tests wrong all this time? ROFL

Other possible ideas:

*	There is something specific to having curves in the mix, and having to pay the cost of linearization makes distance competitive?
*	The specific dataset is playing an important role in the result

I am not, in general, surprised at your results, knowing the different code paths your tests could be running through.

P.

Ah, since there seems to be a real issue, I've also opened a ticket in trac: https://trac.osgeo.org/postgis/ticket/5832#ticket

Regards,

Andrea Aime

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On Sun, Dec 22, 2024 at 4:44 PM Andrea Aime <andrea.aime at geosolutionsgroup.com <mailto:andrea.aime at geosolutionsgroup.com> > wrote:

Hi Paul,

thanks a lot for following up. Comments inline below.

These are literally CurvePolygon type? 

The column type is just "geometry(Geometry,3879)", while ST_GeometryType returns "multisurface" for both.

When doing a ST_AsText instead, you'll get something like:

MULTISURFACE(CURVEPOLYGON(COMPOUNDCURVE((...

for both.

It’s probably getting caught in our lack of full curve support.

I would be interested in the ST_Distance between the point and those two CurvePolygons. (Because, for distance, we have a postgis-native implementation that supports curves). 

=# SELECT ogc_fid, ST_Distance(ST_GeomFromText('POINT (25492818 6677399.98)', 3879), geom) FROM testdata;

 ogc_fid |     st_distance     
---------+---------------------
    1258 | 0.01234572446598792
   12875 |                   0
(2 rows)

Indeed, the correct answer, 12875 contains the point, while the other polygon is close to it.

Whereas for intersection, the calculation is delegated to GEOS *after linearizing the inputs*. In that linearization, could sit the logically problem you’re seeing.

Let's check with different tolerances... yes, changing the tolerance changes the result:

=#  SELECT ogc_fid FROM testdata WHERE ST_Intersects(ST_CurveToLine(geom, 0.01, 1, 1), ST_GeomFromText('POINT (25492818 6677399.98)', 3879));
 ogc_fid 
---------
   12875
(1 row)

#  SELECT ogc_fid FROM testdata WHERE ST_Intersects(ST_CurveToLine(geom, 0.02, 1, 1), ST_GeomFromText('POINT (25492818 6677399.98)', 3879));
 ogc_fid 
---------
    1258
(1 row)

In the immediate future, I guess I could have the GeoTools PostGIS store use either approach, when knowing curves are involved... 

First using && to perform a first rough filter, and then either use either

* ST_Distance equals to 0

* An explicit linearization with a target tolerance (this is an urban application, so I'm guessing they will need centimeter, if not millimeter, precision)

.

Is there a clear winner here in terms of performance, or performance of distance vs linearized intersection is more contextual to the geometries involved?

Cheers

Andrea

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