[gdal-dev] How to compare closed curves with different start points?

[Rahkonen Jukka]

Hi,

I thought that PostGIS would return an empty geometry with ST_Difference, but it does not. I do not know what that means. Maybe PostGIS is linearizing the curve before computing the difference. Your geometry seems to be like a plate with rounded corners and two holes, and I guess that the ring of the rightmost hole is oriented differently.

 This was my query:

select st_difference(
'CURVEPOLYGON (COMPOUNDCURVE (CIRCULARSTRING (85369.63 433446.48, 85368.99 433448.54, 85366.08 433449.62), (85366.08 433449.62, 85320.0 433442.34), CIRCULARSTRING (85320.0 433442.34, 85318.48 433441.52, 85317.85 433439.94), (85317.85 433439.94, 85323.26 433407.01), CIRCULARSTRING (85323.26 433407.01, 85324.24 433405.814, 85325.76 433405.24), (85325.76 433405.24, 85371.68 433412.51), CIRCULARSTRING (85371.68 433412.51, 85373.66 433413.74, 85374.28 433415.25), (85374.28 433415.25, 85369.63 433446.48)), CIRCULARSTRING (85361.39 433438.49, 85365.44 433434.44, 85361.39 433430.39, 85357.34 433434.44, 85361.39 433438.49), CIRCULARSTRING (85327.69 433426.1, 85330.18 433423.61, 85327.69 433421.12, 85325.2 433423.61, 85327.69 433426.1))
','CURVEPOLYGON (COMPOUNDCURVE (CIRCULARSTRING (85320.0 433442.34, 85318.48 433441.52, 85317.85 433439.94), (85317.85 433439.94, 85323.26 433407.01), CIRCULARSTRING (85323.26 433407.01, 85324.24 433405.814, 85325.76 433405.24), (85325.76 433405.24, 85371.68 433412.51), CIRCULARSTRING (85371.68 433412.51, 85373.66 433413.74, 85374.28 433415.25), (85374.28 433415.25, 85369.63 433446.48), CIRCULARSTRING (85369.63 433446.48, 85368.99 433448.54, 85366.08 433449.62), (85366.08 433449.62, 85320.0 433442.34)), CIRCULARSTRING (85357.34 433434.44, 85361.39 433438.49, 85365.44 433434.44, 85361.39 433430.39, 85357.34 433434.44), CIRCULARSTRING (85327.69 433426.1, 85330.18 433423.61, 85327.69 433421.12, 85325.2 433423.61, 85327.69 433426.1))');

-Jukka Rahkonen-




________________________________________
Lähettäjä: gdal-dev <gdal-dev-bounces at lists.osgeo.org> käyttäjän George Mathijssen via gdal-dev <gdal-dev at lists.osgeo.org> puolesta
Lähetetty: Lauantai 23. elokuuta 2025 17.29
Vastaanottaja: gdal-dev at lists.osgeo.org <gdal-dev at lists.osgeo.org>
Aihe: [gdal-dev] How to compare closed curves with different start points?

Hi,In an application that I am currently developing there is a need to compare geometries and I hit an obstacle when comparing OGRCurvePolygons.From a SQL/MM perspective I (mostly) need ST_OrderingEquals, meaning that the coordinates must be in the same order. This is implemented by OGRCurvePolygon as is stated in the documentation.The obstacle however is that there are 3 freedoms when comparing polygons:* the direction of a ring may differ* the start point of a ring may differ* the order of inner rings may differFor example the following 2 curve polygons should be considered equal in the application (apologies for the formatting):CURVEPOLYGON (COMPOUNDCURVE (CIRCULARSTRING (85369.63 433446.48, 85368.99 433448.54, 85366.08 433449.62), (85366.08 433449.62, 85320.0 433442.34), CIRCULARSTRING (85320.0 433442.34, 85318.48 433441.52, 85317.85 433439.94), (85317.85 433439.94, 85323.26 433407.01), CIRCULARSTRING (85323.26 433407.01, 85324.24 433405.814, 85325.76 433405.24), (85325.76 433405.24, 85371.68 433412.51), CIRCULARSTRING (85371.68 433412.51, 85373.66 433413.74, 85374.28 433415.25), (85374.28 433415.25, 85369.63 433446.48)), CIRCULARSTRING (85361.39 433438.49, 85365.44 433434.44, 85361.39 433430.39, 85357.34 433434.44, 85361.39 433438.49), CIRCULARSTRING (85327.69 433426.1, 85330.18 433423.61, 85327.69 433421.12, 85325.2 433423.61, 85327.69 433426.1))CURVEPOLYGON (COMPOUNDCURVE (CIRCULARSTRING (85320.0 433442.34, 85318.48 433441.52, 85317.85 433439.94), (85317.85 433439.94, 85323.26 433407.01), CIRCULARSTRING (85323.26 433407.01, 85324.24 433405.814, 85325.76 433405.24), (85325.76 433405.24, 85371.68 433412.51), CIRCULARSTRING (85371.68 433412.51, 85373.66 433413.74, 85374.28 433415.25), (85374.28 433415.25, 85369.63 433446.48), CIRCULARSTRING (85369.63 433446.48, 85368.99 433448.54, 85366.08 433449.62), (85366.08 433449.62, 85320.0 433442.34)), CIRCULARSTRING (85357.34 433434.44, 85361.39 433438.49, 85365.44 433434.44, 85361.39 433430.39, 85357.34 433434.44), CIRCULARSTRING (85327.69 433426.1, 85330.18 433423.61, 85327.69 433421.12, 85325.2 433423.61, 85327.69 433426.1))The differing directions of rings I can solve with OGRCompoundCurve::isClockwise and OGRCompoundCurve::reversePoints to ensure consistent ring directions before comparing.The differing order of inner rings is solvable by finding matching rings. This is O(N^2), but N is small enough in practice to be acceptable.This leaves me with the problem of comparing rings that have different start points. My first thought was to ask how to change the start point of a closed curve (ring), since I cannot find anything about this in the documentation. However that is not a solution, since you cannot change the start point to any other point on the ring. For example changing the start point to be the mid-point of an arc (circular string) would make the geometry invalid.I could iterate the points of the closed curve/ring, but I would also have to know how each point is connected to the previous/next point (linear, curve). I do not know if this information is available, searching the documentation gave me no result.So the question is: how can I compare closed curves (rings) that have different start points?Thank you for your help.