[PROJ] How does proj deal with ellipsoid with respect to reprojection

Sat Mar 28 23:28:57 PDT 2020

Doing point in polygon in a projection will result in occasional wrong conclusions. A point near de edge can seem to be inside the polygon while it's outside, or the other way around, since a straight line in the projection deviates from the geodesic.

I analysed this problem for the Netherlands (51 - 55 degrees north) in the azimuthal projection (+proj=sterea) of the national coordinate reference system RD (epsg:28992) and in plate-caree projection (+proj=lonlat). The deviation depends on the length, orientation and location of a polygon segment. I computed the maximum possible deviation in the Netherlands for both projections to advise the Dutch government not to allow any segments longer than 200 m in a new digital storage system for policy and zoning borders.

Table for the Netherlands:
Segment length, RD deviation, lonlat deviation;

500 km, 160 m, 6 km;
200 km, 25 m, 1 km;
100 km, 6.4 m, 0.2 km;
50 km, 1.6 m, 60 m;
20 km, 26 cm, 9.7 m;
10 km, 8 cm, 2.4 m;
5 km, 3 cm, 60 cm;
2 km, 5 mm, 9.7 cm;
1 km, 1.3 mm, 2.4 cm;
500 m, 0.3 mm, 6 mm;
200 m, <0.1 mm, 1 mm;
100 m, <0.1 mm, 0.2 mm;
50 m, <0.1 mm, <0.1 mm

This means that when you first split long segments of polygons by adding enough points along the geodesic, you could do a point in polygon even in lonlat. The required distance between the added points depends on the location (latitude). Near the poles it will get a bit tricky, as the maximum deviation increases to 50% of the size of the segment length.

Regards, Jochem

________________________________
From: PROJ <proj-bounces at lists.osgeo.org> on behalf of Pierre Abbat <phma at bezitopo.org>
Sent: Sunday, March 29, 2020 1:27:00 AM
To: proj at lists.osgeo.org <proj at lists.osgeo.org>
Subject: Re: [PROJ] How does proj deal with ellipsoid with respect to reprojection

On Saturday, 28 March 2020 10:58:53 EDT DeTracey, Brendan wrote:
> Hi,
>
> I am using a gnomonic projection for point in polygon testing. The
> transformation is:
>
> projinfo -s EPSG:4326 -t ' +type=crs +ellps=WGS84  +datum=WGS84 +proj=gnom
> +lat_0=61.39107201212929 +lon_0=-58.56360634793518'
>
> Will transformed great circles still be straight lines? Or does the fact
> that my source and target ellipse/datum are the same mean the gnomonic
> projection has the WGS4 coordinates passed directly to it? My confusion
> comes from gnomonic only being defined for a sphere, not an ellipsoid.

In Bezitopo, I use a stereographic projection for point-in-polygon testing.
This avoids the problem with the gnomonic projection that a polygon may cross
the great circle which is projected to infinity. In stereographic, only one
point is projected to infinity, and I chose it to be in the ocean, more than a
megameter from any land, and with unround coordinates. Stereographic turns
great circles into circles, so a spherical polygon turns into a polyarc in the
plane, which I can handle easily.

Pierre
--
When a barnacle settles down, its brain disintegrates.
Já não percebe nada, já não percebe nada.

_______________________________________________
PROJ mailing list
PROJ at lists.osgeo.org
https://lists.osgeo.org/mailman/listinfo/proj
________________________________
From: PROJ <proj-bounces at lists.osgeo.org> on behalf of Pierre Abbat <phma at bezitopo.org>
Sent: Sunday, March 29, 2020 1:27:00 AM
To: proj at lists.osgeo.org <proj at lists.osgeo.org>
Subject: Re: [PROJ] How does proj deal with ellipsoid with respect to reprojection

On Saturday, 28 March 2020 10:58:53 EDT DeTracey, Brendan wrote:
> Hi,
>
> I am using a gnomonic projection for point in polygon testing. The
> transformation is:
>
> projinfo -s EPSG:4326 -t ' +type=crs +ellps=WGS84  +datum=WGS84 +proj=gnom
> +lat_0=61.39107201212929 +lon_0=-58.56360634793518'
>
> Will transformed great circles still be straight lines? Or does the fact
> that my source and target ellipse/datum are the same mean the gnomonic
> projection has the WGS4 coordinates passed directly to it? My confusion
> comes from gnomonic only being defined for a sphere, not an ellipsoid.

In Bezitopo, I use a stereographic projection for point-in-polygon testing.
This avoids the problem with the gnomonic projection that a polygon may cross
the great circle which is projected to infinity. In stereographic, only one
point is projected to infinity, and I chose it to be in the ocean, more than a
megameter from any land, and with unround coordinates. Stereographic turns
great circles into circles, so a spherical polygon turns into a polyarc in the
plane, which I can handle easily.

Pierre
--
When a barnacle settles down, its brain disintegrates.
Já não percebe nada, já não percebe nada.

_______________________________________________
PROJ mailing list
PROJ at lists.osgeo.org
https://lists.osgeo.org/mailman/listinfo/proj

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