[postgis-users] New algorithms on the spheroid: intersecting lines and minimum distance point-line. Current software error assesment.
José Carlos Martínez
jomarlla at cgf.upv.es
Sat Jul 31 09:52:47 PDT 2021
Hi,
I was not expecting that answer and less to hear about calculations on
the sphere when we are talking about geodesy!.
The comparison between the spheroidal (local sphere) and spherical
intersection has already been made in the article. We did it because
some software uses this approach. It is important for us to check each
software methodology in order to be able to rigorously compare the results.
The spherical method is very easy and trivial because it is just using
spherical trigonometry but the errors commited and very large as you can
check in our paper, so please keep it without exposing this
functionality to the end user because it is a very rude approach, and if
so the end user must be warned about that. By the way, the name of the
source code in postgis about geodetic calculations (lwgeodetic) could be
confusing because geodetic coordinates use a spheroid not a sphere, and
geodetic calculations should be done using geodesics lines.
You talked about 1% of distance errors saying that its *not that wrong*.
Umm...do not know how to answer that...I mean 1% its incredible wrong,
even 1 per thousands its not ok for many tasks.
Maybe 1% could be ok for those users who use postgis to make thematic
maps in a small scales but anything else.
I am referring to the maps listed in annexes 1 and 2 of inspire in
Europe, or similar in other countries: cadastral maps, transport
networks, etc. on a large scale, so it means that the error tolerance in
only a few centimeters but the distances of the segments can be long, so
no spherical method can be used, or even a local projected
transformation, at least without knowing the error comitted (error that
you do not know with postgis or other app right now) in advance.
I agree with you about that to build a full set of spatial operators
working on the spheroid is a much more complicated task that just an
intersection of geodesics, but with the two proposed algorithm (geodesic
intersection and minimun distance from a point to a geodesic) you can
already do many things, even just involving linear layers. Do you really
need to build a full topology geodetic library in order to incorporate
in postgis the two funtions I am talking about?
So, this methodoly give you:
1.- Exact solution
2.- Assesment of the commited errors of other methods (spherical,
projected CRS, etc.).
3.- Working with the full globe, no matter the distance for the precision.
Cheers
José
El 28/07/2021 a las 18:54, Paul Ramsey escribió:
> This is very interesting, but from a practical point of view the
> problems around doing intersections on the spheroid are not to do with
> the difficulty of calculating spheroidal intersection points, but the
> difficulty in programming things that are relatively simple in
> cartesian (R2) space in spherical space (S2), like "is this point in
> this ring", because the question of "what does this ring enclose" is
> quite different in S2 than in R2. IE, the complexity of the problem
> does not reside in the spheroidal geometry but in the spherical
> topology. Which is not to say that it cannot be done, Google S2 has
> done a number of constructive geometry functions in spherical space,
> but it's not just a matter of getting the right intersection points.
>
> I would be interested in direct comparisons between spheroidal and
> spherical intersection, rather than comparisons with "whatever the
> heck these tools use under the covers", which your survey shows is
> "quite a wide variety of approaches".
>
> Unfortunately although PostGIS has spherical intersection internally
> (hilariously, I calculate it here [1] but never even let it out of the
> function) it is not exposed to the end user. You could use Google S2
> [2] to generate spherical intersection points though, and compare
> those to spheroidal.
>
> The reason I ask is because comparison of spherical and spheroidal
> *distances* never yield particularly large differences, always under
> 1%. Now, spherical distances are not *right*, but they are also *not
> that wrong* which is presumably why tools like S2 have eschewed
> finding spheroidal intersections. Under the covers you'll find that
> the PostGIS distance functions use spherical calculations to find the
> two points that are closest between two geometries, and only then
> calculate the spheroidal distance between those points.
>
> Thanks for sharing your research,
> Paul
>
> [1]
> https://github.com/postgis/postgis/blob/main/liblwgeom/lwgeodetic.c#L3596
> <https://github.com/postgis/postgis/blob/main/liblwgeom/lwgeodetic.c#L3596>
> [2] http://s2geometry.io/ <http://s2geometry.io/>
>
>
> On Tue, Jul 27, 2021 at 9:34 AM José Carlos Martínez
> <jomarlla at cgf.upv.es <mailto:jomarlla at cgf.upv.es>> wrote:
>
> Hi list,
>
> I want to share our last research about gemetric operations on the
> spheroid [1]
>
> Considering two segments defined by 2 points each one over the
> spheroid.
> We want to get the intersection point defined by these two segments.
>
> Several points to note:
> 1.- We could not find any software (Oracle Spatial, ArcGIS, PostGIS,
> Google Apis) that performs this calculation on the ellipsoid: some
> use
> projected CRS, others just use a local sphere.
> 2.- The error comitted by these software is unknown. And I go
> further,
> these unknown errors could be greater than the cartographic
> precision of
> my geo data? If so, all my geo spatial analysis could be wrong.
> 3.- We designed a new algorithm of fast convergence working on the
> spheroid. We can get the exact intersection point, therefore we can
> asses the error from the current software solutions.
> 4.- Example: working with segments around 50km length, the error is
> around 3 meters (PostGIS, ArcGIS). Table 4 from paper [2] shows the
> large error commited by Oracle Spatial, ArcGIS, and even PostGIS with
> local projected CRS (st_intersection with geography).
> 5.- This proposed algorithm is implemented as a test in PostGIS, Java
> and Maxima.
>
>
> Finally, mention that, in a normal computer, about 20,000
> intersections
> per second have been obtained. Perhaps, now is the time to migrate
> certain geospatial libraries such as JTS (GEOS), GDAL, etc. so
> that they
> carry out the calculations in full on the ellipsoid and thus be
> able to
> forget about the projected CRS, and leave them purely for aesthetic
> purposes.
>
> I will be proud of helping the PostGIS or the JTS team to incorporate
> these geometric operations on the ellipsoid (could be the first
> spatial
> BDD or geospatial library to do that).
>
>
> Cheers,
>
> José
>
>
> All the information, source code, etc. here.
> [1]
> https://cartosig.webs.upv.es/2021/07/27/geodesic-intersection-proposed-algorithm-and-error-assessment-of-current-software/
> <https://cartosig.webs.upv.es/2021/07/27/geodesic-intersection-proposed-algorithm-and-error-assessment-of-current-software/>
>
> [2] https://www.mdpi.com/2076-3417/11/11/5129
> <https://www.mdpi.com/2076-3417/11/11/5129>
>
> Martínez-Llario JC, Baselga S, Coll E. Accurate Algorithms for
> Spatial
> Operations on the Spheroid in a Spatial Database Management System.
> Applied Sciences. 2021; 11(11):5129.
> https://doi.org/10.3390/app11115129
> <https://doi.org/10.3390/app11115129>
>
> [3] https://link.springer.com/article/10.1007/s11200-017-1020-z
> <https://link.springer.com/article/10.1007/s11200-017-1020-z>
>
> Baselga, S., Martínez-Llario, J.C. Intersection and point-to-line
> solutions for geodesics on the ellipsoid. Stud Geophys Geod 62,
> 353–363
> (2018). https://doi.org/10.1007/s11200-017-1020-z
> <https://doi.org/10.1007/s11200-017-1020-z>
>
> [4] https://github.com/jomarlla/geodesicSpatialOperators
> <https://github.com/jomarlla/geodesicSpatialOperators>
>
>
> --
> -------------------------------
> José Carlos Martínez Llario
> http://www.upv.es/ficha-personal/jomarlla
> <http://www.upv.es/ficha-personal/jomarlla>
> https://cartosig.webs.upv.es <https://cartosig.webs.upv.es>
> Producción Cartográfica y SIG.
> Dpto. Ingeniería Cartográfica.
> Univ. Politécnica de Valencia.
> -------------------------------
>
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--
-------------------------------
José Carlos Martínez Llario
http://www.upv.es/ficha-personal/jomarlla
https://cartosig.webs.upv.es
Producción Cartográfica y SIG.
Dpto. Ingeniería Cartográfica.
Univ. Politécnica de Valencia.
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