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/
[2] 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
[3] 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
[4] https://github.com/jomarlla/geodesicSpatialOperators
--
-------------------------------
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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