[postgis-users] New algorithms on the spheroid: intersecting lines and minimum distance point-line. Current software error assesment.

[José Carlos Martínez]

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


-- 
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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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