[Proj] Correction of definition of CRS EPSG 5456 and 5457

[Andre Joost]

Am 22.01.18 um 13:42 schrieb Andre Joost:

>
> I have no clue what values are "correct", since I have not found any
> sample coordinates in both systems.
>
> My best resource available online is
>
> https://dialnet.unirioja.es/descarga/articulo/5381246.pdf
> http://www.revistas.una.ac.cr/index.php/uniciencia/article/download/5930/5822
>
> from Dörries and Rodriguez.
>

Update on that:

The paper includes a set of coordinates for 28 points within Costa Rica. 
The coordinates seem to be geocentric X,Y,Z meters based on Ocotepeque 
on the left and WGS84 on the right.

You can calculate the differences, and get mean values of:
deltX = 213.27 m
deltY = 7.72 m
deltZ = -74.65 m

That is less than 2 meters away from the center point given in 
EPSG:5470. The standard deviation is 5 meters.

You can reproject those coordinates to Costa Rica Norte with:

cs2cs +proj=geocent +ellps=clrk66 +towgs84=213.11,9.37,-74.95,0,0,0,0 
+units=m +no_defs  +to +proj=lcc +lat_1=10.46666666666667 
+lat_0=10.46666666666667 +lon_0=-84.33333333333333 +k_0=0.99995696 
+x_0=500000 +y_0=271820.522 +ellps=clrk66 
+towgs84=213.11,9.37,-74.95,0,0,0,0 +units=m +no_defs  -f "%%.3f" 
coordgeocent-ocotepeque.csv >CRN-ocotepeque.txt

cs2cs +proj=geocent +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m 
+no_defs  +to +proj=lcc +lat_1=10.46666666666667 
+lat_0=10.46666666666667 +lon_0=-84.33333333333333 +k_0=0.99995696 
+x_0=500000 +y_0=271820.522 +ellps=clrk66 
+towgs84=213.11,9.37,-74.95,0,0,0,0 +units=m +no_defs  -f "%%.3f" 
coordgeocent-wgs84.csv >CRN-wgs84.txt

Again, you can calculate the difference, and get a mean diff value of 
less than 7 centimeters, with a standard deviation of 3 meters. One 
point is 11 meters off, and another 7 meters.

The official parameters may have been calculated with more points, but 
you still have to face the fact that last centuries surveying has not 
been more accurate.

Using the standard datum shift of PROJ.4, I get a resulting shift of 7.5 
meters, with standard deviation of less than 4 meters. So it is not that 
bad.

I also tried the deprecated 7parms transformation values, resulting in a 
mean diff of 9 centimeters and 3 meters standard deviation. This is not 
a significant improvement against the 3-parms of EPSG:5470.

HTH,
Andre Joost