[PROJ] Correcting map projection errors

[Thomas Knudsen]

Ken

The scale is the quotient between the length in the map and the length on
the ellipsoid, so essentially you’re right. But note that the figures you
obtain are valid for infinitesimal items only.

For large lengths/areas you should do the computations with geodesics on
the ellipsoid, using e.g. Charles Karney’s Planimeter tool over at
https://geographiclib.sourceforge.io/cgi-bin/Planimeter (online service,
includes link to source etc.)

Also, a day where you have too much time on your hand, see the discussion
over at
http://osgeo-org.1560.x6.nabble.com/Re-Qgis-user-New-Features-in-Shape-Tools-3-2-0-td5378898.html

/Thomas


Den tir. 23. apr. 2019 kl. 06.14 skrev Ken Mankoff <mankoff at 3m411.com>:

> Dear Proj list,
>
> Please excuse duplicates - Even sent this with a different subject "Fwd:
> proj list issue" and I have not gotten any replies. I'm resending with an
> improved subject in case people skipped the email with that subject.
>
> I'm following up on a helpful thread from this list from 2017:
> https://lists.osgeo.org/pipermail/proj/2017-November/007496.html
>
> I'm calculating map projection errors, and want to check my interpretation
> of the results with someone who knows proj better. I'm using EPSG:3413
> projection and the following proj string:
>
> +proj=stere +lat_0=90 +lat_ts=70 +lon_0=-45 +k=1 +x_0=0 +y_0=0 +no_defs
> +a=6378137 +rf=298.257223563 +towgs84=0.000,0.000,0.000 +to_meter=1
>
> To estimate the error in Southern Greenland, I do:
>
> echo -40 60 | proj -VS ${PROJSTR}
>
> and see
>
> #Stereographic
> #       Azi, Sph&Ell
> #       lat_ts=
> # +proj=stere +lat_0=90 +lat_ts=70 +lon_0=-45 +k=1 +x_0=0 +y_0=0 +no_defs
> # +a=6378137 +rf=298.257223563 +towgs84=0.000,0.000,0.000 +to_meter=1
> #Final Earth figure: ellipsoid
> #  Major axis (a): 6378137.000
> #  1/flattening: 298.257224
> #  squared eccentricity: 0.006694379990
> Longitude: 40dW [ -40 ]
> Latitude:  60dN [ 60 ]
> Easting (x):   289632.50
> Northing (y):  -3310514.64
> Meridian scale (h) : 1.03942808  ( 3.943 % error )
> Parallel scale (k) : 1.03942808  ( 3.943 % error )
> Areal scale (s):     1.08041073  ( 8.041 % error )
> Angular distortion (w): 0.000
> Meridian/Parallel angle: 90.00000
> Convergence : 5d [ 5.00000000 ]
> Max-min (Tissot axis a-b) scale error: 1.03943 1.03943
>
> The key values for Northern Greenland are:
>
> echo -40 82 | proj -VS ${PROJSTR}
> ...
> ...
> Meridian scale (h) : 0.97460025  ( -2.54 % error )
> Parallel scale (k) : 0.97460025  ( -2.54 % error )
> Areal scale (s):     0.94984565  ( -5.015 % error )
>
> My question is how to interpret the Areal scale error
>
> I think that in this projection N. Greenland is over-represented by 8%
> area and any areal feature there should be divided by 1.0804 or linear
> features divided by 1.0394 to bring them to true scale. Similarly, in S.
> Greenland I should adjust a areal feature by dividing by 0.94984565. Is
> this correct?
>
> Essentially, does "-2.54 % error" mean that the EPSG:3413 projection is
> smaller than it should be, or that the "true" spheroid is smaller than
> EPSG:3413 here?
>
> Thanks,
>
>   -k.
>
> _______________________________________________
> PROJ mailing list
> PROJ at lists.osgeo.org
> https://lists.osgeo.org/mailman/listinfo/proj
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.osgeo.org/pipermail/proj/attachments/20190423/2797dcc1/attachment.html>