[PROJ] Correcting map projection errors

[Ken Mankoff]

Hi Charles,

Thanks for contributing to the discussion. I'm going offline for the
next 5 weeks and so I can't follow up much more on this, but I'm happy
to hear you think the current method is probably good enough.

I'm not tied to proj4 or any specific tool, but prefer to use existing
user-level tools rather than code my own, even a simple wrapper function
- so for this reason I would rather run your planimeter tool than access
the proj function you link to. Unless that function is exposed through
the proj CLI interface somehow.

Cheers,

  -k.

On 2019-04-24 at 14:21 +0200, Charles Karney <charles at karney.com>
wrote...
> Sorry, I'm coming rather late into this discussion.
>
> * as Thomas Knudsen says the square of the linear projection scale
> will
>    give you the correction factor for small areas, because your
>    projection is conformal. Use the scale at the center of the cell
>    for best accuracy. (My guess is that for this projection, polar
>    stereographic, for Greenland, and for 200m squares, this will give
>    you satisfactory accuracy.)
>
> * instead of using GeographicLib's Planimeter program, you might find
> it
>    simpler to use proj's geod_polygonarea function; this implements
>    the same algorithm. It's documented at
>
>  
> https://geographiclib.sourceforge.io/1.49/C/geodesic_8h.html#aafa25f138d78c387a107ec0221bbb181
>
>    If you are not tied to proj.4, then use the PolygonArea class in
>    GeographicLib
>
>  
> https://geographiclib.sourceforge.io/1.49/classGeographicLib_1_1PolygonAreaT.html
>
> * following up on daan's suggestion: transforming to an equal area
>    projection is possible, but use the azimuthal equal area projection
>    instead of the cylindrical one. The edges of your squares in the
>    polar stereographic projection will be straighter in the azimuthal
>    equal area projection and so the distortion involved in the
>    reprojection will be less.
>
> * an alternative to using an equal area projection is to project the
>    points onto the authalic sphere and then to use the formula for
>    areas on a sphere. This is the route that Oracle takes. This has
>    the advantage of giving small distortion over the whole globe. If
>    you go this route, I recommend compute spherical areas with Eq (64)
>    from my paper "Algorithms for geodesics"
>
>      https://doi.org/10.1007/s00190-012-0578-z