Fisheye-like projection

You might try one of Snyder's Magnifying Glass projections found on http://www.csiss.org/map-projections/Azimuthal.html No 32 to 36.

They are based on this publication: https://pubs.er.usgs.gov/publication/70014498

I'm not sure if there is an online resource with the formulas.

Hägerstrand’s Logarithmic Map might also fit your needs: http://www.ncgia.ucsb.edu/projects/tobler/Projections/sld105.htm

Or a square root azimuthal projection: http://www.ncgia.ucsb.edu/projects/tobler/Projections/sld109.htm

References can be found in http://www.cartoperspectives.org/index.php/journal/article/download/cp59-tobler/307 and in "Small-Scale Map Projection Design" by Frank Canters (available from Google books).


Here's a pseudo-fisheye done in Postgres/Postgis. I used QChainage plugin to create 1000 points along each country border. The points were reprojected around null island (0,0) using the logarithm of distance, but with azimuth preserved.

enter image description here

I used Plat Caree to make it circular, as wgs84 gives a more ellipsoid appearance.

select
    st_asewkt(
        st_endpoint(
            st_scale(
                st_rotate(
                    st_makeline(
                        st_setsrid(st_makepoint(0,0),4326),
                        st_setsrid(st_makepoint(0,1),4326)
                    ),
                    st_azimuth(
                        st_setsrid(
                            st_makepoint(0,0),
                            4326
                        )
                        ,
                        ST_translate(geom,-15.0,-50.0)
                    ) 
                ),
                -(1.0+(7.0*log(ST_Distance(st_setsrid(st_makepoint(0,0),4326),ST_translate(geom,-15.0,-50.0))))),
                (1.0+(7.0*log(ST_Distance(st_setsrid(st_makepoint(0,0),4326),ST_translate(geom,-15.0,-50.0)))))

            )   
        )
    ) as pt

from
    qqq3lines

While not fish eye, you can make this style of map as a cartogram.

The benefits of this is that there are ready made tools for the job and will work with a robust set of datasets.

Just make the value for the Czech Republic much larger than the rest of Europe, adjusting the values to suit needs.

A great tool for this is: ScapeToad

enter image description here