[Octave-patch-tracker] [patch #10022] [octave forge] (mapping) Auxillary Latitudes

[anonymous]

Follow-up Comment #16, patch #10022 (project octave):

Started looking.

Because the source for iso2geo algorithm was known. 
Stared with geo2iso

L82 came from 
https://en.wikipedia.org/wiki/Latitude#Isometric_latitude

Following Synder pg [15]

psi = log(tan(pi/4+phi/2)*((1-ecc.*sin(phi))/(1+e*sin(phi)))^(ecc/2));


Which gives


>> geo2iso(0:10:90)
ans =

     -2.72      7.33     17.70     28.75     40.99     55.19     72.73    
96.71    136.86   2136.24

>> iso2geo (geo2iso (0:10:90))
ans =

   -2.74    7.36   17.54   27.80   38.14   48.54   59.01   69.51   80.05  
90.61


In Synder pg [15] it also states

chi = geo2con(phi);
psi = log ( tan(pi/4 + chi/2) ); 


could be used but also states 

although there is no particular advantage over using the previous equation


The results are

>> geo2iso(0:10:90)
ans =

    -0.00     9.98    20.28    31.24    43.36    57.39    74.66    98.08  
136.58   300.72

>> iso2geo (geo2iso (0:10:90))
ans =

       0   10.00   20.00   30.00   40.00   50.00   60.00   70.00   80.00  
90.00



Next will look at iso2geo



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