xyll <- expand.grid(x= seq(100, 150, length.out = 15), y = seq(-70, -40, length.out = 12))
library(tissot)
ti <- tissot(xyll, "EPSG:3031")
atan2(ti$dy_dlam, ti$dx_dlam)
#> [1] -1.745330 -1.807663 -1.869996 -1.932330 -1.994663 -2.056996 -2.119329
#> [8] -2.181662 -2.243996 -2.306329 -2.368662 -2.430995 -2.493328 -2.555662
#> [15] -2.617995 -1.745330 -1.807663 -1.869996 -1.932330 -1.994663 -2.056996
#> [22] -2.119329 -2.181662 -2.243996 -2.306329 -2.368662 -2.430995 -2.493328
#> [29] -2.555662 -2.617995 -1.745330 -1.807663 -1.869996 -1.932330 -1.994663
#> [36] -2.056996 -2.119329 -2.181662 -2.243996 -2.306329 -2.368662 -2.430995
#> [43] -2.493328 -2.555662 -2.617995 -1.745330 -1.807663 -1.869996 -1.932330
#> [50] -1.994663 -2.056996 -2.119329 -2.181662 -2.243996 -2.306329 -2.368662
#> [57] -2.430995 -2.493328 -2.555662 -2.617995 -1.745330 -1.807663 -1.869996
#> [64] -1.932330 -1.994663 -2.056996 -2.119329 -2.181662 -2.243996 -2.306329
#> [71] -2.368662 -2.430995 -2.493328 -2.555662 -2.617995 -1.745330 -1.807663
#> [78] -1.869996 -1.932330 -1.994663 -2.056996 -2.119329 -2.181662 -2.243996
#> [85] -2.306329 -2.368662 -2.430995 -2.493328 -2.555662 -2.617995 -1.745330
#> [92] -1.807663 -1.869996 -1.932330 -1.994663 -2.056996 -2.119329 -2.181662
#> [99] -2.243996 -2.306329 -2.368662 -2.430995 -2.493328 -2.555662 -2.617995
#> [106] -1.745330 -1.807663 -1.869996 -1.932330 -1.994663 -2.056996 -2.119329
#> [113] -2.181662 -2.243996 -2.306329 -2.368662 -2.430995 -2.493328 -2.555662
#> [120] -2.617995 -1.745330 -1.807663 -1.869996 -1.932330 -1.994663 -2.056996
#> [127] -2.119329 -2.181662 -2.243996 -2.306329 -2.368662 -2.430995 -2.493328
#> [134] -2.555662 -2.617995 -1.745330 -1.807663 -1.869996 -1.932330 -1.994663
#> [141] -2.056996 -2.119329 -2.181662 -2.243996 -2.306329 -2.368662 -2.430995
#> [148] -2.493328 -2.555662 -2.617995 -1.745330 -1.807663 -1.869996 -1.932330
#> [155] -1.994663 -2.056996 -2.119329 -2.181662 -2.243996 -2.306329 -2.368662
#> [162] -2.430995 -2.493328 -2.555662 -2.617995 -1.745330 -1.807663 -1.869996
#> [169] -1.932330 -1.994663 -2.056996 -2.119329 -2.181662 -2.243996 -2.306329
#> [176] -2.368662 -2.430995 -2.493328 -2.555662 -2.617995
ti <- tissot(xyll, "+proj=laea +lon_0=125 +lat_0=-55")
atan2(ti$dy_dlam, ti$dx_dlam)
#> [1] 3.777743e-01 3.227736e-01 2.682444e-01 2.141125e-01 1.603012e-01
#> [6] 1.067320e-01 5.332500e-02 -7.464113e-07 -5.332650e-02 -1.067335e-01
#> [11] -1.603027e-01 -2.141140e-01 -2.682459e-01 -3.227752e-01 -3.777759e-01
#> [16] 3.747563e-01 3.201817e-01 2.660812e-01 2.123799e-01 1.590006e-01
#> [21] 1.058645e-01 5.289107e-02 -7.402528e-07 -5.289255e-02 -1.058659e-01
#> [26] -1.590021e-01 -2.123814e-01 -2.660827e-01 -3.201833e-01 -3.747578e-01
#> [31] 3.717512e-01 3.176017e-01 2.639284e-01 2.106560e-01 1.577068e-01
#> [36] 1.050015e-01 5.245948e-02 -7.343063e-07 -5.246095e-02 -1.050030e-01
#> [41] -1.577083e-01 -2.106575e-01 -2.639299e-01 -3.176032e-01 -3.717527e-01
#> [46] 3.687557e-01 3.150307e-01 2.617838e-01 2.089390e-01 1.564184e-01
#> [51] 1.041422e-01 5.202974e-02 -7.282471e-07 -5.203120e-02 -1.041437e-01
#> [56] -1.564198e-01 -2.089405e-01 -2.617853e-01 -3.150322e-01 -3.687572e-01
#> [61] 3.657664e-01 3.124659e-01 2.596448e-01 2.072268e-01 1.551337e-01
#> [66] 1.032856e-01 5.160138e-02 -7.222408e-07 -5.160282e-02 -1.032871e-01
#> [71] -1.551352e-01 -2.072283e-01 -2.596462e-01 -3.124674e-01 -3.657679e-01
#> [76] 3.627801e-01 3.099043e-01 2.575090e-01 2.055176e-01 1.538515e-01
#> [81] 1.024307e-01 5.117389e-02 -7.162578e-07 -5.117532e-02 -1.024321e-01
#> [86] -1.538530e-01 -2.055191e-01 -2.575105e-01 -3.099058e-01 -3.627816e-01
#> [91] 3.597935e-01 3.073432e-01 2.553741e-01 2.038094e-01 1.525703e-01
#> [96] 1.015765e-01 5.074680e-02 -7.102810e-07 -5.074823e-02 -1.015779e-01
#> [101] -1.525718e-01 -2.038109e-01 -2.553756e-01 -3.073446e-01 -3.597950e-01
#> [106] 3.568032e-01 3.047796e-01 2.532378e-01 2.021004e-01 1.512886e-01
#> [111] 1.007221e-01 5.031964e-02 -7.043382e-07 -5.032105e-02 -1.007236e-01
#> [116] -1.512901e-01 -2.021018e-01 -2.532392e-01 -3.047811e-01 -3.568047e-01
#> [121] 3.538060e-01 3.022108e-01 2.510975e-01 2.003886e-01 1.500051e-01
#> [126] 9.986659e-02 4.989192e-02 -6.983649e-07 -4.989332e-02 -9.986799e-02
#> [131] -1.500065e-01 -2.003900e-01 -2.510989e-01 -3.022123e-01 -3.538075e-01
#> [136] 3.507984e-01 2.996339e-01 2.489509e-01 1.986721e-01 1.487182e-01
#> [141] 9.900889e-02 4.946315e-02 -6.922688e-07 -4.946454e-02 -9.901028e-02
#> [146] -1.487196e-01 -1.986735e-01 -2.489524e-01 -2.996353e-01 -3.507999e-01
#> [151] 3.477771e-01 2.970458e-01 2.467956e-01 1.969489e-01 1.474264e-01
#> [156] 9.814807e-02 4.903285e-02 -6.862745e-07 -4.903423e-02 -9.814945e-02
#> [161] -1.474278e-01 -1.969503e-01 -2.467970e-01 -2.970472e-01 -3.477785e-01
#> [166] 3.447385e-01 2.944437e-01 2.446291e-01 1.952170e-01 1.461284e-01
#> [171] 9.728314e-02 4.860052e-02 -6.802149e-07 -4.860188e-02 -9.728450e-02
#> [176] -1.461297e-01 -1.952184e-01 -2.446305e-01 -2.944451e-01 -3.447399e-01
ti <- tissot(xyll, "+proj=merc")
atan2(ti$dy_dlam, ti$dx_dlam)
#> [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [149] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ti <- tissot(xyll, "+proj=cea")
atan2(ti$dy_dlam, ti$dx_dlam)
#> [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [149] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Created on 2026-06-10 with reprex v2.1.1