# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'map_projection.2.png'
unset border
set angles degrees
set key at screen 0.98, 0.95 right top vertical Right noreverse enhanced autotitle nobox
set key noinvert samplen 0.3 spacing 1 width 0 height 0
set size ratio 0.5 1,1
set style data lines
unset xtics
unset ytics
set title "{/:Bold Hammer} equal-area map projection" 
set xrange [ -3.14159 : 3.14159 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set yrange [ -1.57080 : 1.57080 ] noreverse nowriteback
set y2range [ * : * ] noreverse writeback
set zrange [ * : * ] noreverse writeback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set lmargin  1
set rmargin  1
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
α(λ,φ) = acos(cos(φ) * cos(λ/2.))
x_W3(λ, φ) = 0.5 * (λ*cos(φ1) + (2*cos(φ)*sin(λ/2.))/sinc(α(λ,φ)))
y_W3(λ, φ) = 0.5 * (φ + sin(φ)/sinc(α(λ,φ)))
x_Hammer(λ, φ) = (2*sqrt(2)*cos(φ)*sin(λ/2)) / sqrt(1.0 + cos(φ)*cos(λ/2))
y_Hammer(λ, φ) = sqrt(2)*sin(φ) / sqrt(1.0 + cos(φ)*cos(λ/2))
Z(x,y) = sqrt( 1.0 - (x/4)**2 - (y/2)**2 )
lon(x,y) = 2. * atan( x*Z(x,y) / (4*Z(x,y)**2 - 2) )
lat(x,y) = asin(Z(x,y)*y)
NO_ANIMATION = 1
π = 3.14159265358979
φ1 = 0.880689235420357
## Last datafile plotted: "world.dat"
plot for [λ=-180:180:10] [φ=-90:90] '+' using (x_Hammer(λ,φ)):(y_Hammer(λ,φ)) with lines lc "cyan" lw .5 notitle,      for [φ = -90:90:30] [λ=-180:180:10] '+' using (x_Hammer(λ,φ)):(y_Hammer(λ,φ)) with lines lc "cyan" lw .5 notitle,      'world.dat' using (x_Hammer($1,$2)):(y_Hammer($1,$2)) with filledcurve fc "brown" title "fill",      'world.dat' using (x_Hammer($1,$2)):(y_Hammer($1,$2)) with lines lc "black" title "outline"