# set terminal png truecolor nocrop enhanced font arial 9 size 512,384 
# set output 'transparent_solids.2.png'
unset border
set style fill  transparent solid 0.65 border
set dummy u,v
unset key
set label 1 "Kuen's Surface" at screen 0.6, 0.9, 0 left norotate font "frscript,25" back nopoint offset character 0, 0, 0
set style line 2  linetype 2 linecolor rgb "#a0a0f0"  linewidth 0.500 pointtype 2 pointsize default
set style line 3  linetype -1 linewidth 0.500 pointtype 3 pointsize default
set object  1 rect from screen 0, 0, 0 to screen 1, 1, 0 behind lw 1.0 fc  rgb "gray"  fillstyle   solid 1.00 border -1
set parametric
set view 122, 357, 1.35, 1.08
set isosamples 51, 51
set hidden3d offset 1 trianglepattern 3 undefined 1 altdiagonal bentover
set ticslevel 0
set noxtics
set noytics
set noztics
set urange [ -4.50000 : 4.50000 ] noreverse nowriteback
set vrange [ 0.0500000 : 3.09159 ] noreverse nowriteback
set lmargin screen 0.1
set bmargin screen 0.1
set rmargin screen 0.9
set tmargin screen 0.9
set pm3d depthorder
set pm3d interpolate 1,1 flush begin noftriangles hidden3d 3 corners2color mean
unset colorbox
x(u,v) = 2.*a*(cos(u)+u*sin(u))*sin(v) / (1+u**2.*(sin(v))**2)
y(u,v) = 2.*a*(sin(u)-u*cos(u))*sin(v) / (1+u**2.*(sin(v))**2)
z(u,v) = a*log(tan(v/2.))+2.*cos(v)/(1+u**2.*(sin(v))**2)
a = 1.0
splot x(u,v), y(u,v), z(u,v) with pm3d