# set terminal svg size 600,400 dynamic enhanced font 'arial,10' mousing name "transparent_solids_2" butt dashlength 1.0 
# set output 'transparent_solids.2.svg'
unset border
set style fill  transparent solid 0.65 border
set dummy u, v
unset key
set label 1 "Kuen's Surface" at screen 0.57, 0.9, 0 left norotate font "frscript,20" back nopoint
set object  1 rect from screen 0, 0 to screen 1, 1
set object  1 behind clip lw 1.0  dashtype solid fc  rgb "gray"  fillstyle   solid 1.00 border lt -1
set parametric
set view 122, 357, 1.35, 1.08
set isosamples 51, 51
set hidden3d back offset 1 trianglepattern 3 undefined 1 altdiagonal bentover
set style data lines
set xyplane relative 0
unset xtics
unset ytics
unset ztics
set urange [ -4.50000 : 4.50000 ] noreverse nowriteback
set vrange [ 0.0500000 : 3.09159 ] noreverse nowriteback
set xrange [ * : * ] noreverse writeback
set x2range [ * : * ] noreverse writeback
set yrange [ * : * ] noreverse writeback
set y2range [ * : * ] noreverse writeback
set zrange [ * : * ] noreverse writeback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set lmargin at screen 0.1
set bmargin at screen 0.1
set rmargin at screen 0.9
set tmargin at screen 0.9
set pm3d depthorder 
set pm3d interpolate 1,1 flush begin noftriangles border lt black linewidth 0.500 dashtype solid corners2color mean
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
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)
NO_ANIMATION = 1
a = 1.0
splot x(u,v), y(u,v), z(u,v) with pm3d