#!/usr/local/bin/gnuplot -persist
# set terminal pngcairo  transparent enhanced fontscale 1.0 size 600, 400 
# set output 'piecewise.3.png'
set border 16 front lt black linewidth 1.000 dashtype solid
set key at screen 0.5, 0.15 center center vertical Right noreverse enhanced autotitle nobox
unset parametric
set style data lines
set xyplane at 0
unset xtics
unset ytics
set title "Piecewise function of one parameter in 3D" 
set title  font ",15" textcolor lt -1 norotate
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 colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
part1(x) = 0.5 + (9.*x-x**3)/ 24.
part2(x) = 1.0 + (x-3.0)**3 / 48.
NO_ANIMATION = 1
save_encoding = "utf8"
part1 = "part1: for x < 1  norm(x) ≈  ½ + (9x-x^3) / 24"
part2 = "part2: for x > 1  norm(x) ≈   1 +  (x-3)^3 / 48"
## Last datafile plotted: "+"
splot [-2:2][-2:2] sample    [h=1:5]   '+' using (cos(h)):(sin(h)):(h) lw 2,    [h=5:10]  '+' using (cos(h)):(sin(h)):(h) lw 4,    [h=10:15] '+' using (cos(h)):(sin(h)):(h) lw 2