Intended to replace en:File:Parabola_in_projective_space.png, which is in a raster format.

Made in gnuplot. The code:

#!/usr/bin/gnuplot -persist

set parametric
set urange  [-0.9999:0.9999]
set vrange [-1:1]
set isosamples 25, 25

set xrange [-2:2]
set yrange [-2:2]
set zrange [-1:1]

set style line 1 lt rgb "#dddddd" lw 1
set style line 2 lt rgb "#9999ff" lw 1
set style line 3 lt rgb "#0000ff" lw 1
set style line 4 lt rgb "#ff9999" lw 1
set style line 5 lt rgb "#ff0000" lw 1

set border 15 ls 1
unset key
set noxtics
set noytics
set noztics

set view 55, 25
set terminal svg

# For scaling [-1:1] to [-∞:∞]
scale(x) = (x/((1-x)*(1+x)))

splot cos(u*pi)*cos(v*pi), sin(u*pi)*cos(v*pi), sin(v*pi) ls 1, \
      (u*2),(u*2)**2,-1 ls 2, \
      scale(u)/sqrt(scale(u)**2+scale(u)**4+1), scale(u)**2/sqrt(scale(u)**2+scale(u)**4+1), -1/sqrt(scale(u)**2+scale(u)**4+1) ls 3, \
      -scale(u)/sqrt(scale(u)**2+scale(u)**4+1), -scale(u)**2/sqrt(scale(u)**2+scale(u)**4+1), 1/sqrt(scale(u)**2+scale(u)**4+1) ls 3, \
      (u*2),(u*2)**3,-1 ls 4, \
      scale(u)/sqrt(scale(u)**2+scale(u)**6+1), scale(u)**3/sqrt(scale(u)**2+scale(u)**6+1), -1/sqrt(scale(u)**2+scale(u)**6+1) ls 5, \
      -scale(u)/sqrt(scale(u)**2+scale(u)**6+1), -scale(u)**3/sqrt(scale(u)**2+scale(u)**6+1), 1/sqrt(scale(u)**2+scale(u)**6+1) ls 5

Then the svg was cropped by changing the output to contain this line:

<svg width="600" height="600" viewBox="145 130 310 280"

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