File:Envelope cast.svg

#!/usr/bin/gnuplot
#Gnuplot 5.0+

set term svg font 'Helvetica, 24'
set output 'envelope_cast.svg'

# In this program, the envelope equation is y = (v^2)/(2g) - (ĝ^2)/(2v^2). We take g = 10, v = 10.
# The cast trajectory curve family is y = x tan \theta -(ĝ^2)/(2v^2 cos^2\theta)
g = 10;
v = 10;
# n is the number of the trajectories
n = 101;

set multiplot
set samples 1000

set xrange [-11:11]
set yrange [0:5]
set xtics 2
set ytics 1
set xzeroaxis lt -1 lc rgb "black" lw 1
set yzeroaxis lt -1 lc rgb "black" lw 1

unset label

# Draw the trajectories of the cast objects.
set key off

#theta = pi/n*i;
# The following uses the fact 1/cos^2(theta) = tan(theta)*tan(theta)+1.

plot for [i=1:n-1] x*tan(pi/n*i)-(g*x*x)*(tan(pi/n*i)*tan(pi/n*i)+1)/(2*v*v) lc rgb "red" lw 1;

unset multiplot

set term x11
set output