gnuplot change color of the connecting lines - graph

Question

I am using gnuplot for the following. I have n equations which I want to plot based on the xaxis value. Here is a sample
set xrange[0:25]
f1(x) = x
f2(x) = 3*x
f3(x) = 10*x
plot (x>0)&&(x<10)?f1(x):(x<20)?f2(x):f3(x)
I know that we can set the color of the line easily by using the below. But it changes the whole color
set style line 1 lt 1 lw 3 pt 3 lc rgb "blue"
But what I want is to make the connecting lines a different color. ie if you plot the above graph you will 5 lines. 3 original lines (from the function) and 2 lines (the almost vertical lines) connecting them. I want to change the color of the connecting lines.
Note 1: These functions are automatically generated by a program, and the number of functions could be large. Even the exact plot command is automatically generated
Note 2: I want a way to differentiate my original lines with the interpolated lines which joins my original lines.
Any help is appreciated

Answer 1

What you actually have is one line defined piecewise, and there isn't an easy way to define colors for line segments within a piecewise line in gnuplot.
Easy way (plot a data file)
I would recommend making a data file looking like this:
# x y color
0 0 0
10 10 0
10 10 1
10 30 1
10 30 0
20 60 0
20 60 1
20 200 1
20 200 0
25 250 0
Notice the double points at x=10 and x=20. This is so the line segments meet at the transitions.
Now plot it with linecolor variable:
#!/usr/bin/env gnuplot
reset
set terminal pdfcairo enhanced color dashed rounded lw 5 size 3,2 font 'Arial,14'
set output 'output2.pdf'
set style data lines
set key top left
set tics scale 0.5 out nomirror
plot 'data.dat' u 1:2:3 lc variable
It looks like this:
You can change the palette (set palette) to determine the colors, and you can have more than 2 color values in the data file if you want.
Harder way (only OK for few segments)
You could define 2n-1 separate lines and connect them:
#!/usr/bin/env gnuplot
reset
set terminal pdfcairo enhanced color dashed rounded lw 5 size 3,2 font 'Arial,14'
set output 'output.pdf'
set style data lines
set key top left
set tics scale 0.5 out nomirror
# points every 0.001 units in the range 0:25
set samples 25001
# main lines
f1(x) = (x <= 9.999) ? x : 1/0
f3(x) = (x >= 10.001) && (x <= 19.999) ? 3*x : 1/0
f5(x) = (x >= 20.001) ? 10*x : 1/0
# define slopes and y-offsets of connecting lines
m2 = (f3(10.001)-f1(9.999))/0.002
b2 = (30.0-10.0)/2.0 + 10.0
m4 = (f5(20.001)-f3(19.999))/0.002
b4 = (200.0-60.0)/2.0 + 60.0
# connecting functions
f2(x) = (x >= 9.999) && (x <= 10.001) ? m2*(x-10) + b2 : 1/0
f4(x) = (x >= 19.999) && (x <= 20.001) ? m4*(x-20) + b4 : 1/0
plot [0:25] f1(x), f2(x), f3(x), f4(x), f5(x)
Which looks like this:

Answer 2

You can define a secondary function to define the breakpoints of your function, which is automatically coloring the right linepiece. The below code is easy to extend to different functions and breakpoints (i.e., you can just change x1 or x2). Adding multiple points is also straightforward.
xmin=0.
xmax=25.
x0=0.
x1=10.
x2=20.
nsample=200.
dx=(xmax-xmin)/nsample
print dx
set xrange[xmin:xmax]
set sample nsample
f1(x) = x
f2(x) = 3*x
f3(x) = 10*x
f4(x) = (x>x0)&&(x<x1)?f1(x):(x<x2)?f2(x):f3(x)
f5(x) = x
f5(x) = ( (x>x1&&x<=x1+dx) || (x>x2&&x<=x2+dx) )?1:0
set cbrange [0:1]
unset key
plot '+' using 1:(f4($1)):(f5($1)) lc variable with lines
Not that I have use the special filename '+', which just constructs a data file with equally space datapoints (following nsample).

Answer 3

If it is ok to skip the connecting lines, then you can use a simplified version of #andyras second variant. Just define all functions to be 1/0 when outside a specified range:
set style data lines
unset key
f1(x) = (x > 0) && (x < 10) ? x : 1/0
f2(x) = (x > 10) && (x < 20) ? 3*x : 1/0
f3(x) = (x > 20) ? 10*x : 1/0
plot [0:25] f1(x), f2(x), f3(x)
Following yet another possibility. This assumes, that you can select a sampling high enough, so that the "jumps" which connect the functions are always greater than inside a function:
set style data lines
unset key
set xrange[0:25]
f1(x) = x
f2(x) = 3*x
f3(x) = 10*x
f(x) = ( (x>0)&&(x<10)?f1(x):(x<20)?f2(x):f3(x) )
set samples 1000
curr = 0
prev = 0
lim = 1
plot '+' using (prev = curr, curr=f($1), $1):(f($1)):(abs(curr-prev) < lim ? 0 : 1) lc var