Image:Fresnel integrals.svg

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Fresnel_integrals.svg‎ (19KB, MIME type: image/svg+xml)

This is a file from the Wikimedia Commons. The description on its description page there is shown below.

[edit] Summary

This picture shows the two Fresnel integral functions. I made it working with Octave and Gnuplot, post-processing the output with Sodipodi.

First I created a file called fresnelS.m with the following content:


function y = fresnelS(x)
y = zeros(1,length(x));
F = @(t) sin(t.^2);

for i = 1:length(x)
    y(i) = quad(F,0,x(i));
end

then I created another file called fresnelC.m with the following content:


function y = fresnelC(x)
y = zeros(1,length(x));
F = @(t) cos(t.^2);

for i = 1:length(x)
    y(i) = quad(F,0,x(i));
end

In the same directory where these two files are, I ran the following Octave code:



t = 0:0.01:5;
S = fresnelS(t);
C = fresnelC(t);

F = [t; S; C];
F = F';
save -ascii 'fresnel_integrals.dat' F;

thus creating the file fresnel_integrals.dat. Then, to create the image, I used the following Gnuplot code:


# set the output
set terminal svg
set output "fresnel_integrals.svg"

set title "Fresnel Integrals"

# axis properties
set xrange [0:5]
set yrange [0:1]
set xlabel "x"
set xzeroaxis linetype -1 linewidth 0.5
set yzeroaxis linetype -1 linewidth 0.5
set xtics axis
set ytics axis

plot "fresnel_integrals.dat" using 1:2 title "S(x)" with lines linewidth 2,\
     "fresnel_integrals.dat" using 1:3 title "C(x)" with lines linewidth 2

Finally I opened it with Sodipodi to change the stroke style.

[edit] Licensing

I, the author of this work, hereby publish it under the following licenses:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".