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#
# Fresnel integrals expressed in terms of complex error function
# Should these be provided as built-in functions?
# Would it be better to use an implementation not requiring libcerf?
#
if (!strstrt(GPVAL_COMPILE_OPTIONS,"+LIBCERF")) {
print "This copy of gnuplot was not linked against libcerf"
exit;
}
save_encoding = GPVAL_ENCODING
set encoding utf8
set title "{/:Bold Fresnel integrals C(z), S(z)}" offset 0,-1
set key reverse Left left invert
set for [l=1:3] linetype l lw 2
set border 3
set tics nomirror
set margins 10,10,4,4
set xrange [0:pi]
set yrange [0:1]
set ytics 0.0, 0.25, 0.75
plot cdawson(x), FresnelS(x), FresnelC(x), 0.5 lc "black" dt '...' notitle
pause -1 "<cr> to continue"
reset
set label 1 at screen 0.1, 0.9
set label 2 at screen 0.1, 0.8
set label 3 at screen 0.1, 0.7
set label 1 "{/:Bold Clothoid using Fresnel integrals}"
set label 2 "x = FresnelC(z) = {/*2 ∫@_{/*0.5 0}^{/*.5 x}} {/:Italic cos(@^π⁄_2 t^2)dt}\n"
set label 3 "y = FresnelS(z) = {/*2 ∫@_{/*0.5 0}^{/*.5 x}} {/:Italic sin(@^π⁄_2 t^2)dt}\n"
set xrange [-1:1]
set yrange [-1:1]
set size square
set sample 1000
unset border
set xzeroaxis
set yzeroaxis
set xtics axis add ("" 0)
set ytics axis add ("" 0)
unset key
plot sample [t=-9:9] '+' using (FresnelC(t)) : (FresnelS(t)) with lines lc "blue" lw .6
pause -1 "<cr> to continue"
reset
set encoding save_encoding
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