# Gnuplot programme for creating an "illuminance angles graph"
# -- it is a trivial sinus function with an origin shiftet to 45 deg and
# pi/2 and an amplitude of pi/2.
# However, in such coordinates, it shows nicely,
# cones of which angular radius, or rings of space angles between such cones,
# contribute most and least to a reading of lamberian detector.
# The first 10 degrees and the last ones (from 80 to 90 degrees)
# can be often neglected.
# Script by Jan Hollan, 2013
#set term png size 1024,768
set term pdf enhanced
set encoding iso_8859_1
set out 'illuminance.pdf'
set grid
set title \
'Illuminance by a uniform luminance from a cone growing from 0 to 2 {/Symbol p} sr'
set ylabel '{/Symbol p}·(1-cos(2x))/2, the integral over the cone / 1 sr'
set x2label 'Angular radius / 1 rad'
set x2range [0:pi/2]
set x2tics 0.2
# set y2label 'Space angle / 1 square degree'
# set y2range '
set xlabel '(Angular radius / 1 degree)'
r(x)=pi*x/180
plot [0:90] \
pi*(1-cos(2*r(x)))/2 lw 3 title ''
#set out 'space_an_dg2.png'
#d=1/((1*pi/180)**2)
# plot [0:90] d*2*pi*(1-cos(r(x))) title 'true, 2*pi*(1-cos(x))', \
# d*pi*(r(x)**2) title 'planar approximation, pi*(x**2)' ,\
# d*pi*(1-cos(2*r(x)))/2 title 'effective for planar illumination, pi*(1-cos(2x)/2)'