#!/usr/bin/python
#
# Graph the light intensity from a two dimensional array of isotropic
# LEDs in a plane parallel to the two dimensional array of LEDs:
#
#     ./isotropic.array.py > output
#
#     To plot using gnuplot(1):
#
#        set title "Relative Light Intensity, (to one isotropic LED)"
#        set xlabel "X, LED #"
#        set ylabel "Y, LED #"
#        set zlabel "Light Intensity" rotate by 90
#        set grid x
#        set grid y
#        set grid z
#        show grid
#        splot [x=0:15][y=0:10][z=0:150] "output" using 1:2:3 with lines
#
#     To find the intensity of light in the center:
#
#        cut -f3 output  | sort -n | tail -1
#
# For an isotropic light source a perpendicular distance, d, from a
# point, p, in a plane, the light intensity measured at a distance, l,
# from p in the plane would be proportional to the hypotenuse, h,
# squared, i.e.:
#
#     h^2 = d^2 + l^2
#     I is proportional to 1 / h^2
#     I is proportional to 1 / (d^2 + l^2), by substitution
#
#     If l = 0, (i.e., the reference value directly under the
#     isotropic light source):
#
#     I(0) = 1 / d^2
#     I(l) / I(0) = (1 / (d^2 + l^2)) / (1 / d^2)
#                 = d^2 / (d^2 + l^2)
#                 = 1 / (1 + (l^2 / d^2))
#
# Note that this value is the RELATIVE intensity of light at a
# distance l from the perpendicular under the light source in the
# plane, (i.e., relative to directly under the isotropic light
# source.) If l = 0, this value is unity.
#
# So, the value of the intensity of an isotropic light source, at a
# perpendicular distance, d, from a plane decreases at 1 / d^2. The
# RELATIVE intensity of light at a distance l in the plane to that
# value is 1 / (1 + (l^2 / d^2)), which is useful for calculating the
# variation in the intensity of light projected on the plane from an
# array of identical isotropic light sources.
#
# x = number of LEDs on the x axis of the two dimensional array.
#
# y = number of LEDs on the y axis of the two dimensional array.
#
# d = distance between LED array and parallel plane, inches.
#
# s = distance between LEDs, inches, (60 LEDs per meter for SMD 5050,
#     which are approximated as an isotropic radiator.)
#
import math
#
x = 15
y = 10
d = 5.0
s = 39.37 / 60.0
#
for i in range (x):

    for j in range (y):
        sum = 0

        for ii in range (x):

            for jj in range (y):
                sum = sum + 1.0 / (1.0 + ((s * math.sqrt ((ii - i) ** 2 + (jj - j) ** 2)) / d) ** 2)

        print ("%d\t%d\t%f" % (i, j, sum))

    print ("")