Clean list of points depending on close range (+-5) - bash

Question

How to clean a list of points in a variable regarding on if it is
the same point or
a close by point (+-5).
Example each line is one point with to coordinates:
points="808,112\n807,113\n809,113\n155,183\n832,572"
echo "$points"
#808,112
#807,113
#809,113
#155,183
#832,572
#196,652
I would like to ignore points within a range of +-5 counts. The result should be:
echo "$points_clean"
#808,112
#155,183
#832,572
#196,652
I thought about looping through the list, but I need help to how to check if point coordinates already exist in the new list:
points_clean=$(for point in $points; do
x=$(echo "$point" | cut -d, -f1)
y=$(echo "$point" | cut -d, -f2)
# check if same or similar point coordinates already in $points_clean
echo "$x,$y"
done)

Answer 1

This seems to work with Bash 4.x (support for process substitution is needed):
#!/bin/bash
close=100
points="808,112\n807,113\n809,113\n155,183\n832,572"
echo -e "$points"
clean=()
distance()
{
echo $(( ($1 - $3) * ($1 - $3) + ($2 - $4) * ($2 - $4) ))
}
while read x1 y1
do
ok=1
for point in "${clean[#]}"
do
echo "compare $x1 $y1 with $point"
set -- $point
if [[ $(distance $x1 $y1 $1 $2) -le $close ]]
then
ok=0
break
fi
done
if [ $ok = 1 ]
then clean+=("$x1 $y1")
fi
done < <( echo -e "$points" | tr ',' ' ' | sort -u )
echo "Clean:"
printf "%s\n" "${clean[#]}" | tr ' ' ','
The sort is optional and may slow things down. Identical points will be too close together, so the second instance of a given coordinate will be eliminated even if the first wasn't.
Sample output:
808,112
807,113
809,113
155,183
832,572
compare 807 113 with 155 183
compare 808 112 with 155 183
compare 808 112 with 807 113
compare 809 113 with 155 183
compare 809 113 with 807 113
compare 832 572 with 155 183
compare 832 572 with 807 113
Clean:
155,183
807,113
832,572
The workaround for Bash 3.x (as found on Mac OS X 10.10.4, for example) is a tad painful; you need to send the output of the echo | tr | sort command to a file, then redirect the input of the pair of loops from that file (and clean up afterwards). Or you can put the pair of loops and the code that follows (the echo of the clean array) inside the scope of { …; } command grouping.
In response to the question 'what defines close?', wittich commented:
Let's say ±5 counts. Eg. 808(±5,) 112(±5). That's why the second and third point would be "cleaned".
OK. One way of looking at that would be to adjust the close value to 50 in my script (allowing a difference of 52 + 52), but that rejects points connected by a line of length just over 7, though. You could revise the distance function to do ±5; it takes a bit more work and maybe an auxilliary abs function, or you could return the square of the larger delta and compare that with 25 (52 of course). You can play with what the criterion should be to your hearts content.
Note that Bash shell arithmetic is integer arithmetic (only); you need Korn shell (ksh) or Z shell (zsh) to get real arithmetic in the shell, or you need to use bc or some other calculator.