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#!/usr/bin/awk
#
# See ../README.md
#
#
# Run as: awk -f ch-2.awk < input-file
#
#
# See https://stackoverflow.com/questions/2049582/
#
#
# This determines on which side of the line through ($x1, $y1) and
# ($x2, $y2) the origin lies. If > 0, then the origin lies to the left
# of the line, if < 0, the origin lies to the right of the line, if
# = 0, the origin lies on the line.
#
function side (x1, y1, x2, y2) {
return (y2 - y1) * x2 - (x2 - x1) * y2
}
{
# x1 y1 x2 y2 x3 y3
# $1 $2 $3 $4 $5 $6
#
# Determine where the origin is relative to the three lines
# through the vertices of the triangle. Note we have to go
# in a specific order through the points. (Either clock wise,
# or counter clockwise, as long as we're consistent).
#
s1 = side($3, $4, $5, $6)
s2 = side($5, $6, $1, $2)
s3 = side($1, $2, $3, $4)
#
# If the origin either lies to the left (or on) each of the
# lines, or to the right (or on) each of the lines, the origin
# lies inside the triangle. If not, it does not.
#
print (s1 <= 0 && s2 <= 0 && s3 <= 0 ||
s1 >= 0 && s2 >= 0 && s3 >= 0 ? 1 : 0)
}
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