#!/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)
}