foreach my $key (keys %points_by_name) {
    my $intersectionfound=0;
    for (my $i=0; $i<=@{$points_by_name{$key}}-4; $i+=2) {
        if (sub(@{$points_by_name{$key}}[$i..$i+3],$x2, $y2, $x3, $y3)
                and not $intersectionfound) {
            # found the first intersection of $key
        }
    }
}