use Math::Trig qw(atan deg2rad rad2deg);

sub _thick_line {
    my ($image, $thickness, $color, $x1, $y1, $x2, $y2) = @_;

    my $angle = _angle($x1, $y1, $x2, $y2);
    my $mirror1 = $angle + 90;
    my $mirror2 = $angle - 90;

    my $m1c = $thickness*cos(deg2rad $mirror1)/2;
    my $m1s = $thickness*sin(deg2rad $mirror1)/2;
    my $m2c = $thickness*cos(deg2rad $mirror2)/2;
    my $m2s = $thickness*sin(deg2rad $mirror2)/2;

    my $x1a = $x1 + $m1c; # bottom left
    my $y1a = $y1 + $m1s;
    my $x1b = $x1 + $m2c; # top left
    my $y1b = $y1 + $m2s;

    my $x2a = $x2 + $m1c; # bottom right
    my $y2a = $y2 + $m1s;
    my $x2b = $x2 + $m2c; # top right
    my $y2b = $y2 + $m2s;

    $image->polygon(
        aa => 1,
        color => $color,
        points => [
            [$x1a, $y1a],
            [$x2a, $y2a],
            [$x2b, $y2b],
            [$x1b, $y1b],
        ],
    );
}

sub _angle {
    my ($x1, $y1, $x2, $y2) = @_;
    my $x = $x2 - $x1;
    my $y = $y2 - $y1;

    # short circuit the extreme cases
    return   0 if $x  > 0 and $y == 0;
    return 180 if $x  < 0 and $y == 0;
    return  90 if $x == 0 and $y  > 0;
    return 270 if $x == 0 and $y  < 0;

    # calculate the rest
    return rad2deg atan($y/$x);
}