Your code looks very clean to me. However, I prefer to write
_thick_line a little more compact.
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;
$image->polygon(
aa => 1,
color => $color,
points => [
[ $x1 + $m1c, $y1 + $m1s ], # bottom left
[ $x2 + $m1c, $y2 + $m1s ], # bottom right
[ $x2 + $m2c, $y2 + $m2s ], # top right
[ $x1 + $m2c, $y1 + $m2s ], # top left
],
);
}