Here is an example of doing a centered rotation in Goo. There is a line in the timeout, that does a set_simple_transform.

#!/usr/bin/perl -w
use strict;
use warnings;
use Goo::Canvas;
use Gtk2 '-init';
use Glib qw(TRUE FALSE);

my $window = Gtk2::Window->new('toplevel');
$window->signal_connect('delete_event' => sub { Gtk2->main_quit; });
$window->set_size_request(640, 600);

my $swin = Gtk2::ScrolledWindow->new;
$swin->set_shadow_type('in');
$window->add($swin);

my $canvas = Goo::Canvas->new();
$canvas->set_size_request(800, 650);
$canvas->set_bounds(0, 0, 1000, 1000);
$swin->add($canvas);
my $root = $canvas->get_root_item();

# first offset set
my $pts_ref = [50,50,180,120,90,100,50,50]; 
my $line = Goo::Canvas::Polyline->new(
        $root, TRUE,
         $pts_ref, 
         'stroke-color' => 'black',
        'line-width' => 3,
         'fill-color-rgba' => 0x3cb37180,
    );

my ($midx, $midy) = _get_CM( @$pts_ref );

my $ellipse = Goo::Canvas::Ellipse->new(
        $root, $midx-2, $midy-2,$midx+2, $midy+2,
        'stroke-color' => 'goldenrod',
        'line-width' => 8
    );

my $ellipse1 = Goo::Canvas::Ellipse->new(
        $root, -2, -2, +2, +2,
        'stroke-color' => 'black',
        'line-width' => 4
    );

$ellipse1->translate($midx,$midy);
# end first set

my $xd = 100;
my $yd = 100;
$root->translate($xd,$yd);

my $id = Glib::Timeout->add (10, sub {
             $xd += .1;
             $yd += .1;
             $line->rotate (10, $midx, $midy);
             $root->set_simple_transform ($xd, $yd,1,0); #or a group
             # $item->set_simple_transform ($x, $y, $scale, $rotation)
+ 
             return 1;
                });

$window->show_all();
Gtk2->main;

################################################
# This sub finds the center of mass of a polygon.
# I grabbed the algorithm somewhere from the web.
# I grabbed it from Ala Qumsieh's RotCanvas :-)
sub _get_CM {
    my ($x, $y, $area);

    my $i = 0;

    while ($i < $#_) {
    my $x0 = $_[$i];
    my $y0 = $_[$i+1];

    my ($x1, $y1);
    if ($i+2 > $#_) {
        $x1 = $_[0];
        $y1 = $_[1];
    } else {
        $x1 = $_[$i+2];
        $y1 = $_[$i+3];
    }

    $i += 2;

    my $a1 = 0.5*($x0 + $x1);
    my $a2 = ($x0**2 + $x0*$x1 + $x1**2)/6;
    my $a3 = ($x0*$y1 + $y0*$x1 + 2*($x1*$y1 + $x0*$y0))/6;
    my $b0 = $y1 - $y0;

    $area += $a1 * $b0;
    $x    += $a2 * $b0;
    $y    += $a3 * $b0;
    }

    return split ' ', sprintf "%.0f %0.f" => $x/$area, $y/$area;
}
#############################################
__END__
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