$item->set_simple_transform ($x, $y, $scale, $rotation)
[download]

It's one of those things you just need to play with to get right. Look at the 'animation' section of the Goo demo.

As far as the x,y coordinates of the mouse I think you need to setup an event handler on the canvas and the items.

sub event_handler{

my ( $widget, $event ) = @_;
 print $widget ,' ',$event->type,"\n";

my ($x,$y) = ($event->x,$event->y);
        print "$x  $y\n";

}
[download]

Just to show you how difficult a centered rotation can be, here is an example on the Gnome2::Canvas, you will then appreciate Goo's 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__
[download]

Don't scale the canvas, scale the item.