How to make Gtk+ window background transparent?

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I changed the alphademo example to draw a button instead of the red circle.

This application draws the button on a 400×400 transparent window.

When you click on the window the application shows/hides the title bar.

#include <gtk/gtk.h>
#include <gdk/gdkscreen.h>
#include <cairo.h>

static void screen_changed(GtkWidget *widget, GdkScreen *old_screen, gpointer user_data);
static gboolean expose(GtkWidget *widget, GdkEventExpose *event, gpointer user_data);
static void clicked(GtkWindow *win, GdkEventButton *event, gpointer user_data);

int main(int argc, char **argv)
{
    gtk_init(&argc, &argv);

    GtkWidget *window = gtk_window_new(GTK_WINDOW_TOPLEVEL);
    gtk_window_set_position(GTK_WINDOW(window), GTK_WIN_POS_CENTER);
    gtk_window_set_default_size(GTK_WINDOW(window), 400, 400);
    gtk_window_set_title(GTK_WINDOW(window), "Alpha Demo");
    g_signal_connect(G_OBJECT(window), "delete-event", gtk_main_quit, NULL);

    gtk_widget_set_app_paintable(window, TRUE);

    g_signal_connect(G_OBJECT(window), "expose-event", G_CALLBACK(expose), NULL);
    g_signal_connect(G_OBJECT(window), "screen-changed", G_CALLBACK(screen_changed), NULL);

    gtk_window_set_decorated(GTK_WINDOW(window), FALSE);
    gtk_widget_add_events(window, GDK_BUTTON_PRESS_MASK);
    g_signal_connect(G_OBJECT(window), "button-press-event", G_CALLBACK(clicked), NULL);

    GtkWidget* fixed_container = gtk_fixed_new();
    gtk_container_add(GTK_CONTAINER(window), fixed_container);
    GtkWidget* button = gtk_button_new_with_label("button1");
    gtk_widget_set_size_request(button, 100, 100);
    gtk_container_add(GTK_CONTAINER(fixed_container), button);

    screen_changed(window, NULL, NULL);

    gtk_widget_show_all(window);
    gtk_main();

    return 0;
}


gboolean supports_alpha = FALSE;
static void screen_changed(GtkWidget *widget, GdkScreen *old_screen, gpointer userdata)
{
    /* To check if the display supports alpha channels, get the colormap */
    GdkScreen *screen = gtk_widget_get_screen(widget);
    GdkColormap *colormap = gdk_screen_get_rgba_colormap(screen);

    if (!colormap)
    {
        printf("Your screen does not support alpha channels!\n");
        colormap = gdk_screen_get_rgb_colormap(screen);
        supports_alpha = FALSE;
    }
    else
    {
        printf("Your screen supports alpha channels!\n");
        supports_alpha = TRUE;
    }

    gtk_widget_set_colormap(widget, colormap);
}

static gboolean expose(GtkWidget *widget, GdkEventExpose *event, gpointer userdata)
{
   cairo_t *cr = gdk_cairo_create(widget->window);

    if (supports_alpha)
        cairo_set_source_rgba (cr, 1.0, 1.0, 1.0, 0.0); /* transparent */
    else
        cairo_set_source_rgb (cr, 1.0, 1.0, 1.0); /* opaque white */

    /* draw the background */
    cairo_set_operator (cr, CAIRO_OPERATOR_SOURCE);
    cairo_paint (cr);

    cairo_destroy(cr);

    return FALSE;
}

static void clicked(GtkWindow *win, GdkEventButton *event, gpointer user_data)
{
    /* toggle window manager frames */
    gtk_window_set_decorated(win, !gtk_window_get_decorated(win));
}

Compiled on Ubuntu 10.04:

gcc alpha.c -o alpha -I/usr/include/gtk-2.0 -I/usr/lib/gtk-2.0/include -I/usr/include/glib-2.0 -I/usr/lib/glib-2.0/include -I/usr/include/cairo -I/usr/include/pango-1.0 -I/usr/include/atk-1.0 -lgtk-x11-2.0

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