C言語についての質問

#include <gtk/gtk.h>
#include <math.h>

gboolean redraw(GtkWidget *w, gpointer user_data);
gboolean draw(GtkWidget *w, gpointer user_data);

int main(int argc, char **argv)
{
  GtkWidget *win, *l1, *l2, *l3, *l4, *vbox, *hbox, *b1, *b2;
  gtk_init(&argc, &argv);

  /* make a window */
  win = gtk_window_new(GTK_WINDOW_TOPLEVEL);
  g_signal_connect(win, "destroy", gtk_main_quit, NULL);

  /* make a label, make a drawing area */
  l1 = gtk_label_new("New");
  l2 = gtk_drawing_area_new();
  l3 = gtk_label_new("Redraw");
  l4 = gtk_label_new("EXIT");

  /*make a button*/
  b1 = gtk_button_new();
  b2 = gtk_button_new();

  /* make a vbox */
  vbox = gtk_vbox_new(FALSE, 0);
  gtk_container_add(GTK_CONTAINER(win), vbox);
  gtk_box_pack_start(GTK_BOX(vbox), l1, TRUE, TRUE, 0);
  gtk_box_pack_start(GTK_BOX(vbox), l2, TRUE, TRUE, 0);
  g_signal_connect(l2, "expose_event", G_CALLBACK(draw), NULL);
  gtk_widget_set_size_request(l2, 400, 200);

  /* make a hbox */
  hbox = gtk_hbox_new(TRUE, 0);
  gtk_box_pack_start(GTK_BOX(vbox), hbox, TRUE, TRUE, 0);

  gtk_box_pack_start(GTK_BOX(hbox), b2, TRUE, TRUE, 0);
  g_signal_connect(b2, "clicked", G_CALLBACK(redraw), NULL);
  gtk_container_add(GTK_CONTAINER(b2), l3);

  gtk_box_pack_start(GTK_BOX(hbox), b1, TRUE, TRUE, 0);
  g_signal_connect(b1, "clicked", gtk_main_quit, NULL);
  gtk_container_add(GTK_CONTAINER(b1), l4);

  gtk_widget_show_all(win);

  gtk_main();

  return 0;
}

gboolean redraw(GtkWidget *w, gpointer user_data)
{ 
}

gboolean draw(GtkWidget *w, gpointer user_data) 
{
  gdk_draw_rectangle(w->window, w->style->fg_gc[GTK_WIDGET_STATE(w)],
         TRUE, 100, 50, 200, 100);

  return TRUE;
}

中央の部分に描画された図形がRedrawボタンを押すと消えたり現れたりするプログラムをredraw関数内に書きたいのですがアイデアが浮かびません。どなたかお力添えお願いできないでしょうか?