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    "Create a GUI using ``tkinter`` to interactively draw points and visualize the **minimum enclosing circle** (as computed in the optimization lecture using ``scipy.optimize.minimize``).\n",
    "\n",
    "_Note_: The circle found using ``minimize`` might not be smallest possible, since ``minimize`` is not guaranteed to find the find the minimum. For (more complicated) algorithms guaranteed to find a minimum enclosing circle see https://en.wikipedia.org/wiki/Smallest-circle_problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "periodic-bangladesh",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize\n",
    "\n",
    "def dist(p, q):\n",
    "    return ((p[0] - q[0]) ** 2 + (p[1] - q[1]) ** 2) ** 0.5\n",
    "\n",
    "def max_dist(p, S):\n",
    "    return max(dist(p, q) for q in S)\n",
    "\n",
    "def minimum_enclosing_circle(points):\n",
    "    '''Find mindste cirkel med scipy minimize - fejler nogle gange !!!'''\n",
    "\n",
    "    def f(p):\n",
    "        return max_dist(p, points)\n",
    "    \n",
    "    solution = minimize(f, [0, 0])\n",
    "    radius = solution.fun\n",
    "    center = solution.x\n",
    "    \n",
    "    return center, radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "acceptable-privilege",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tkinter as tk\n",
    "\n",
    "# Til at opdatere canvasen\n",
    "\n",
    "def draw_circle(point, radius=3, fill='white'):\n",
    "    x, y = point\n",
    "    canvas.create_oval(x - radius, y - radius, x + radius, y + radius, fill=fill)\n",
    "\n",
    "def redraw():\n",
    "    canvas.delete('all')  # fjern alle eksisterende punkter\n",
    "    if len(points) >= 2:\n",
    "        center, radius = minimum_enclosing_circle(points)\n",
    "        draw_circle(center, radius, fill='red')\n",
    "        draw_circle(center, 5, fill='yellow')\n",
    "        info_var.set(f'radius = {radius:.2f}')\n",
    "    else:\n",
    "        info_var.set('Tegn nogle punkter')\n",
    "    for point in points:\n",
    "        draw_circle(point)\n",
    "        \n",
    "# Håndtering af tryk på taster og knapper på skærmen\n",
    "        \n",
    "def do_quit(event=None):\n",
    "    root.destroy()\n",
    "    \n",
    "def clear_all():\n",
    "    points.clear()\n",
    "    redraw()\n",
    "\n",
    "def undo(event):\n",
    "    if points:\n",
    "        deleted_points.append(points.pop())\n",
    "        redraw()\n",
    "        \n",
    "def redo(event):\n",
    "    if deleted_points:\n",
    "        points.append(deleted_points.pop())\n",
    "        redraw()\n",
    "    \n",
    "# Håndtering af tryk på venstre museknap\n",
    "    \n",
    "def new_point(event):\n",
    "    global current_point, current_point_moved\n",
    "    \n",
    "    x, y = event.x, event.y\n",
    "    point = (x, y)\n",
    "    \n",
    "    nearest = min(points, \n",
    "                  key=lambda p: dist(point, p),\n",
    "                  default=None)\n",
    "    if nearest != None and dist(point, nearest) <= 10:\n",
    "        current_point = points.index(nearest)\n",
    "        current_point_moved = False\n",
    "    else:    \n",
    "        points.append(point)\n",
    "        current_point = len(points) - 1\n",
    "        current_point_moved = True\n",
    "        redraw()\n",
    "        \n",
    "def move_point(event):\n",
    "    global current_point_moved \n",
    "    \n",
    "    x, y = event.x, event.y\n",
    "    point = (x,y)\n",
    "    \n",
    "    if current_point != None:\n",
    "        current_point_moved = True\n",
    "        points[current_point] = point\n",
    "        redraw()\n",
    "    \n",
    "def release_point(event):\n",
    "    global current_point\n",
    "    \n",
    "    if not current_point_moved:\n",
    "        deleted_points.append(points[current_point])\n",
    "        del points[current_point]\n",
    "        redraw()\n",
    "    current_point = None\n",
    "\n",
    "# Opret vindue\n",
    "\n",
    "root = tk.Tk()\n",
    "root.title('Mindste omsluttende circel')\n",
    "\n",
    "kasse = tk.Frame(root)  # Til at indeholde knapperne i bunden af skærmen\n",
    "quit_button = tk.Button(kasse, text='Quit (Ctrl-q)', command=do_quit)\n",
    "quit_button.pack(side=tk.LEFT, padx=5, pady=5)\n",
    "\n",
    "clear_button = tk.Button(kasse, text='Clear all', command=clear_all)\n",
    "clear_button.pack(side=tk.LEFT, padx=5, pady=5)\n",
    "\n",
    "info_var = tk.StringVar()\n",
    "#info_label = tk.Label(kasse, text='Tegn nogle punkter', fg='red')\n",
    "info_label = tk.Label(kasse, textvariable=info_var, fg='red')\n",
    "info_label.pack(side=tk.RIGHT, padx=5, pady=5)\n",
    "\n",
    "kasse.pack(side=tk.BOTTOM, expand=True, fill=tk.X)\n",
    "\n",
    "canvas = tk.Canvas(root, width=500, height=400, bg='green')\n",
    "canvas.pack(side=tk.TOP, fill=tk.BOTH, expand=True)\n",
    "    \n",
    "points = []\n",
    "deleted_points = []\n",
    "current_point = None\n",
    "current_point_moved = False\n",
    "\n",
    "canvas.bind('<ButtonPress-1>', new_point)\n",
    "canvas.bind('<B1-Motion>', move_point)\n",
    "canvas.bind('<ButtonRelease-1>', release_point)\n",
    "\n",
    "root.bind('<Control-z>', undo)\n",
    "root.bind('<Control-y>', redo)\n",
    "root.bind('<Control-q>', do_quit)\n",
    "\n",
    "redraw()\n",
    "tk.mainloop()"
   ]
  }
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