divideAndConquer.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "19942bf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "%run geometria.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f08b4d4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "Tolerance = 10e-12"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2674c7ae",
   "metadata": {},
   "source": [
    "# Funkcje pomocnicze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c2a1e3c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def det(a, b, c):\n",
    "    return a[0] * b[1] + b[0] * c[1] + a[1] * c[0] - c[0] * b[1] - b[0] * a[1] - a[0] * c[1]\n",
    "\n",
    "def orient(a, b, c):\n",
    "    determinant = det(a, b, c)\n",
    "    if determinant > Tolerance: # lewa strona\n",
    "        return 1\n",
    "    elif determinant < -Tolerance: # prawa strona\n",
    "        return -1\n",
    "    else: # współliniowe\n",
    "        return 0\n",
    "    \n",
    "def trivial(points, first, last): # Wyznaczanie otoczki dla <= 3 punktów.\n",
    "    if last - first < 0:\n",
    "        return []\n",
    "    if last - first == 0:\n",
    "        return [points[first]]\n",
    "    if last - first == 1:\n",
    "        if points[first] == points[last]:\n",
    "            return [points[first]]\n",
    "        return [points[first], points[last]]\n",
    "    if last - first == 2:\n",
    "        if orient(points[first], points[first+1], points[first+2]) == 1:\n",
    "            return [points[first], points[first+1], points[first+2]]\n",
    "        elif (points[first][0] ==  points[first+1][0] and orient(points[first], points[first+1], points[first+2]) != 0) or orient(points[first], points[first + 1], points[first + 2]) == -1:\n",
    "            return [points[first], points[first+2], points[first+1]]\n",
    "        else:\n",
    "            return [points[first], points[first+2]]\n",
    "\n",
    "        \n",
    "def find_max_x(hull): # Wyznaczanie indeksu punktu otoczki o największej wartości zmiennej x.\n",
    "    n = len(hull)\n",
    "    max_x = -float(\"inf\")\n",
    "    max_x_index = -1\n",
    "    for i in range(n):\n",
    "        if hull[i][0] > max_x:\n",
    "            max_x = hull[i][0]\n",
    "            max_x_index = i\n",
    "    \n",
    "    return max_x_index\n",
    "\n",
    "def find_min_x(hull): # Wyznaczanie indeksu punktu otoczki o najmniejszej wartości zmiennej x.\n",
    "    n = len(hull)\n",
    "    n = len(hull)\n",
    "    min_x = float(\"inf\")\n",
    "    min_x_index = -1\n",
    "    for i in range(n):\n",
    "        if hull[i][0] < min_x:\n",
    "            min_x = hull[i][0]\n",
    "            min_x_index = i\n",
    "    \n",
    "    return min_x_index\n",
    "          "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b153de7",
   "metadata": {},
   "source": [
    "# Główny algorytm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6132615e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def merger(hull1, hull2, hulls, scenes): # Funkcja łącząca otoczki sąsiadujących zbiorów.\n",
    "    new_hull = []\n",
    "    n1 = len(hull1)\n",
    "    n2 = len(hull2)\n",
    "\n",
    "    max_x_index = find_max_x(hull1)\n",
    "    min_x_index = find_min_x(hull2)\n",
    "    \n",
    "    # Wyznaczanie górnej stycznej otoczek.\n",
    "    index1 = max_x_index\n",
    "    index2 = min_x_index\n",
    "    flag = False\n",
    "    while not flag:\n",
    "        flag = True\n",
    "        while orient(hull1[index1 % n1], hull1[(index1 + 1) % n1], hull2[index2 % n2]) <= 0:\n",
    "            index1 = (index1 + 1) % n1\n",
    "\n",
    "        while orient(hull1[index1 % n1], hull2[(index2 + n2 - 1) % n2], hull2[index2 % n2]) <= 0:\n",
    "            index2 = (index2 + n2 - 1) % n2\n",
    "            flag = False\n",
    "            \n",
    "    upper1, upper2 = index1, index2\n",
    "    \n",
    "    # Wyznaczanie dolnej stycznej otoczek.\n",
    "    index1 = max_x_index\n",
    "    index2 = min_x_index\n",
    "    flag = False\n",
    "    while not flag:\n",
    "        flag = True\n",
    "        while orient(hull1[(index1 + n1 - 1) % n1], hull1[index1 % n1], hull2[index2 % n2]) <= 0:\n",
    "            index1 = (index1 + n1 - 1) % n1\n",
    "\n",
    "        while orient(hull1[index1 % n1], hull2[index2 % n2], hull2[(index2 + 1) % n2]) <= 0:\n",
    "            index2 = (index2 + 1) % n2\n",
    "            flag = False\n",
    "\n",
    "    lower1, lower2 = index1, index2\n",
    "\n",
    "    \n",
    "    lines = []\n",
    "    points_scene = []\n",
    "    for hull in hulls:\n",
    "        n = len(hull)\n",
    "        for i in range(n):\n",
    "            lines.append([hull[i], hull[(i + 1) % n]])\n",
    "            points_scene.append(hull[i])\n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                         PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                         LinesCollection([(hull1[upper1], hull2[upper2]), (hull1[lower1], hull2[lower2])],\n",
    "                                         color='forestgreen')]))\n",
    "    \n",
    "    hulls.remove(hull1)\n",
    "    hulls.remove(hull2)\n",
    "    \n",
    "    # Sklejanie otoczek\n",
    "    new_hull.append(hull1[lower1])\n",
    "    new_hull.append(hull2[lower2])\n",
    "    if lower2 != upper2:\n",
    "        index1 = lower2 + 1\n",
    "        while index1 % n2 != upper2:\n",
    "            new_hull.append(hull2[index1 % n2])\n",
    "            index1 += 1\n",
    "        new_hull.append(hull2[upper2])\n",
    "\n",
    "    if upper1 != lower1:\n",
    "        new_hull.append(hull1[upper1])\n",
    "        index2 = upper1 + 1\n",
    "        while index2 % n1 != lower1:\n",
    "            new_hull.append(hull1[index2 % n1])\n",
    "            index2 += 1\n",
    "\n",
    "    return new_hull\n",
    "\n",
    "\n",
    "def divide(points, first, last, hulls, scenes): # Funkcja rekurencyjna dzieląca zbiór, na mniejsze podzbiory.\n",
    "    if last - first < 3:\n",
    "        hull = trivial(points, first, last)\n",
    "        hulls.append(hull)\n",
    "        lines = []\n",
    "        points_scene = []\n",
    "        for hull in hulls:\n",
    "            n = len(hull)\n",
    "            for i in range(n):\n",
    "                lines.append([hull[i], hull[(i + 1) % n]])\n",
    "                points_scene.append(hull[i])\n",
    "        scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                             PointsCollection(points_scene, color='green')],\n",
    "                            [LinesCollection(deepcopy(lines), color='lime')]))\n",
    "\n",
    "        return hull\n",
    "\n",
    "    mid = (last + first) // 2\n",
    "\n",
    "    hull1 = divide(points, first, mid, hulls, scenes)\n",
    "    hull2 = divide(points, mid + 1, last, hulls, scenes)\n",
    "\n",
    "    if len(hull1) == 0:\n",
    "        hulls.remove(hull1)\n",
    "        return hull2\n",
    "    if len(hull2) == 0:\n",
    "        hulls.remove(hull2)\n",
    "        return hull1\n",
    "\n",
    "    hull = merger(hull1, hull2, hulls, scenes)\n",
    "    hulls.append(hull)\n",
    "\n",
    "    lines = []\n",
    "    points_scene = []\n",
    "    for hull in hulls:\n",
    "        n = len(hull)\n",
    "        for i in range(n):\n",
    "            lines.append([hull[i], hull[(i + 1) % n]])\n",
    "            points_scene.append(hull[i])\n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                         PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime')]))\n",
    "\n",
    "    return hull\n",
    "\n",
    "\n",
    "def convex_hull(points):\n",
    "    hulls = []\n",
    "    scenes = []\n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink')]))\n",
    "    \n",
    "    # Punkty zostają posortowane.\n",
    "    sorted_points = sorted(points, key=lambda p: (p[0], p[1]))\n",
    "\n",
    "    # Z postortowanego zbioru usuwane są punkty o takiej samej współrzędnej x, z pominięciem tych punktów, \n",
    "    # które dla tego samego x mają najmneijszą i największą wartość y.\n",
    "    new_points = []\n",
    "    new_points.append(sorted_points[0])\n",
    "    last_x = sorted_points[0][0]\n",
    "    i = 1\n",
    "    while i < len(sorted_points):\n",
    "        if sorted_points[i][0] != last_x:\n",
    "            new_points.append(sorted_points[i])\n",
    "            last_x = sorted_points[i][0]\n",
    "        else:\n",
    "            while i < len(sorted_points) and sorted_points[i][0] == last_x:\n",
    "                i += 1\n",
    "            i -= 1\n",
    "            new_points.append(sorted_points[i])\n",
    "            last_x = sorted_points[i][0]\n",
    "        i += 1\n",
    "    n = len(new_points)\n",
    "    \n",
    "    hull = divide(new_points, 0, n - 1, hulls, scenes)\n",
    "    return hull, scenes\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "173f662d",
   "metadata": {},
   "source": [
    "# Testowanie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2cf15193",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Liczba punktów otoczki:  9\n",
      "Punkty otoczki:  [(12.475774468596068, 0.30703084461719543), (99.86657362138202, 2.524588913059933), (96.10631148217324, 95.38887213903391), (84.4093000502974, 98.27772859053752), (15.003581515082798, 98.97190057211759), (4.730882876925923, 86.78522315647383), (0.6706164542720661, 67.00997094755665), (0.9894364055142768, 20.673616508767868), (8.159038339441171, 6.910599748864277)]\n"
     ]
    },
    {
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       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_points(amount, low, high):\n",
    "    a = np.random.rand(amount).astype(np.float64) * (high - low) + low\n",
    "    b = np.random.rand(amount).astype(np.float64) * (high - low) + low\n",
    "    return list(zip(a, b))\n",
    "\n",
    "data = generate_points(100, 0, 100)\n",
    "hull, scenes = convex_hull(data)\n",
    "print(\"Liczba punktów otoczki: \", len(hull))\n",
    "print(\"Punkty otoczki: \", hull)\n",
    "plot = Plot(scenes=scenes)\n",
    "plot.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38bd05a2",
   "metadata": {},
   "source": [
    "# Algorytm bez wizualizacji"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "20591103",
   "metadata": {},
   "outputs": [],
   "source": [
    "def merger_(hull1, hull2, hulls): # Funkcja łącząca otoczki sąsiadujących zbiorów.\n",
    "    new_hull = []\n",
    "    n1 = len(hull1)\n",
    "    n2 = len(hull2)\n",
    "\n",
    "    max_x_index = find_max_x(hull1)\n",
    "    min_x_index = find_min_x(hull2)\n",
    "    \n",
    "    # Wyznaczanie górnej stycznej otoczek.\n",
    "    index1 = max_x_index\n",
    "    index2 = min_x_index\n",
    "    flag = False\n",
    "    while not flag:\n",
    "        flag = True\n",
    "        while orient(hull1[index1 % n1], hull1[(index1 + 1) % n1], hull2[index2 % n2]) <= 0:\n",
    "            index1 = (index1 + 1) % n1\n",
    "\n",
    "        while orient(hull1[index1 % n1], hull2[(index2 + n2 - 1) % n2], hull2[index2 % n2]) <= 0:\n",
    "            index2 = (index2 + n2 - 1) % n2\n",
    "            flag = False\n",
    "            \n",
    "    upper1, upper2 = index1, index2\n",
    "    \n",
    "    # Wyznaczanie dolnej stycznej otoczek.\n",
    "    index1 = max_x_index\n",
    "    index2 = min_x_index\n",
    "    flag = False\n",
    "    while not flag:\n",
    "        flag = True\n",
    "        while orient(hull1[(index1 + n1 - 1) % n1], hull1[index1 % n1], hull2[index2 % n2]) <= 0:\n",
    "            index1 = (index1 + n1 - 1) % n1\n",
    "\n",
    "        while orient(hull1[index1 % n1], hull2[index2 % n2], hull2[(index2 + 1) % n2]) <= 0:\n",
    "            index2 = (index2 + 1) % n2\n",
    "            flag = False\n",
    "\n",
    "    lower1, lower2 = index1, index2\n",
    "    \n",
    "    hulls.remove(hull1)\n",
    "    hulls.remove(hull2)\n",
    "    \n",
    "    # Sklejanie otoczek\n",
    "    new_hull.append(hull1[lower1])\n",
    "    new_hull.append(hull2[lower2])\n",
    "    if lower2 != upper2:\n",
    "        index1 = lower2 + 1\n",
    "        while index1 % n2 != upper2:\n",
    "            new_hull.append(hull2[index1 % n2])\n",
    "            index1 += 1\n",
    "        new_hull.append(hull2[upper2])\n",
    "\n",
    "    if upper1 != lower1:\n",
    "        new_hull.append(hull1[upper1])\n",
    "        index2 = upper1 + 1\n",
    "        while index2 % n1 != lower1:\n",
    "            new_hull.append(hull1[index2 % n1])\n",
    "            index2 += 1\n",
    "\n",
    "    return new_hull\n",
    "\n",
    "\n",
    "def divide_(points, first, last, hulls): # Funkcja rekurencyjna dzieląca zbiór na mniejsze podzbiory.\n",
    "    if last - first < 3:\n",
    "        hull = trivial(points, first, last)\n",
    "        hulls.append(hull)\n",
    "        return hull\n",
    "\n",
    "    mid = (last + first) // 2\n",
    "\n",
    "    hull1 = divide_(points, first, mid, hulls)\n",
    "    hull2 = divide_(points, mid + 1, last, hulls)\n",
    "\n",
    "    if len(hull1) == 0:\n",
    "        hulls.remove(hull1)\n",
    "        return hull2\n",
    "    if len(hull2) == 0:\n",
    "        hulls.remove(hull2)\n",
    "        return hull1\n",
    "\n",
    "    hull = merger_(hull1, hull2, hulls)\n",
    "    hulls.append(hull)\n",
    "\n",
    "    return hull\n",
    "\n",
    "\n",
    "def convex_hull_(points):\n",
    "    hulls = []\n",
    "    # Punkty zostają posortowane.\n",
    "    sorted_points = sorted(points, key=lambda p: (p[0], p[1]))\n",
    "\n",
    "    # Z postortowanego zbioru usuwane są punkty o takiej samej współrzędnej x, z pominięciem tych punktów, \n",
    "    # które dla tego samego x mają najmneijszą i największą wartość y.\n",
    "    new_points = []\n",
    "    new_points.append(sorted_points[0])\n",
    "    last_x = sorted_points[0][0]\n",
    "    i = 1\n",
    "    while i < len(sorted_points):\n",
    "        if sorted_points[i][0] != last_x:\n",
    "            new_points.append(sorted_points[i])\n",
    "            last_x = sorted_points[i][0]\n",
    "        else:\n",
    "            while i < len(sorted_points) and sorted_points[i][0] == last_x:\n",
    "                i += 1\n",
    "            i -= 1\n",
    "            new_points.append(sorted_points[i])\n",
    "            last_x = sorted_points[i][0]\n",
    "        i += 1\n",
    "    n = len(new_points)\n",
    "    \n",
    "    hull = divide_(new_points, 0, n - 1, hulls)\n",
    "    return hull"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfe78314",
   "metadata": {},
   "source": [
    "# Łączenie otoczek - wizualizacja"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "06da6fc3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def merger_2(hull1, hull2, hulls, scenes): # Funkcja łącząca otoczki sąsiadujących zbiorów.\n",
    "    new_hull = []\n",
    "    n1 = len(hull1)\n",
    "    n2 = len(hull2)\n",
    "\n",
    "    max_x_index = find_max_x(hull1)\n",
    "    min_x_index = find_min_x(hull2)\n",
    "    \n",
    "    # Wyznaczanie górnej stycznej otoczek.\n",
    "    index1 = max_x_index\n",
    "    index2 = min_x_index\n",
    "    flag = False\n",
    "    lines = []\n",
    "    points_scene = []\n",
    "    for hull in hulls:\n",
    "        n = len(hull)\n",
    "        for i in range(n):\n",
    "            lines.append([hull[i], hull[(i + 1) % n]])\n",
    "            points_scene.append(hull[i])\n",
    "    while not flag:\n",
    "        flag = True\n",
    "        while orient(hull1[index1 % n1], hull1[(index1 + 1) % n1], hull2[index2 % n2]) <= 0:\n",
    "            scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                         PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                         LinesCollection([(hull1[index1], hull2[index2])], color='blueviolet')]))\n",
    "            index1 = (index1 + 1) % n1\n",
    "            \n",
    "            \n",
    "        while orient(hull1[index1 % n1], hull2[(index2 + n2 - 1) % n2], hull2[index2 % n2]) <= 0:\n",
    "            scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                         PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                         LinesCollection([(hull1[index1], hull2[index2])], color='blueviolet')]))\n",
    "            index2 = (index2 + n2 - 1) % n2\n",
    "            flag = False\n",
    "            \n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                    PointsCollection(points_scene, color='green')],\n",
    "                    [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                    LinesCollection([(hull1[index1], hull2[index2])], color='blueviolet')]))\n",
    "            \n",
    "    upper1, upper2 = index1, index2\n",
    "    \n",
    "    # Wyznaczanie dolnej stycznej otoczek.\n",
    "    index1 = max_x_index\n",
    "    index2 = min_x_index\n",
    "    flag = False\n",
    "    while not flag:\n",
    "        flag = True\n",
    "        while orient(hull1[(index1 + n1 - 1) % n1], hull1[index1 % n1], hull2[index2 % n2]) <= 0:\n",
    "            scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                        PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                        LinesCollection([(hull1[upper1], hull2[upper2])], color = 'forestgreen'),\n",
    "                        LinesCollection([(hull1[index1], hull2[index2])], color = 'blueviolet')]))\n",
    "            index1 = (index1 + n1 - 1) % n1\n",
    "\n",
    "        while orient(hull1[index1 % n1], hull2[index2 % n2], hull2[(index2 + 1) % n2]) <= 0:\n",
    "            scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                        PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                        LinesCollection([(hull1[upper1], hull2[upper2])], color = 'forestgreen'),\n",
    "                        LinesCollection([(hull1[index1], hull2[index2])], color = 'blueviolet')]))\n",
    "            index2 = (index2 + 1) % n2\n",
    "            flag = False\n",
    "            \n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                    PointsCollection(points_scene, color='green')],\n",
    "                    [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                    LinesCollection([(hull1[upper1], hull2[upper2])], color = 'forestgreen'),\n",
    "                    LinesCollection([(hull1[index1], hull2[index2])], color = 'blueviolet')]))\n",
    "\n",
    "    lower1, lower2 = index1, index2\n",
    "\n",
    "    \n",
    "    lines = []\n",
    "    points_scene = []\n",
    "    for hull in hulls:\n",
    "        n = len(hull)\n",
    "        for i in range(n):\n",
    "            lines.append([hull[i], hull[(i + 1) % n]])\n",
    "            points_scene.append(hull[i])\n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                         PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime'),\n",
    "                         LinesCollection([(hull1[upper1], hull2[upper2]), (hull1[lower1], hull2[lower2])],\n",
    "                                         color='forestgreen')]))\n",
    "    \n",
    "    hulls.remove(hull1)\n",
    "    hulls.remove(hull2)\n",
    "    \n",
    "    # Sklejanie otoczek\n",
    "    new_hull.append(hull1[lower1])\n",
    "    new_hull.append(hull2[lower2])\n",
    "    if lower2 != upper2:\n",
    "        index1 = lower2 + 1\n",
    "        while index1 % n2 != upper2:\n",
    "            new_hull.append(hull2[index1 % n2])\n",
    "            index1 += 1\n",
    "        new_hull.append(hull2[upper2])\n",
    "\n",
    "    if upper1 != lower1:\n",
    "        new_hull.append(hull1[upper1])\n",
    "        index2 = upper1 + 1\n",
    "        while index2 % n1 != lower1:\n",
    "            new_hull.append(hull1[index2 % n1])\n",
    "            index2 += 1\n",
    "\n",
    "    return new_hull\n",
    "\n",
    "\n",
    "def divide_2(points, first, last, hulls, scenes): # Funkcja rekurencyjna dzieląca zbiór, na mniejsze podzbiory.\n",
    "    if last - first < 3:\n",
    "        hull = trivial(points, first, last)\n",
    "        hulls.append(hull)\n",
    "        lines = []\n",
    "        points_scene = []\n",
    "        for hull in hulls:\n",
    "            n = len(hull)\n",
    "            for i in range(n):\n",
    "                lines.append([hull[i], hull[(i + 1) % n]])\n",
    "                points_scene.append(hull[i])\n",
    "        scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                             PointsCollection(points_scene, color='green')],\n",
    "                            [LinesCollection(deepcopy(lines), color='lime')]))\n",
    "\n",
    "        return hull\n",
    "\n",
    "    mid = (last + first) // 2\n",
    "\n",
    "    hull1 = divide_2(points, first, mid, hulls, scenes)\n",
    "    hull2 = divide_2(points, mid + 1, last, hulls, scenes)\n",
    "\n",
    "    if len(hull1) == 0:\n",
    "        hulls.remove(hull1)\n",
    "        return hull2\n",
    "    if len(hull2) == 0:\n",
    "        hulls.remove(hull2)\n",
    "        return hull1\n",
    "\n",
    "    hull = merger_2(hull1, hull2, hulls, scenes)\n",
    "    hulls.append(hull)\n",
    "\n",
    "    lines = []\n",
    "    points_scene = []\n",
    "    for hull in hulls:\n",
    "        n = len(hull)\n",
    "        for i in range(n):\n",
    "            lines.append([hull[i], hull[(i + 1) % n]])\n",
    "            points_scene.append(hull[i])\n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink'),\n",
    "                         PointsCollection(points_scene, color='green')],\n",
    "                        [LinesCollection(deepcopy(lines), color='lime')]))\n",
    "\n",
    "    return hull\n",
    "\n",
    "\n",
    "def convex_hull_2(points):\n",
    "    scenes = []\n",
    "    hulls = []\n",
    "    scenes.append(Scene([PointsCollection(data, color='hotpink')]))\n",
    "    \n",
    "    # Punkty zostają posortowane.\n",
    "    sorted_points = sorted(points, key=lambda p: (p[0], p[1]))\n",
    "\n",
    "    # Z postortowanego zbioru usuwane są punkty o takiej samej współrzędnej x, z pominięciem tych punktów, \n",
    "    # które dla tego samego x mają najmneijszą i największą wartość y.\n",
    "    new_points = []\n",
    "    new_points.append(sorted_points[0])\n",
    "    last_x = sorted_points[0][0]\n",
    "    i = 1\n",
    "    while i < len(sorted_points):\n",
    "        if sorted_points[i][0] != last_x:\n",
    "            new_points.append(sorted_points[i])\n",
    "            last_x = sorted_points[i][0]\n",
    "        else:\n",
    "            while i < len(sorted_points) and sorted_points[i][0] == last_x:\n",
    "                i += 1\n",
    "            i -= 1\n",
    "            new_points.append(sorted_points[i])\n",
    "            last_x = sorted_points[i][0]\n",
    "        i += 1\n",
    "    n = len(new_points)\n",
    "    \n",
    "    hull = divide_2(new_points, 0, n - 1, hulls, scenes)\n",
    "    return hull, scenes"
   ]
  }
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