{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6a385c73",
   "metadata": {
    "tags": []
   },
   "source": [
    "# サイクロイドのアニメーション作成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "71ccfa51-dfc1-457b-ac8b-963a93cc01d6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "以下の手順でサイクロイドを描画するアニメーションを作成できます。\n",
       "\n",
       "1. 必要なライブラリをインポートします。\n",
       "\n",
       "```python\n",
       "import numpy as np\n",
       "import matplotlib.pyplot as plt\n",
       "from matplotlib.animation import FuncAnimation\n",
       "```\n",
       "\n",
       "2. サイクロイドの式を定義します。\n",
       "\n",
       "```python\n",
       "def cycloid(t, r):\n",
       "    x = r * (t - np.sin(t))\n",
       "    y = r * (1 - np.cos(t))\n",
       "    return x, y\n",
       "```\n",
       "\n",
       "3. アニメーションのフレームを作成する関数を定義します。\n",
       "\n",
       "```python\n",
       "def animate(i):\n",
       "    t = np.linspace(0, 4 * np.pi, 1000)\n",
       "    x, y = cycloid(t + i * 0.1, 1)\n",
       "    line.set_data(x, y)\n",
       "    return line,\n",
       "```\n",
       "\n",
       "4. アニメーションを描画します。\n",
       "\n",
       "```python\n",
       "fig, ax = plt.subplots()\n",
       "line, = ax.plot([], [], lw=2)\n",
       "ax.set_aspect('equal')\n",
       "ax.set_xlim(-5, 25)\n",
       "ax.set_ylim(-5, 5)\n",
       "ani = FuncAnimation(fig, animate, frames=100, interval=50)\n",
       "plt.show()\n",
       "```\n",
       "\n",
       "これで、サイクロイドを描画するアニメーションが作成されます。`r`の値を変更することで、サイクロイドの大きさを調整できます。また、`interval`の値を変更することで、アニメーションの速度を調整できます。"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%ai_ask\n",
    "jupyterのpythonでサイクロイドを描画するアニメーションを作りたい"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c78a3c2d-fbcd-472d-8e76-57fcc2fbcab6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img7b4799c3288f4b0f900fa1ea2e46c6c8\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider7b4799c3288f4b0f900fa1ea2e46c6c8\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim7b4799c3288f4b0f900fa1ea2e46c6c8.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select7b4799c3288f4b0f900fa1ea2e46c6c8\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_7b4799c3288f4b0f900fa1ea2e46c6c8\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_7b4799c3288f4b0f900fa1ea2e46c6c8\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_7b4799c3288f4b0f900fa1ea2e46c6c8\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_7b4799c3288f4b0f900fa1ea2e46c6c8\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_7b4799c3288f4b0f900fa1ea2e46c6c8\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_7b4799c3288f4b0f900fa1ea2e46c6c8\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
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       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
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       "    var loop_select_id = \"_anim_loop_select7b4799c3288f4b0f900fa1ea2e46c6c8\";\n",
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       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim7b4799c3288f4b0f900fa1ea2e46c6c8 = new Animation(frames, img_id, slider_id, 50.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7213c7d22f10>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.animation\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.rcParams[\"animation.html\"] = \"jshtml\"\n",
    "plt.rcParams['figure.dpi'] = 150\n",
    "plt.ioff()\n",
    "fig, ax = plt.subplots()\n",
    "from matplotlib.animation import FuncAnimation\n",
    "\n",
    "def cycloid(t, r):\n",
    "    x = r * (t - np.sin(t))\n",
    "    y = r * (1 - np.cos(t))\n",
    "    return x, y\n",
    "\n",
    "def animate(i):\n",
    "    t = np.linspace(0, 4 * np.pi, 1000)\n",
    "    x, y = cycloid(t + i * 0.1, 1)\n",
    "    line.set_data(x, y)\n",
    "    return line,\n",
    "\n",
    "#fig, ax = plt.subplots()\n",
    "line, = ax.plot([], [], lw=2)\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlim(-5, 25)\n",
    "ax.set_ylim(-5, 5)\n",
    "FuncAnimation(fig, animate, frames=100, interval=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f5ab47-1620-4cb6-9b9d-1330fb7d022f",
   "metadata": {},
   "source": [
    "## ニュートンがケプラーの第二法則を証明したサイクロイド"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05b51e8e",
   "metadata": {},
   "source": [
    "* [Python Matplotlib Tips: Draw cycloid animation using matplotlib.animation.ArtistAnimation](https://pythonmatplotlibtips.blogspot.com/2017/12/cycloid-animation-artistanimation.html)\n",
    "* [[matplotlib animation] 13. サイクロイド(cycloid) – サボテンパイソン](https://sabopy.com/py/matplotlib-animation-13/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "badebfe7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "def update(num):\n",
    "    if len(round_circles) > 0:\n",
    "        round_circles.pop().remove()\n",
    "        round_circles2.pop().remove()\n",
    "        cycloids.pop().remove()\n",
    "        points.pop().remove()\n",
    "        \n",
    "    round_circle,  = plt.plot(cycloid_c[num]+x,  R+y,  'b:', lw=1)\n",
    "    round_circle2, = plt.plot(cycloid_c[num]+x2, R+y2, 'b-', lw=1)\n",
    "    cycloid, = plt.plot(cycloid_x[:num+1] ,cycloid_y[:num+1], 'r-', lw=1)\n",
    "    point, = plt.plot(cycloid_x[num], cycloid_y[num], 'ko', markersize=4)\n",
    "    \n",
    "    round_circles.append(round_circle)\n",
    "    round_circles2.append(round_circle2)\n",
    "    cycloids.append(cycloid)\n",
    "    points.append(point)\n",
    "    \n",
    "    theta_str = r'$\\theta=$'\n",
    "    ax.set_title(theta_str + str(theta[num]/np.pi)[:4] + str(r' $\\pi$'))\n",
    "\n",
    "ax.grid()\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "#plot data\n",
    "e = 0.0167 # earth\n",
    "#e = 0.0935 # mars\n",
    "#e = 0.9673 # 1P/Halley\n",
    "#e=0.6\n",
    "a = 1\n",
    "b = np.sqrt(a**2-e**2)\n",
    "R = a/e\n",
    "theta = np.linspace(0,3*np.pi,200)\n",
    "phi   = np.linspace(0,2*np.pi,100)\n",
    "\n",
    "x = R*np.cos(phi)\n",
    "y = R*np.sin(phi)\n",
    "round_circles =[]\n",
    "\n",
    "x2 = R*np.cos(phi)*e\n",
    "y2 = R*np.sin(phi)*e\n",
    "round_circles2 =[]\n",
    "\n",
    "cycloid_x = R*e*(1/e*theta-np.sin(theta))\n",
    "cycloid_y = R*(1-np.cos(theta)*e)\n",
    "cycloids=[]\n",
    "\n",
    "cycloid_c = R*theta\n",
    "points=[]\n",
    "\n",
    "ani = animation.FuncAnimation(fig, update, 200, interval=100)\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e55cacde",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50abdcf0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.8"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}