Untitled3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>V</th>\n",
       "      <th>Psi</th>\n",
       "      <th>Theta</th>\n",
       "      <th>Fi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.9</td>\n",
       "      <td>5.1</td>\n",
       "      <td>75</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>75</td>\n",
       "      <td>-122</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>75</td>\n",
       "      <td>-25</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     X    Y   V  Psi  Theta  Fi\n",
       "0  2.9  5.1  75    5      0   0\n",
       "1  3.1  1.0  75 -122      0   0\n",
       "2  5.0  3.0  75  -25      0   0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L1, L2, Alpha = 5, 2, 7000\n",
    "\n",
    "Initial_value = pd.DataFrame({'X': [2.9, 3.1, 5],\n",
    "                              'Y': [5.1, 1, 3],\n",
    "                              'V': [75, 75, 75],\n",
    "                              'Psi': [5, -122, -25],\n",
    "                              'Theta': [0, 0, 0],\n",
    "                              'Fi': [0, 0, 0]\n",
    "                             })\n",
    "Initial_value.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Values = Initial_value.values\n",
    "Values[0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate(In_val): \n",
    "    \n",
    "    P = np.zeros((len(Values), 4, 4), dtype='float16')\n",
    "    \n",
    "    for i, Value in enumerate(Values):\n",
    "        \n",
    "        row_0 = np.array([cos(Value[5])*cos(Value[4])*cos(Value[3])-sin(Value[5])*sin(Value[3]),\n",
    "                          -cos(Value[5])*cos(Value[4])*sin(Value[3])-sin(Value[5])*cos(Value[3]),\n",
    "                          cos(Value[5])*sin(Value[4]),\n",
    "                          Value[0]], dtype='float16')\n",
    "  \n",
    "        row_1 = np.array([sin(Value[5])*cos(Value[4])*cos(Value[3])+cos(Value[5])*sin(Value[3]),\n",
    "                          -sin(Value[5])*cos(Value[4])*sin(Value[3])+cos(Value[5])*cos(Value[3]),\n",
    "                          sin(Value[5])*sin(Value[4]),\n",
    "                          Value[1]], dtype='float16')\n",
    "    \n",
    "        row_2 = np.array([-sin(Value[4])*cos(Value[3]),\n",
    "                          sin(Value[4])*sin(Value[3]),\n",
    "                          cos(Value[4]),\n",
    "                          0], dtype='float16')\n",
    "    \n",
    "        row_3 = np.array([0, 0, 0, 1], dtype='float16')\n",
    "        \n",
    "        P[i, :, :] = np.reshape(np.concatenate((row_0, row_1, row_2, row_3), axis=0), (4, 4))\n",
    "    \n",
    "    return(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0.2615   0.11    -0.959    2.9    ]\n",
      "  [-0.3877   0.922   -0.       5.1    ]\n",
      "  [ 0.884    0.3718   0.2837   0.     ]\n",
      "  [ 0.       0.       0.       1.     ]]\n",
      "\n",
      " [[-0.799   -0.3362  -0.4988   3.1    ]\n",
      "  [-0.3877   0.922   -0.       1.     ]\n",
      "  [ 0.4597   0.1934  -0.8667   0.     ]\n",
      "  [ 0.       0.       0.       1.     ]]\n",
      "\n",
      " [[ 0.9136   0.3843   0.1323   5.     ]\n",
      "  [-0.3877   0.922    0.       3.     ]\n",
      "  [-0.122   -0.05133  0.991    0.     ]\n",
      "  [ 0.       0.       0.       1.     ]]]\n"
     ]
    }
   ],
   "source": [
    "P = rotate(Values)\n",
    "print(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "def equation_salution(l1, l2, in_val):\n",
    "    \n",
    "    c2 = (Values[:,0]**2 + Values[:,1]**2 - l1**2 - l2**2) / (2 * l1 * l2)\n",
    "    s2 = np.sqrt(1 - c2**2)\n",
    "    \n",
    "    Q2 = np.arctan2(s2, c2)\n",
    "    \n",
    "    gamma = np.arctan2((l1+l2*c2), (l2*s2))\n",
    "    r = np.sqrt((l1+l2*c2)**2 + (l2*s2))\n",
    "    \n",
    "    k1 = r * np.cos(gamma)\n",
    "    k2 = r * np.sin(gamma)\n",
    "    \n",
    "    Q1 = np.arctan2(Values[:,0], Values[:,1]) - np.arctan2(k2, k1)\n",
    "    Q3 = np.deg2rad(Values[:,3]) - Q2-Q1\n",
    "    \n",
    "    Q = np.reshape(np.concatenate((Q1, Q2, Q3), axis=0), (len(Values), len(Values)))\n",
    "    \n",
    "    return(np.rad2deg(Q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ -41.22024299   -3.91190668  -11.56713085]\n",
      " [  74.27621866  156.85309447   75.52248781]\n",
      " [ -28.05597567 -274.94118779  -88.95535696]]\n"
     ]
    }
   ],
   "source": [
    "print(equation_salution(L1, L2, Values))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def T_matrises(In_val):\n",
    "    T_1 = np.array(In_val[0, 0:1], dtype='float16')\n",
    "    T_2 = np.array(In_val[1, 0:1], dtype='float16')\n",
    "    T_3 = np.array(In_val[2, 0:1], dtype='float16')\n",
    "    \n",
    "    return T_1, T_2, T_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def abcd_computing(In_val):\n",
    "    size = len(In_val)\n",
    "    \n",
    "    A = np.linalg.det(np.transpose(np.array([In_val[:,1], \n",
    "                                   np.zeros(size),\n",
    "                                   np.ones(size)])))\n",
    "    \n",
    "    B = np.linalg.det(np.transpose(np.array([In_val[:,2], \n",
    "                                   In_val[:,0],\n",
    "                                   np.ones(size)])))\n",
    "    \n",
    "    C = np.linalg.det(np.transpose(np.array([In_val[:,0], \n",
    "                                   In_val[:,1],\n",
    "                                   np.ones(size)])))\n",
    "    \n",
    "    D = np.linalg.det(np.transpose(np.array([In_val[:,0], \n",
    "                                   In_val[:,1],\n",
    "                                   In_val[:,1]])))\n",
    "    return A, B, C, D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def xyz_p1_computing(A, B, C, D):\n",
    "    X_p1 = -(A*D) / (A**2 + B**2 + C**2)\n",
    "    Y_p1 = -(B*D) / (A**2 + B**2 + C**2)\n",
    "    Z_p1 = -(C*D) / (A**2 + B**2 + C**2)\n",
    "    \n",
    "    return X_p1, Y_p1, Z_p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cosinuses_guides(A, B, C, D):\n",
    "    \n",
    "    if D < 0:\n",
    "        k = 1\n",
    "    else:\n",
    "        k = -1\n",
    "    \n",
    "    a_x_p1 = A / (k * sqrt(A**2 + B**2 + C**2))\n",
    "    a_y_p1 = B / (k * sqrt(A**2 + B**2 + C**2))\n",
    "    a_z_p1 = C / (k * sqrt(A**2 + B**2 + C**2))\n",
    "    \n",
    "    return a_x_p1, a_y_p1, a_z_p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def radius_calculating(In_value):\n",
    "    \n",
    "    m_a = (In_value[1,1]-In_value[0,1]) / (In_value[1,0]-In_value[0,0])\n",
    "    m_b = (In_value[2,1]-In_value[1,1]) / (In_value[2,0]-In_value[1,0])\n",
    "    \n",
    "    x_numerator = (m_a*m_b * (In_value[0,1]-In_value[2,1]) +\n",
    "                   m_b * (In_value[0,0]+In_value[1,0]) -\n",
    "                   m_a * (In_value[1,0]+In_value[2,0]))\n",
    "    \n",
    "    x_denumerator = 2 * (m_b-m_a)\n",
    "    \n",
    "    a = x_numerator / x_denumerator\n",
    "    \n",
    "    b = ((-1/m_a) * (a - (In_value[0,0]+In_value[1,0]) / 2) + \n",
    "                    (In_value[0,1]+In_value[1,1]) / 2)\n",
    "    \n",
    "    R = np.sqrt((a-In_value[0,0])**2 + (b-In_value[0,1])**2)\n",
    "    \n",
    "    return (a, b, R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "(a, b, R) = radius_calculating(Values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def arc_equation(In_value, a, b, R, step=0.1):\n",
    "    \"\"\"\n",
    "    Return array whith X and Y values.\n",
    "    Step is needed for better or worse trajectory smoothing.\n",
    "    \"\"\"\n",
    "    x_max = np.max(In_value[:,0])\n",
    "    x_min = np.min(In_value[:,0])\n",
    "    \n",
    "    x = np.arange(x_min, x_max + step, step)\n",
    "    X = np.concatenate((x, x[::-1]), axis=0)\n",
    "    \n",
    "    D = 4*b**2 + 4*(R**2 - b**2 - a**2 + 2*a*x - x**2)\n",
    "\n",
    "    y_1 = (2*b + np.sqrt(D))/2\n",
    "    y_2 = (2*b - np.sqrt(D))/2\n",
    "    \n",
    "    Y = np.concatenate((y_1, y_2[::-1]), axis=0)\n",
    "    return X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       " * http://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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = arc_equation(Values, a, b, R, step=0.01)\n",
    "plt.plot(x, y)\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Q1_Q2_Q3_values(X, Y, L1, L2):\n",
    "    \"\"\"\n",
    "    \n",
    "    \"\"\"\n",
    "    B = np.sqrt(X**2 + Y**2)\n",
    "\n",
    "    q1 = np.arccos(X/B)\n",
    "    q2 = np.arccos((L1**2 - L2**2 + B**2) / (2*B*L1))\n",
    "    \n",
    "    Q1 = q1 - q2\n",
    "    Q2 = np.pi - np.arccos((L1**2 + L2**2 - B**2) / (2 * L1*L2))\n",
    "    \n",
    "    return Q1, Q2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q1, Q2 = Q1_Q2_Q3_values(x, y, L1, L2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def coordinates_for_every_unit(Q1, Q2, L1, L2):\n",
    "    \"\"\"\n",
    "    \n",
    "    \"\"\"\n",
    "    X_L1, Y_L1 = L1*np.cos(Q1), L1*np.sin(Q1)\n",
    "    X_L2, Y_L2 = X_L1 + L2*np.cos(Q1 + Q2), Y_L1 + L2*np.sin(Q1 + Q2)\n",
    "    \n",
    "    return X_L1, X_L2, Y_L1, Y_L2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_L1, X_L2, Y_L1, Y_L2 = coordinates_for_every_unit(Q1, Q2, L1, L2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.760910712269423 3.2947762616507212 2.899999999999998 5.100000000000001\n"
     ]
    }
   ],
   "source": [
    "print(X_L1[0], Y_L1[0], X_L2[0], Y_L2[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ploting(X_L1, X_L2, Y_L1, Y_L2, m=2, line_lw=3, grid_lw=0.2):\n",
    "    n = len(X_L1)\n",
    "\n",
    "    fig = plt.figure(figsize=(6,4))\n",
    "    \n",
    "    def animate(i, x, y, m):\n",
    "        '''\n",
    "        кадр анимации,\n",
    "        i - номер кадра\n",
    "        x, y - данные\n",
    "        m - число пропускаемых кадров\n",
    "        '''\n",
    "        plt.clf()\n",
    "        plt.plot(x[:i*m], y[:i*m], color='black', lw=3)\n",
    "        \n",
    "        plt.xlim(0, 7)\n",
    "        plt.ylim(-0.4, 1.2)\n",
    "        plt.grid(ls='solid', lw=0.2)\n",
    "        \n",
    "    anim = animation.FuncAnimation(fig, animate,  fargs=(X_L1, Y_L1, m), frames=int(n/m), interval=1, repeat=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-14-46ccda62eef9>, line 9)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-14-46ccda62eef9>\"\u001b[0;36m, line \u001b[0;32m9\u001b[0m\n\u001b[0;31m    L1, # length of firs unit\u001b[0m\n\u001b[0m     ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "class Manipulator(Trajectory):\n",
    "    \"\"\"Manipulator class\n",
    "    \n",
    "    init_values is a DataFrame which contane start, finish \n",
    "    and intermidiete points of trajectory; Psi, Fi and Theta angels.\n",
    "    \"\"\"\n",
    "    def __init__(self,\n",
    "                 init_values # initial Data Frame\n",
    "                 L1, # length of firs unit\n",
    "                 L2, # length of second unit\n",
    "                 A): # \n",
    "        self.params = (init_values, L1, L2, A)\n",
    "    \n",
    "    def Q1_Q2_Q3_values(X, Y, L1, L2):\n",
    "    \"\"\"\n",
    "    \n",
    "    \"\"\"\n",
    "    B = np.sqrt(X**2 + Y**2)\n",
    "\n",
    "    q1 = np.arccos(X/B)\n",
    "    q2 = np.arccos((L1**2 - L2**2 + B**2) / (2*B*L1))\n",
    "    \n",
    "    Q1 = q1 - q2\n",
    "    Q2 = np.pi - np.arccos((L1**2 + L2**2 - B**2) / (2 * L1*L2))\n",
    "    \n",
    "    return Q1, Q2 \n",
    "    \n",
    "    def coordinates_for_every_unit(Q1, Q2, L1, L2):\n",
    "    \"\"\"\n",
    "    \n",
    "    \"\"\"\n",
    "    X_L1, Y_L1 = L1*np.cos(Q1), L1*np.sin(Q1)\n",
    "    X_L2, Y_L2 = X_L1 + L2*np.cos(Q1 + Q2), Y_L1 + L2*np.sin(Q1 + Q2)\n",
    "    \n",
    "    return X_L1, X_L2, Y_L1, Y_L2\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Trajectory:\n",
    "    \"\"\"\n",
    "    \"\"\"\n",
    "    def __init__(self,\n",
    "                 init_values,\n",
    "                 discret_step=0.01):\n",
    "        self.In_value = init_values.values\n",
    "        self.step = discret_step\n",
    "    \n",
    "    def radius_calculating(self):\n",
    "        \"\"\"\n",
    "        \"\"\"\n",
    "        m_a = (In_value[1,1]-In_value[0,1]) / (In_value[1,0]-In_value[0,0])\n",
    "        m_b = (In_value[2,1]-In_value[1,1]) / (In_value[2,0]-In_value[1,0])\n",
    "    \n",
    "        x_numerator = (m_a*m_b * (In_value[0,1]-In_value[2,1]) +\n",
    "                       m_b * (In_value[0,0]+In_value[1,0]) -\n",
    "                       m_a * (In_value[1,0]+In_value[2,0]))\n",
    "    \n",
    "        x_denumerator = 2 * (m_b-m_a)\n",
    "    \n",
    "        a = x_numerator / x_denumerator\n",
    "    \n",
    "        b = ((-1/m_a) * (a - (In_value[0,0]+In_value[1,0]) / 2) + \n",
    "                        (In_value[0,1]+In_value[1,1]) / 2)\n",
    "    \n",
    "        R = np.sqrt((a-In_value[0,0])**2 + (b-In_value[0,1])**2)\n",
    "    \n",
    "        return a, b, R\n",
    "    \n",
    "    def arc_equation(self, radius_calculating):\n",
    "        \"\"\"\n",
    "        Return array whith X and Y values.\n",
    "        Step is needed for better or worse trajectory smoothing.\n",
    "        \"\"\"\n",
    "        x_max = np.max(In_value[:,0])\n",
    "        x_min = np.min(In_value[:,0])\n",
    "    \n",
    "        x = np.arange(x_min, x_max + step, step)\n",
    "        X = np.concatenate((x, x[::-1]), axis=0)\n",
    "    \n",
    "        D = 4*b**2 + 4*(R**2 - b**2 - a**2 + 2*a*x - x**2)\n",
    "\n",
    "        y_1 = (2*b + np.sqrt(D))/2\n",
    "        y_2 = (2*b - np.sqrt(D))/2\n",
    "    \n",
    "        Y = np.concatenate((y_1, y_2[::-1]), axis=0)\n",
    "        \n",
    "        return X, Y "
   ]
  }
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