{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1001\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(function(root) {\n",
       "  function now() {\n",
       "    return new Date();\n",
       "  }\n",
       "\n",
       "  var force = true;\n",
       "\n",
       "  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n",
       "    root._bokeh_onload_callbacks = [];\n",
       "    root._bokeh_is_loading = undefined;\n",
       "  }\n",
       "\n",
       "  var JS_MIME_TYPE = 'application/javascript';\n",
       "  var HTML_MIME_TYPE = 'text/html';\n",
       "  var EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n",
       "  var CLASS_NAME = 'output_bokeh rendered_html';\n",
       "\n",
       "  /**\n",
       "   * Render data to the DOM node\n",
       "   */\n",
       "  function render(props, node) {\n",
       "    var script = document.createElement(\"script\");\n",
       "    node.appendChild(script);\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when an output is cleared or removed\n",
       "   */\n",
       "  function handleClearOutput(event, handle) {\n",
       "    var cell = handle.cell;\n",
       "\n",
       "    var id = cell.output_area._bokeh_element_id;\n",
       "    var server_id = cell.output_area._bokeh_server_id;\n",
       "    // Clean up Bokeh references\n",
       "    if (id != null && id in Bokeh.index) {\n",
       "      Bokeh.index[id].model.document.clear();\n",
       "      delete Bokeh.index[id];\n",
       "    }\n",
       "\n",
       "    if (server_id !== undefined) {\n",
       "      // Clean up Bokeh references\n",
       "      var cmd = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n",
       "      cell.notebook.kernel.execute(cmd, {\n",
       "        iopub: {\n",
       "          output: function(msg) {\n",
       "            var id = msg.content.text.trim();\n",
       "            if (id in Bokeh.index) {\n",
       "              Bokeh.index[id].model.document.clear();\n",
       "              delete Bokeh.index[id];\n",
       "            }\n",
       "          }\n",
       "        }\n",
       "      });\n",
       "      // Destroy server and session\n",
       "      var cmd = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n",
       "      cell.notebook.kernel.execute(cmd);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  /**\n",
       "   * Handle when a new output is added\n",
       "   */\n",
       "  function handleAddOutput(event, handle) {\n",
       "    var output_area = handle.output_area;\n",
       "    var output = handle.output;\n",
       "\n",
       "    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n",
       "    if ((output.output_type != \"display_data\") || (!output.data.hasOwnProperty(EXEC_MIME_TYPE))) {\n",
       "      return\n",
       "    }\n",
       "\n",
       "    var toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n",
       "\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n",
       "      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n",
       "      // store reference to embed id on output_area\n",
       "      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n",
       "    }\n",
       "    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n",
       "      var bk_div = document.createElement(\"div\");\n",
       "      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n",
       "      var script_attrs = bk_div.children[0].attributes;\n",
       "      for (var i = 0; i < script_attrs.length; i++) {\n",
       "        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n",
       "        toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n",
       "      }\n",
       "      // store reference to server id on output_area\n",
       "      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n",
       "    }\n",
       "  }\n",
       "\n",
       "  function register_renderer(events, OutputArea) {\n",
       "\n",
       "    function append_mime(data, metadata, element) {\n",
       "      // create a DOM node to render to\n",
       "      var toinsert = this.create_output_subarea(\n",
       "        metadata,\n",
       "        CLASS_NAME,\n",
       "        EXEC_MIME_TYPE\n",
       "      );\n",
       "      this.keyboard_manager.register_events(toinsert);\n",
       "      // Render to node\n",
       "      var props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n",
       "      render(props, toinsert[toinsert.length - 1]);\n",
       "      element.append(toinsert);\n",
       "      return toinsert\n",
       "    }\n",
       "\n",
       "    /* Handle when an output is cleared or removed */\n",
       "    events.on('clear_output.CodeCell', handleClearOutput);\n",
       "    events.on('delete.Cell', handleClearOutput);\n",
       "\n",
       "    /* Handle when a new output is added */\n",
       "    events.on('output_added.OutputArea', handleAddOutput);\n",
       "\n",
       "    /**\n",
       "     * Register the mime type and append_mime function with output_area\n",
       "     */\n",
       "    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n",
       "      /* Is output safe? */\n",
       "      safe: true,\n",
       "      /* Index of renderer in `output_area.display_order` */\n",
       "      index: 0\n",
       "    });\n",
       "  }\n",
       "\n",
       "  // register the mime type if in Jupyter Notebook environment and previously unregistered\n",
       "  if (root.Jupyter !== undefined) {\n",
       "    var events = require('base/js/events');\n",
       "    var OutputArea = require('notebook/js/outputarea').OutputArea;\n",
       "\n",
       "    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n",
       "      register_renderer(events, OutputArea);\n",
       "    }\n",
       "  }\n",
       "\n",
       "  \n",
       "  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n",
       "    root._bokeh_timeout = Date.now() + 5000;\n",
       "    root._bokeh_failed_load = false;\n",
       "  }\n",
       "\n",
       "  var NB_LOAD_WARNING = {'data': {'text/html':\n",
       "     \"<div style='background-color: #fdd'>\\n\"+\n",
       "     \"<p>\\n\"+\n",
       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
       "     \"<ul>\\n\"+\n",
       "     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n",
       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
       "     \"</ul>\\n\"+\n",
       "     \"<code>\\n\"+\n",
       "     \"from bokeh.resources import INLINE\\n\"+\n",
       "     \"output_notebook(resources=INLINE)\\n\"+\n",
       "     \"</code>\\n\"+\n",
       "     \"</div>\"}};\n",
       "\n",
       "  function display_loaded() {\n",
       "    var el = document.getElementById(\"1001\");\n",
       "    if (el != null) {\n",
       "      el.textContent = \"BokehJS is loading...\";\n",
       "    }\n",
       "    if (root.Bokeh !== undefined) {\n",
       "      if (el != null) {\n",
       "        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n",
       "      }\n",
       "    } else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(display_loaded, 100)\n",
       "    }\n",
       "  }\n",
       "\n",
       "\n",
       "  function run_callbacks() {\n",
       "    try {\n",
       "      root._bokeh_onload_callbacks.forEach(function(callback) {\n",
       "        if (callback != null)\n",
       "          callback();\n",
       "      });\n",
       "    } finally {\n",
       "      delete root._bokeh_onload_callbacks\n",
       "    }\n",
       "    console.debug(\"Bokeh: all callbacks have finished\");\n",
       "  }\n",
       "\n",
       "  function load_libs(css_urls, js_urls, callback) {\n",
       "    if (css_urls == null) css_urls = [];\n",
       "    if (js_urls == null) js_urls = [];\n",
       "\n",
       "    root._bokeh_onload_callbacks.push(callback);\n",
       "    if (root._bokeh_is_loading > 0) {\n",
       "      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n",
       "      return null;\n",
       "    }\n",
       "    if (js_urls == null || js_urls.length === 0) {\n",
       "      run_callbacks();\n",
       "      return null;\n",
       "    }\n",
       "    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n",
       "    root._bokeh_is_loading = css_urls.length + js_urls.length;\n",
       "\n",
       "    function on_load() {\n",
       "      root._bokeh_is_loading--;\n",
       "      if (root._bokeh_is_loading === 0) {\n",
       "        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n",
       "        run_callbacks()\n",
       "      }\n",
       "    }\n",
       "\n",
       "    function on_error() {\n",
       "      console.error(\"failed to load \" + url);\n",
       "    }\n",
       "\n",
       "    for (var i = 0; i < css_urls.length; i++) {\n",
       "      var url = css_urls[i];\n",
       "      const element = document.createElement(\"link\");\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.rel = \"stylesheet\";\n",
       "      element.type = \"text/css\";\n",
       "      element.href = url;\n",
       "      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n",
       "      document.body.appendChild(element);\n",
       "    }\n",
       "\n",
       "    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.0.min.js\": \"jtq3UzIrk2TfDZfSNGEN0ICKrRWmtzZSQm6i1Xnd3hY3UfU9m98vuEL7JUv7Iway\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.0.min.js\": \"rRlSZb4FImflqQNhKcvkZq8b+FqcNFxP9CmCO8Vgo9uNXe6wk6yNMlKMrXn+TjeM\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.0.min.js\": \"MJyUmyL5f4wPlABPEp4CF5HzMeAPMvzucE8gEGNH15tAWgHFb2hsPNIEkva89XtP\"};\n",
       "\n",
       "    for (var i = 0; i < js_urls.length; i++) {\n",
       "      var url = js_urls[i];\n",
       "      var element = document.createElement('script');\n",
       "      element.onload = on_load;\n",
       "      element.onerror = on_error;\n",
       "      element.async = false;\n",
       "      element.src = url;\n",
       "      if (url in hashes) {\n",
       "        element.crossOrigin = \"anonymous\";\n",
       "        element.integrity = \"sha384-\" + hashes[url];\n",
       "      }\n",
       "      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n",
       "      document.head.appendChild(element);\n",
       "    }\n",
       "  };\n",
       "\n",
       "  function inject_raw_css(css) {\n",
       "    const element = document.createElement(\"style\");\n",
       "    element.appendChild(document.createTextNode(css));\n",
       "    document.body.appendChild(element);\n",
       "  }\n",
       "\n",
       "  \n",
       "  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.0.min.js\"];\n",
       "  var css_urls = [];\n",
       "  \n",
       "\n",
       "  var inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (var i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (force === true) {\n",
       "        display_loaded();\n",
       "      }} else if (Date.now() < root._bokeh_timeout) {\n",
       "      setTimeout(run_inline_js, 100);\n",
       "    } else if (!root._bokeh_failed_load) {\n",
       "      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "      root._bokeh_failed_load = true;\n",
       "    } else if (force !== true) {\n",
       "      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\n",
       "\n",
       "  }\n",
       "\n",
       "  if (root._bokeh_is_loading === 0) {\n",
       "    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "    run_inline_js();\n",
       "  } else {\n",
       "    load_libs(css_urls, js_urls, function() {\n",
       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "      run_inline_js();\n",
       "    });\n",
       "  }\n",
       "}(window));"
      ],
      "application/vnd.bokehjs_load.v0+json": "\n(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  var force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\n  \n\n  \n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  var NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    var el = document.getElementById(\"1001\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error() {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (var i = 0; i < css_urls.length; i++) {\n      var url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    const hashes = {\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.0.min.js\": \"jtq3UzIrk2TfDZfSNGEN0ICKrRWmtzZSQm6i1Xnd3hY3UfU9m98vuEL7JUv7Iway\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.0.min.js\": \"rRlSZb4FImflqQNhKcvkZq8b+FqcNFxP9CmCO8Vgo9uNXe6wk6yNMlKMrXn+TjeM\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.0.min.js\": \"MJyUmyL5f4wPlABPEp4CF5HzMeAPMvzucE8gEGNH15tAWgHFb2hsPNIEkva89XtP\"};\n\n    for (var i = 0; i < js_urls.length; i++) {\n      var url = js_urls[i];\n      var element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error;\n      element.async = false;\n      element.src = url;\n      if (url in hashes) {\n        element.crossOrigin = \"anonymous\";\n        element.integrity = \"sha384-\" + hashes[url];\n      }\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  \n  var js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.2.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.2.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.2.0.min.js\"];\n  var css_urls = [];\n  \n\n  var inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (var i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      var cell = $(document.getElementById(\"1001\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bokeh.plotting import show, figure, output_notebook\n",
    "from bokeh.models.widgets import RadioGroup, Button\n",
    "from bokeh.layouts import row\n",
    "from random import random\n",
    "import numpy as np\n",
    "import time\n",
    "import math\n",
    "\n",
    "output_notebook()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = np.matrix([\n",
    "    [-0.5, -0.5, -0.5],\n",
    "    [0.5, -0.5, -0.5],\n",
    "    [0.5, 0.5, -0.5],\n",
    "    [-0.5, 0.5, -0.5],\n",
    "    [-0.5, -0.5, 0.5],\n",
    "    [0.5, -0.5, 0.5],\n",
    "    [0.5, 0.5, 0.5],\n",
    "    [-0.5, 0.5, 0.5],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def projection_2D(vertices=vertices):\n",
    "    return projection_matrix.dot(vertices.T).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate(thetaX=0, thetaY=0, thetaZ=0, vertices=vertices):\n",
    "    \n",
    "    sin = math.sin(thetaX);\n",
    "    cos = math.cos(thetaX);\n",
    "    \n",
    "    rotateX = np.matrix([\n",
    "        [1, 0, 0],\n",
    "        [0, cos, -sin],\n",
    "        [0, sin, cos],\n",
    "    ])\n",
    "    \n",
    "    sin = math.sin(thetaY);\n",
    "    cos = math.cos(thetaY);\n",
    "    \n",
    "    rotateY = np.matrix([\n",
    "        [cos, 0, sin],\n",
    "        [0, 1, 0],\n",
    "        [-sin, 0, cos],\n",
    "    ])\n",
    "    \n",
    "    sin = math.sin(thetaZ);\n",
    "    cos = math.cos(thetaZ);\n",
    "    \n",
    "    rotateZ = np.matrix([\n",
    "        [cos, -sin, 0],\n",
    "        [sin, cos, 0],\n",
    "        [0, 0, 1]\n",
    "    ])\n",
    "        \n",
    "    return vertices.dot(rotateX.dot(rotateY.dot(rotateZ)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale(s=1, vertices=vertices):\n",
    "    return vertices * s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def translate(dx=0, dy=0, dz=0, vertices=vertices):\n",
    "    return vertices + np.matrix([\n",
    "        [dx, dy, dz],\n",
    "        [dx, dy, dz],\n",
    "        [dx, dy, dz],\n",
    "        [dx, dy, dz],\n",
    "        [dx, dy, dz],\n",
    "        [dx, dy, dz],\n",
    "        [dx, dy, dz],\n",
    "        [dx, dy, dz]\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw(vertices=vertices):\n",
    "    vertices = rotate(thetaX=1,thetaY=1,thetaZ=1,vertices=vertices)\n",
    "    projection = projection_2D(vertices)\n",
    "    \n",
    "    for i in range(len(edges)):\n",
    "        point1 = projection[edges[i][0]]\n",
    "        point2 = projection[edges[i][1]]\n",
    "        \n",
    "        cube[i].data_source.data = {\n",
    "            'x':[point1[0, 0],point2[0, 0]],\n",
    "            'y':[point1[0, 1],point2[0, 1]]\n",
    "        }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hitWall(vertices=vertices, rotateAngle=0, scaleSize=1, translateAngle=(1, 1)):\n",
    "    x_max = float(\"-inf\")\n",
    "    x_min = float(\"inf\")\n",
    "    y_max = float(\"-inf\")\n",
    "    y_min = float(\"inf\")\n",
    "    \n",
    "    for ptr in cube:\n",
    "        \n",
    "        x_min = min(x_min, ptr.data_source.data['x'][0], ptr.data_source.data['x'][1])\n",
    "        y_min = min(y_min, ptr.data_source.data['y'][0], ptr.data_source.data['y'][1])\n",
    "        \n",
    "        x_max = max(x_max, ptr.data_source.data['x'][0], ptr.data_source.data['x'][1])\n",
    "        y_max = max(y_max, ptr.data_source.data['y'][0], ptr.data_source.data['y'][1])\n",
    "    \n",
    "    center = [(x_max + x_min)/2, (y_max + y_min)/2]\n",
    "    ctr.data_source.data = {'x':[center[0]],'y':[center[1]]}\n",
    "    \n",
    "    angle_x = translateAngle[0]\n",
    "    angle_y = translateAngle[1]\n",
    "    \n",
    "    if center[0]<0:\n",
    "        angle_y = 1\n",
    "    if center[0]>10:\n",
    "        angle_y = -1\n",
    "    if center[1]<0:\n",
    "        angle_x = -1\n",
    "    if center[1]>10:\n",
    "        angle_x = 1\n",
    "        \n",
    "    translateAngle = (angle_x, angle_y)\n",
    "    return (rotateAngle, scaleSize, translateAngle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def animate():\n",
    "    rotated_vertices=vertices\n",
    "    \n",
    "    rotateAngle = 0.005\n",
    "    scaleSize = 1\n",
    "    scaleFector = 1.002\n",
    "    translateAngle = (-1,1)\n",
    "\n",
    "    x = 0\n",
    "    y = 0\n",
    "    \n",
    "    for j in range(0, 2000):\n",
    "        \n",
    "        x = x + translateAngle[0]\n",
    "        y = y + translateAngle[1]\n",
    "\n",
    "        rotated_vertices = rotate(\n",
    "            thetaX=rotateAngle, \n",
    "            thetaY=rotateAngle, \n",
    "            thetaZ=rotateAngle, \n",
    "            vertices=rotated_vertices\n",
    "        )\n",
    "        \n",
    "        scaled_vertices = scale(s=scaleSize, vertices=rotated_vertices)     \n",
    "        draw_vertices = translate(dx=x/25, dy=y/25, dz=0, vertices=scaled_vertices) \n",
    "        draw(vertices = draw_vertices)\n",
    "\n",
    "        rotateAngle, scaleSize, translateAngle = hitWall(\n",
    "            vertices = draw_vertices, \n",
    "            rotateAngle = rotateAngle,\n",
    "            scaleSize = scaleSize,\n",
    "            translateAngle = translateAngle\n",
    "        )\n",
    "        \n",
    "        if scaleSize > 2:\n",
    "            scaleFector = 0.998\n",
    "        \n",
    "        if scaleSize < 1:\n",
    "            scaleFector = 1.002\n",
    "        \n",
    "        scaleSize *= scaleFector\n",
    "        time.sleep(0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def handler(doc):\n",
    "    doc.add_root(row(f,start_but))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.bokehjs_exec.v0+json": "",
      "text/html": [
       "\n",
       "<script id=\"1104\">\n",
       "  var xhr = new XMLHttpRequest()\n",
       "  xhr.responseType = 'blob';\n",
       "  xhr.open('GET', \"http://localhost:56131/autoload.js?bokeh-autoload-element=1104&bokeh-absolute-url=http://localhost:56131&resources=none\", true);\n",
       "  \n",
       "  xhr.onload = function (event) {\n",
       "    var script = document.createElement('script'),\n",
       "    src = URL.createObjectURL(event.target.response);\n",
       "    script.src = src;\n",
       "    document.body.appendChild(script);\n",
       "  };\n",
       "xhr.send();\n",
       "</script>"
      ]
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "server_id": "619c814b8c4e48eaa44a336624d4b636"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = figure(\n",
    "    x_range = (-1, 11),\n",
    "    y_range = (-1, 11),\n",
    "    plot_width = 500,\n",
    "    plot_height = 500\n",
    ")\n",
    "\n",
    "f.line([0,10,10,0,0],[0,0,10,10,0])\n",
    "ctr = f.scatter(x=[0],y=[0])\n",
    "\n",
    "cube = []\n",
    "for i in range(0, 12):\n",
    "    cube.append(f.line([],[]))\n",
    "\n",
    "projection_matrix = np.matrix([\n",
    "    [1, 0 ,0],\n",
    "    [0, 1 ,0]\n",
    "]) \n",
    "\n",
    "edges = [\n",
    "    [0, 1], [1, 2], [2, 3], [3, 0],\n",
    "    [4, 5], [5, 6], [6, 7], [7, 4],\n",
    "    [0, 4], [1, 5], [2, 6], [3, 7]\n",
    "]\n",
    "\n",
    "start_but = Button(label=\"Start\", button_type=\"success\")\n",
    "start_but.on_click(animate)   \n",
    "\n",
    "draw()\n",
    "show(handler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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