FacesVerticesIntegrals.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import warnings\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "NUMBER_OF_RECTANGLES = 100\n",
    "\n",
    "\n",
    "def f(A, B, V, t):\n",
    "    PQx = V.x - (A.x + ((B.x - A.x) * t))\n",
    "    PQy = V.y - (A.y + ((B.y - A.y) * t))\n",
    "    PQz = 0\n",
    "    PQ = [PQx, PQy, PQz]\n",
    "    AB = [\n",
    "        B.x - A.x,\n",
    "        B.y - A.y,\n",
    "        B.z - A.z\n",
    "    ]\n",
    "    magnitudePQ = math.sqrt(PQx ** 2.0 + PQy ** 2.0 + PQz ** 2.0)\n",
    "    forceMagnitude = 1 / magnitudePQ\n",
    "    forceDirection = np.cross(PQ, [0, 0, 1]) / magnitudePQ\n",
    "    forceVector = forceMagnitude * forceDirection\n",
    "    return np.dot(forceVector, AB)\n",
    "\n",
    "\n",
    "def integral(A, B, V):\n",
    "    \"\"\"Do the line integral\"\"\"\n",
    "    numberofRectangles = NUMBER_OF_RECTANGLES\n",
    "    startingt = 0.0\n",
    "    endingt = 1.0\n",
    "    width = (endingt - startingt) / numberofRectangles\n",
    "    runningSum = 0.0\n",
    "    for i in range(numberofRectangles):\n",
    "        height = f(A, B, V, startingt + i * width)\n",
    "        area = height * width\n",
    "        runningSum += area\n",
    "    return runningSum\n",
    "\n",
    "\n",
    "class Vertex(object):\n",
    "    \"\"\"The three dimensional coordinates of a vertex\"\"\"\n",
    "    def __init__(self, id, x, y, z):\n",
    "        self.id = id\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        self.z = z\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str([self.x, self.y, self.z])\n",
    "\n",
    "    def __eq__(self, other):\n",
    "        return self.id == other.id\n",
    "\n",
    "    def to_array(self):\n",
    "        return np.array([self.x, self.y, self.z])\n",
    "\n",
    "    def is_blocked(self, faces):\n",
    "        \"\"\"True when this vertex is blocked from view by faces\"\"\"\n",
    "        for face in faces.values():\n",
    "            if face.is_blocking(self):\n",
    "                return True\n",
    "        return False\n",
    "\n",
    "    @staticmethod\n",
    "    def load(filename):\n",
    "        # vertices (vid, x, y, z)\n",
    "        np_vertices = np.loadtxt(filename, delimiter=\"\\t\", skiprows=1,\n",
    "                                 dtype=[('id', 'i4'), ('x', 'f8'), ('y', 'f8'), ('z', 'f8')])\n",
    "        vertices = {}\n",
    "        for id, x, y, z in np_vertices:\n",
    "            vertices[id] = Vertex(id, x, y, z)\n",
    "        return vertices\n",
    "\n",
    "\n",
    "class Edge(object):\n",
    "    \"\"\"The vertex ID's of two vertices\"\"\"\n",
    "    def __init__(self, id, v1, v2):\n",
    "        self.id = id\n",
    "        self.v1 = v1\n",
    "        self.v2 = v2\n",
    "\n",
    "    def __repr__(self):\n",
    "        return str([self.v1, self.v2])\n",
    "\n",
    "    def __iter__(self):\n",
    "        return iter([self.v1, self.v2])\n",
    "\n",
    "    def __eq__(self, other):\n",
    "        return self.id == other.id\n",
    "\n",
    "    @staticmethod\n",
    "    def load(filename, vertices):\n",
    "        # edge vertices (eid, vid, vid)\n",
    "        np_edges = np.loadtxt(filename, delimiter=\"\\t\", skiprows=1, dtype=\"i4,i4,i4\")\n",
    "\n",
    "        edges = {}\n",
    "        for id, v1, v2 in np_edges:\n",
    "            edges[id] = Edge(id, vertices[v1], vertices[v2])\n",
    "        return edges\n",
    "\n",
    "\n",
    "class Face(object):\n",
    "    def __init__(self, id, edges):\n",
    "        \"\"\"The list of edges must form a path\"\"\"\n",
    "        self.id = id\n",
    "        self.edges = edges\n",
    "        self.vertices = Face._sort_vertices_into_path(edges)\n",
    "\n",
    "    def __str__(self):\n",
    "        return \"\\n\".join(map(str, self.vertices))\n",
    "\n",
    "    def is_behind(self, vertex):\n",
    "        \"\"\"True if the vertex is behind the plane of this face\n",
    "        \"\"\"\n",
    "        # ok to use three vertices of the plane (Nige:28/7/15)\n",
    "        V = vertex.to_array()\n",
    "        A, B, C = [self.vertices[i].to_array() for i in [0, 1, 2]]\n",
    "        AB = B - A\n",
    "        AC = C - A\n",
    "        ABxAC = np.cross(AB, AC)\n",
    "        result = (((A[0] - V[0]) * (ABxAC[0]) + (A[1] - V[1]) * (ABxAC[1])) / (ABxAC[2])) + (A[2] - V[2])\n",
    "        return result > 0\n",
    "\n",
    "    def is_inside(self, vertex):\n",
    "        \"\"\"True if the vertex is blocked by this face\n",
    "\n",
    "        Accumulate the integral of each edge in this face with the vertex. If the total is\n",
    "        zero, then the vertex is visible.\n",
    "        \"\"\"\n",
    "        try:\n",
    "            total = 0.0\n",
    "            for idx in range(len(self.vertices)):\n",
    "                tegral = integral(self.vertices[idx], self.vertices[idx - 1], vertex)\n",
    "                total += tegral\n",
    "            result = abs(total) > 1 / NUMBER_OF_RECTANGLES  # relate the margin of error to number of rectangles\n",
    "            return result\n",
    "        except ZeroDivisionError:\n",
    "            return False\n",
    "\n",
    "    def is_blocking(self, vertex):\n",
    "        \"\"\"True when in line and is behind; whatever they mean\"\"\"\n",
    "        return self.is_inside(vertex) and self.is_behind(vertex)\n",
    "\n",
    "    @staticmethod\n",
    "    def _sort_vertices_into_path(in_edges):\n",
    "        \"\"\"converts a series of edges into a path of vertices\n",
    "\n",
    "        # assemble the vertices as a path around the edges of the face\n",
    "        # by putting all the edges in a list and picking a start vertex\n",
    "        # then find a cojoining edge, append the opposite vertex, and removing the edge,\n",
    "        # until all the edges have been used.\n",
    "        \"\"\"\n",
    "        edges = in_edges.copy()\n",
    "        path = [edges[0].v1]\n",
    "        edges.pop(0)\n",
    "        while len(edges):\n",
    "            for idx, edge in enumerate(edges):\n",
    "                if edge.v1 == path[-1]:\n",
    "                    path.append(edge.v2)\n",
    "                    edges.pop(idx)\n",
    "                    break\n",
    "                elif edge.v2 == path[-1]:\n",
    "                    path.append(edge.v1)\n",
    "                    edges.pop(idx)\n",
    "                    break\n",
    "            else:\n",
    "                raise Exception(\"These edges are expected to form a path: %s\" % [e.id for e in in_edges])\n",
    "        return path\n",
    "\n",
    "    @staticmethod\n",
    "    def load(filename, edges, vertices):\n",
    "\n",
    "        # get the edges of the face (fid, eid, eid, eid, eid)\n",
    "        # if the last edge is null indicate with a -1 edge id\n",
    "        convertfunc = lambda x: -1 if x == b'NULL' else x\n",
    "        np_faceedges = np.loadtxt(filename, delimiter=\"\\t\", skiprows=1,\n",
    "                                  converters={4: convertfunc},\n",
    "                                  dtype=[('id', 'i4'), ('edge1', 'i4'), ('edge2', 'i4'), ('edge3', 'i4'), ('edge4', 'i4')])\n",
    "\n",
    "        # for every face\n",
    "        faces = {}\n",
    "        # get the edges\n",
    "        for id, *edgeids in np_faceedges:\n",
    "            try:\n",
    "                face_edges = [edges[id] for id in edgeids if id >= 0]\n",
    "                faces[id] = Face(id, face_edges)\n",
    "            except KeyError:\n",
    "                # warnings.warn(\"Face %s discarded because not all these edges are known (%s, %s, %s, %s).\" % (id, eid1, eid2, eid3, eid4))\n",
    "                pass\n",
    "        return faces\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded 775 vertices, 1520 edges, 752 faces.\n"
     ]
    }
   ],
   "source": [
    "vertices = Vertex.load('../headmesh/NVertices.txt')\n",
    "edges = Edge.load('../headmesh/NEdgeVertices.txt', vertices)\n",
    "faces = Face.load('../headmesh/NFaceEdges.txt', edges, vertices)\n",
    "print(\"Loaded %s vertices, %s edges, %s faces.\" % (len(vertices), len(edges), len(faces)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.0, -4.0, 0]\n",
      "[4.0, 4.0, 0]\n",
      "[-4.0, 4.0, 0]\n",
      "[4.0, -4.0, 0]\n",
      "['A', 'D', 'C', 'B']\n",
      "0 False \n",
      "\n",
      "3.99 True \n",
      "\n",
      "4.0 False \n",
      "\n",
      "4.01 True \n",
      "\n",
      "4.1 False \n",
      "\n"
     ]
    }
   ],
   "source": [
    "A = Vertex('A', -4., -4., 0)\n",
    "B = Vertex('B', 4., -4., 0)\n",
    "C = Vertex('C', -4., 4., 0)\n",
    "D = Vertex('D', 4., 4., 0)\n",
    "\n",
    "edges = [Edge(1, A, B), Edge(2, B, C), Edge(3, C, D), Edge(4, D, A)]\n",
    "face = Face(0, edges)\n",
    "print(face)\n",
    "print([v.id for v in face.vertices])\n",
    "\n",
    "v1 = Vertex(1, 0, 0, 0)\n",
    "print(v1.y, face.is_inside(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 3.99, -0.1)\n",
    "print(v1.y, face.is_inside(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.00, -0.0)\n",
    "print(v1.y, face.is_inside(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.01, .1)\n",
    "print(v1.y, face.is_inside(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.10, -0.1)\n",
    "print(v1.y, face.is_inside(v1), '\\n')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.616909981, -1.094609976, 11.25370026]\n",
      "[-1.599470019, -0.900170028, 11.08759975]\n",
      "[-1.801380038, -1.165879965, 10.89350033]\n",
      "['A', 'C', 'B']\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "'Face' object has no attribute 'is_in_line_with'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-52-adb0a0ef24cf>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[0mv1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mVertex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m2.076020002\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m3.637000084\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m10.35280037\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 11\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mv1\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mface\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_in_line_with\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mv1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'\\n'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     13\u001b[0m \u001b[0mv1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mVertex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3.99\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m0.1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'Face' object has no attribute 'is_in_line_with'"
     ]
    }
   ],
   "source": [
    "A = Vertex('A', -1.6169099810000001, -1.0946099760000001, 11.25370026)\n",
    "B = Vertex('B', -1.801380038, -1.165879965, 10.89350033)\n",
    "C = Vertex('C', -1.599470019, -0.90017002800000001, 11.087599750000001)\n",
    "\n",
    "edges = [Edge(1, A, B), Edge(2, B, C), Edge(3, C, A)]\n",
    "face = Face(0, edges)\n",
    "print(face)\n",
    "print([v.id for v in face.vertices])\n",
    "\n",
    "v1 = Vertex(1, -2.076020002, -3.637000084, 10.35280037)\n",
    "print(v1.y, face.is_in_line_with(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 3.99, -0.1)\n",
    "print(v1.y, face.is_in_line_with(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.00, -0.0)\n",
    "print(v1.y, face.is_in_line_with(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.01, .1)\n",
    "print(v1.y, face.is_in_line_with(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.10, -0.1)\n",
    "print(v1.y, face.is_in_line_with(v1), '\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 1, 3] => ['B', 'A', 'C']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[2, 1, 3] => ['B', 'A', 'C']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[1, 2, 3] => ['A', 'C', 'B']\n",
      "[1, 2, 3] => ['A', 'C', 'B']\n",
      "[1, 2, 3] => ['A', 'C', 'B']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[1, 2, 3] => ['A', 'C', 'B']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[2, 1, 3] => ['B', 'A', 'C']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[1, 2, 3] => ['A', 'C', 'B']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[2, 1, 3] => ['B', 'A', 'C']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[2, 1, 3] => ['B', 'A', 'C']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[1, 2, 3] => ['A', 'C', 'B']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[1, 2, 3] => ['A', 'C', 'B']\n",
      "[3, 2, 1] => ['C', 'B', 'A']\n",
      "[3, 1, 2] => ['C', 'B', 'A']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n",
      "[2, 3, 1] => ['B', 'A', 'C']\n",
      "[1, 3, 2] => ['A', 'C', 'B']\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "A = Vertex('A', -4., 4., 0)\n",
    "B = Vertex('B', 4., 4., 0)\n",
    "C = Vertex('C', 4., -4., 0)\n",
    "#D = Vertex('D', -4., -4., 0)\n",
    "e1 = Edge(1, A, B)\n",
    "e2 = Edge(2, B, C)\n",
    "e3 = Edge(3, C, A)\n",
    "#e4 = Edge(4, D, A)\n",
    "# valid_paths = [\n",
    "#     [A, B, C, D], [B, C, D, A], [C, D, A, B], [D, A, B, C],\n",
    "#     [A, D, C, B], [D, C, B, A], [C, B, A, D], [B, A, D, C]\n",
    "# ]\n",
    "valid_paths = [\n",
    "    [A, B, C], [B, C, A], [C, A, B],\n",
    "    [A, C, B], [C, B, A], [B, A, C]\n",
    "]\n",
    "edges = [e1, e2, e3]\n",
    "for _ in range(50):\n",
    "    random.shuffle(edges)\n",
    "    face = Face(1, edges)\n",
    "    print([e.id for e in edges], \"=>\", [v.id for v in face.vertices])\n",
    "    assert(face.vertices in valid_paths)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1191327043588686"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = Vertex(1, 4, 4, 0)\n",
    "B = Vertex(2, -4, 4, 0)\n",
    "V = Vertex(3, -3.9, 0, 0)\n",
    "\n",
    "integral(A, B, V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Vertex' object has no attribute 'v1'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-62-6de3f3a1a234>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mv4\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mVertex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m \u001b[0mface\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mFace\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mv1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mv4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[0mv1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mVertex\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3.99\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m0.1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-59-54d8b1461051>\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, id, edges)\u001b[0m\n\u001b[0;32m    105\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mid\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mid\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    106\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0medges\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0medges\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 107\u001b[1;33m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvertices\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mFace\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_sort_vertices_into_path\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0medges\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    108\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    109\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m__str__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-59-54d8b1461051>\u001b[0m in \u001b[0;36m_sort_vertices_into_path\u001b[1;34m(in_edges)\u001b[0m\n\u001b[0;32m    152\u001b[0m         \"\"\"\n\u001b[0;32m    153\u001b[0m         \u001b[0medges\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0min_edges\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 154\u001b[1;33m         \u001b[0mpath\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0medges\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mv1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    155\u001b[0m         \u001b[0medges\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    156\u001b[0m         \u001b[1;32mwhile\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0medges\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAttributeError\u001b[0m: 'Vertex' object has no attribute 'v1'"
     ]
    }
   ],
   "source": [
    "v1 = Vertex(1, -4., -4., 0)\n",
    "v2 = Vertex(2, 4., -4., 0)\n",
    "v3 = Vertex(3, -4., 4., 0)\n",
    "v4 = Vertex(4, 4., 4., 0)\n",
    "\n",
    "face = Face(0, [v1, v2, v3, v4])\n",
    "\n",
    "v1 = Vertex(1, 0, 3.99, -0.1)\n",
    "print(v1.z, face.is_behind(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.00, -0.0)\n",
    "print(v1.z, face.is_behind(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.01, .1)\n",
    "print(v1.z, face.is_behind(v1), '\\n')\n",
    "\n",
    "v1 = Vertex(1, 0, 4.10, -0.1)\n",
    "print(v1.z, face.is_behind(v1), '\\n')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.6169099810000001, -1.0946099760000001, 11.25370026]\n",
      "[-1.801380038, -1.165879965, 10.89350033]\n",
      "[-1.599470019, -0.90017002800000001, 11.087599750000001] \n",
      "\n",
      "v0 [-1.6169099810000001, -1.0946099760000001, 11.25370026] False\n",
      "v1 [-1.616909981, -1.094609976, 0.0] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.277114369022\n",
      "result -1.39896759776\n",
      "is_behind False\n",
      "\n",
      "v749 [-1.653570056, -1.122009993, -8.0032100679999996] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.415615978585\n",
      "result -0.932769775731\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -12.003210068] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.380990576194\n",
      "result -1.01754228939\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -11.003210068] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.346365173804\n",
      "result -1.11926386501\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -10.003210068] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.311739771413\n",
      "result -1.24358217554\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -9.0032100679999996] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.277114369022\n",
      "result -1.39896759776\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -8.0032100679999996] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.242488966631\n",
      "result -1.59872850514\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -7.0032100679999996] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.207863564241\n",
      "result -1.86504077591\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -6.0032100679999996] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.17323816185\n",
      "result -2.23780960843\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -5.0032100679999996] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.138612759459\n",
      "result -2.7968134005\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -4.0032100679999996] False\n",
      "is_behind\n",
      "A [ -1.61690998  -1.09460998  11.25370026]\n",
      "B [ -1.80138004  -1.16587997  10.89350033]\n",
      "C [ -1.59947002  -0.90017003  11.08759975]\n",
      "AB [-0.18447006 -0.07126999 -0.36019993]\n",
      "AC [ 0.01743996  0.19443995 -0.16610051]\n",
      "ABAC [ 0.08187524 -0.03692244 -0.0346254 ]\n",
      "numer -0.387674023135\n",
      "demon 0.103987357068\n",
      "result -3.72808804901\n",
      "is_behind False\n",
      "v749 [-1.653570056, -1.122009993, -3.0032100679999996] False\n"
     ]
    }
   ],
   "source": [
    "face = faces[36]\n",
    "v0 = face.vertices[0]\n",
    "print(face, '\\n')\n",
    "print(\"v0\", v0, face.is_blocking(v0))\n",
    "\n",
    "v1 = Vertex(1, -1.6169099810000001, -1.0946099760000001, 0.)\n",
    "print('v1', v1, face.is_blocking(v1))\n",
    "\n",
    "v749 = vertices[749]\n",
    "print('\\nv749', v749, face.is_blocking(v749))\n",
    "v749.z -= 5.\n",
    "for mod in range(10):\n",
    "    v749.z += 1.\n",
    "    print('v749', v749, face.is_blocking(v749))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vertex\n",
      "[4.5775899889999998, -12.382800100000001, -0.36562800400000001]\n",
      "Face\n",
      "[[-6.0531401630000001, -4.8197398189999996, 6.010980129], [-5.5431098939999996, -6.2721600530000003, 5.9813899990000001], [-4.9101099970000002, -5.644229889, 7.4963197709999996], [-5.2279100420000004, -4.6442799570000002, 7.5121898649999999]]\n",
      "\n",
      "This face is blocking this vertex?\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "face = faces[656]\n",
    "vertex = vertices[449]\n",
    "print(\"Vertex\")\n",
    "print(vertex)\n",
    "print(\"Face\")\n",
    "print(face.vertices)\n",
    "print(\"\\nThis face is blocking this vertex?\")\n",
    "print(face.is_blocking(vertex))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vertex:  [1.4822599889999999, -9.4975204469999994, 8.6801795960000003]\n",
      "Edge:  [[1.4822599889999999, -9.4975204469999994, 8.6801795960000003], [1.045789957, -9.7227897639999998, 6.7623200419999998]]\n",
      "Face:\n",
      " [1.4822599889999999, -9.4975204469999994, 8.6801795960000003]\n",
      "[2.3399600980000002, -9.1642999649999997, 8.2300500870000004]\n",
      "[1.045789957, -9.7227897639999998, 6.7623200419999998]\n"
     ]
    }
   ],
   "source": [
    "print(\"Vertex: \", vertices[0])\n",
    "print(\"Edge: \", edges[0])\n",
    "print(\"Face:\\n\", faces[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vertex [-1.6169099810000001, -1.0946099760000001, 11.25370026]\n",
      "is_behind\n",
      "A [  1.93268001   2.68939996 -10.09669971]\n",
      "B [ 1.67683005 -1.12414002 -8.00249958]\n",
      "C [ 0.01165    -0.980479   -8.33932972]\n",
      "AB [-0.25584996 -3.81353998  2.09420013]\n",
      "AC [-1.92103001 -3.66987896  1.75736999]\n",
      "ABAC [ 0.98366028 -3.57339826 -6.38698638]\n",
      "numer 54.4572996398\n",
      "demon -71.8772302378\n",
      "result -0.757643268384\n",
      "is_behind False\n",
      "is_behind\n",
      "A [-1.26735997  1.47167003  9.67045975]\n",
      "B [ -1.46402001  -0.223911    10.58269978]\n",
      "C [-2.0968101  -0.63485402  9.81933975]\n",
      "AB [-0.19666004 -1.69558103  0.91224003]\n",
      "AC [-0.82945013 -2.10652405  0.14888   ]\n",
      "ABAC [ 1.66921746 -0.72737887 -0.9921308 ]\n",
      "numer -10.877543837\n",
      "demon -11.1651426502\n",
      "result 0.974241366889\n",
      "is_behind True\n",
      "This face is blocking: 489\n",
      "[-1.2673599719999999, 1.471670032, 9.6704597470000007]\n",
      "[-1.4640200139999999, -0.223911002, 10.58269978]\n",
      "[-2.0968101020000001, -0.63485401900000005, 9.8193397519999994]\n",
      "[-1.725489974, 1.1278699640000001, 9.3631601329999992]\n",
      "is_behind\n",
      "A [-2.29465008 -1.20367003  9.68992996]\n",
      "B [-2.0968101  -0.63485402  9.81933975]\n",
      "C [-2.7549901  -1.00154996  9.53512001]\n",
      "AB [ 0.19783998  0.56881601  0.12940979]\n",
      "AC [-0.46034002  0.20212007 -0.15480995]\n",
      "ABAC [-0.11421469 -0.02894491  0.3018362 ]\n",
      "numer 3.00533627105\n",
      "demon 3.3967741482\n",
      "result 0.884761876983\n",
      "is_behind True\n",
      "This face is blocking: 503\n",
      "[-2.2946500780000001, -1.2036700250000001, 9.6899299620000008]\n",
      "[-2.0968101020000001, -0.63485401900000005, 9.8193397519999994]\n",
      "[-2.7549901010000002, -1.0015499590000001, 9.53512001]\n",
      "[-3.076740026, -2.122200012, 9.4955301280000004]\n",
      "is_behind\n",
      "A [-1.72548997  1.12786996  9.36316013]\n",
      "B [-2.14384007  0.85966098  9.20827961]\n",
      "C [-2.7549901  -1.00154996  9.53512001]\n",
      "AB [-0.4183501  -0.26820898 -0.15488052]\n",
      "AC [-1.02950013 -2.12941992  0.17195988]\n",
      "ABAC [-0.37592685  0.23138895  0.61472186]\n",
      "numer 6.31081464608\n",
      "demon 6.91789555409\n",
      "result 0.912244857809\n",
      "is_behind True\n",
      "This face is blocking: 649\n",
      "[-1.725489974, 1.1278699640000001, 9.3631601329999992]\n",
      "[-2.143840075, 0.85966098300000005, 9.2082796099999999]\n",
      "[-2.7549901010000002, -1.0015499590000001, 9.53512001]\n",
      "[-2.0968101020000001, -0.63485401900000005, 9.8193397519999994]\n",
      "is_behind\n",
      "A [ -1.91931999  -1.24451005  10.58380032]\n",
      "B [ -1.84685004  -1.69857001  10.3760004 ]\n",
      "C [ -1.79992998  -1.58644998  10.69820023]\n",
      "AB [ 0.07246995 -0.45405996 -0.20779992]\n",
      "AC [ 0.11939001 -0.34193993  0.11439991]\n",
      "ABAC [-0.12299951 -0.03309979  0.02942985]\n",
      "numer 0.353637645249\n",
      "demon 0.33119475991\n",
      "result 1.06776340708\n",
      "is_behind True\n",
      "This face is blocking: 652\n",
      "[-1.9193199869999999, -1.2445100549999999, 10.58380032]\n",
      "[-1.8468500379999999, -1.6985700130000001, 10.376000400000001]\n",
      "[-1.799929976, -1.5864499809999999, 10.698200229999999]\n",
      "[-1.801380038, -1.165879965, 10.89350033]\n",
      "is_behind\n",
      "A [ -1.59947002  -0.90017003  11.08759975]\n",
      "B [ -1.09626997  -0.86747199  11.97070026]\n",
      "C [ -1.03664005  -0.56753498  11.83819962]\n",
      "AB [ 0.50320005  0.03269804  0.88310051]\n",
      "AC [ 0.56282997  0.33263504  0.75059987]\n",
      "ABAC [-0.26920704  0.11933354  0.14897854]\n",
      "numer 1.67032265308\n",
      "demon 1.67655981763\n",
      "result 0.996279784069\n",
      "is_behind True\n",
      "This face is blocking: 670\n",
      "[-1.599470019, -0.90017002800000001, 11.087599750000001]\n",
      "[-1.0962699650000001, -0.867471993, 11.970700259999999]\n",
      "[-1.036640048, -0.56753498300000005, 11.838199619999999]\n",
      "[-1.5458600520000001, -0.76886302200000001, 10.998399729999999]\n"
     ]
    }
   ],
   "source": [
    "vertex = vertices[172]\n",
    "print(\"Vertex\", vertex)\n",
    "for fid in faces.keys():\n",
    "    face = faces[fid]\n",
    "    if face.is_blocking(vertex):\n",
    "        print(\"This face is blocking:\", fid)\n",
    "        print(face)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Face\n",
      "[[-1.6169099810000001, -1.0946099760000001, 11.25370026], [-1.801380038, -1.165879965, 10.89350033], [-1.599470019, -0.90017002800000001, 11.087599750000001]]\n",
      "Vertex 700 False\n",
      "Vertex 701 False\n",
      "Vertex 702 False\n",
      "Vertex 703 False\n",
      "Vertex 704 False\n",
      "Vertex 705 False\n",
      "Vertex 706 False\n",
      "Vertex 707 False\n",
      "Vertex 708 False\n",
      "Vertex 709 False\n",
      "Vertex 710 False\n",
      "Vertex 711 False\n",
      "Vertex 712 False\n",
      "Vertex 713 False\n",
      "Vertex 714 False\n",
      "Vertex 715 False\n",
      "Vertex 716 False\n",
      "Vertex 717 False\n",
      "Vertex 718 False\n",
      "Vertex 719 False\n",
      "Vertex 720 False\n",
      "Vertex 721 False\n",
      "Vertex 722 False\n",
      "Vertex 723 False\n",
      "Vertex 724 False\n",
      "Vertex 725 False\n",
      "Vertex 726 False\n",
      "Vertex 727 False\n",
      "Vertex 728 False\n",
      "Vertex 729 False\n",
      "Vertex 730 False\n",
      "Vertex 731 False\n",
      "Vertex 732 False\n",
      "Vertex 733 False\n",
      "Vertex 734 False\n",
      "Vertex 735 False\n",
      "Vertex 736 False\n",
      "Vertex 737 False\n",
      "Vertex 738 False\n",
      "Vertex 739 False\n",
      "Vertex 740 False\n",
      "Vertex 741 False\n",
      "Vertex 742 False\n",
      "Vertex 743 False\n",
      "Vertex 744 False\n",
      "Vertex 745 False\n",
      "Vertex 746 False\n",
      "Vertex 747 False\n",
      "Vertex 748 False\n",
      "Vertex 749 True\n",
      "Vertex 750 False\n",
      "Vertex 751 False\n",
      "Vertex 752 False\n",
      "Vertex 753 False\n",
      "Vertex 754 False\n",
      "Vertex 755 False\n",
      "Vertex 756 False\n",
      "Vertex 757 False\n",
      "Vertex 758 False\n",
      "Vertex 759 False\n",
      "Vertex 760 False\n",
      "Vertex 761 False\n",
      "Vertex 762 False\n",
      "Vertex 763 False\n",
      "Vertex 764 False\n",
      "Vertex 765 False\n",
      "Vertex 766 False\n",
      "Vertex 767 False\n",
      "Vertex 768 False\n",
      "Vertex 769 False\n",
      "Vertex 770 False\n",
      "Vertex 771 False\n",
      "Vertex 772 False\n",
      "Vertex 773 False\n",
      "Vertex 774 False\n"
     ]
    },
    {
     "ename": "KeyError",
     "evalue": "775",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-61-a8117803d82f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m700\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m800\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m     \u001b[0mvertex\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mvertices\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      7\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Vertex\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvertex\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mid\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mface\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mis_blocking\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvertex\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyError\u001b[0m: 775"
     ]
    }
   ],
   "source": [
    "face = faces[36]\n",
    "print(\"Face\")\n",
    "print(face.vertices)\n",
    "\n",
    "for i in range(700, 800):\n",
    "    vertex = vertices[i]\n",
    "    print(\"Vertex\", vertex.id, face.is_blocking(vertex))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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