{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Picturing vectors in three-dimensional space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3D Drawing in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from draw3d import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Points3D((2,2,2),(1,-2,-2)),\n",
    "    Arrow3D((2,2,2)),\n",
    "    Arrow3D((1,-2,-2)),\n",
    "    Segment3D((2,2,2), (1,-2,-2))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Points3D((2,2,2),(1,-2,-2))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Points3D((2,2,2),(1,-2,-2)),\n",
    "    Arrow3D((2,2,2)),\n",
    "    Arrow3D((1,-2,-2)),\n",
    "    Segment3D((2,2,2), (1,-2,-2))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Points3D((2,2,2),(1,-2,-2)),\n",
    "    Arrow3D((2,2,2)),\n",
    "    Arrow3D((1,-2,-2)),\n",
    "    Segment3D((2,2,2), (1,-2,-2)),\n",
    "    Box3D(2,2,2),\n",
    "    Box3D(1,-2,-2)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Draw the 3D arrow and point representing the coordinates $(-1,-2,2)$, as well as the dashed box that makes the arrow look 3D.  Do this drawing by hand as practice, but from now on we’ll use Python to draw for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v = (-1,-2,2)\n",
    "draw3d(\n",
    "    Points3D(v),\n",
    "    Arrow3D(v),\n",
    "    Box3D(*v)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini project:** There are eight 3D vectors that have every coordinate equal to $+1$ or $-1$.  For instance, $(1,-1,1)$ is one of them.  Plot all of these eight vectors as points.  Then, figure out how to connect them with line segments (using `Segment3D` objects) to form the outline of a cube.  Hint: you’ll need 12 segments in total."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "pm1 = [1,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = [(x,y,z) for x in pm1 for y in pm1 for z in pm1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "edges = [((-1,y,z),(1,y,z)) for y in pm1 for z in pm1] +\\\n",
    "                [((x,-1,z),(x,1,z)) for x in pm1 for z in pm1] +\\\n",
    "                [((x,y,-1),(x,y,1)) for x in pm1 for y in pm1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Points3D(*vertices,color=blue),\n",
    "    *[Segment3D(*edge) for edge in edges]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vector arithmetic in 3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding 3D vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add(*vectors):\n",
    "    by_coordinate = zip(*vectors)\n",
    "    coordinate_sums = [sum(coords) for coords in by_coordinate]\n",
    "    return tuple(coordinate_sums)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, 4), (1, 4, 2), (3, -4, -2)]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(zip(*[(1,1,3),(2,4,-4),(4,2,-2)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[7, 7, -3]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[sum(coords) for coords in [(1, 2, 4), (1, 4, 2), (3, -4, -2)]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add(*vectors):\n",
    "    return tuple(map(sum,zip(*vectors)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7, 7, -3)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "add((1,1,3),(2,4,-4),(4,2,-2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing lengths and distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def length(v):\n",
    "    return sqrt(sum([coord ** 2 for coord in v]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length((3,4,12))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Draw $(4,0,3)$ and $(-1,0,1)$ as Arrow3D objects, such that they are placed tip-to-tail in both orders in 3D.  What is their vector sum?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 0, 4)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "add((4,0,3),(-1,0,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw3d(\n",
    "    Arrow3D((4,0,3),color=red),\n",
    "    Arrow3D((-1,0,1),color=blue),\n",
    "    Arrow3D((3,0,4),(4,0,3),color=blue),\n",
    "    Arrow3D((-1,0,1),(3,0,4),color=red),\n",
    "    Arrow3D((3,0,4),color=purple)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Suppose we set `vectors1=[(1,2,3,4,5), (6,7,8,9,10)]` and `vectors2=[(1,2), (3,4), (5,6)]`.  Without evaluating in Python, what are the results of `len(zip(*vectors1))` and `len(zip(*vectors2))`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "vectors1=[(1,2,3,4,5), (6,7,8,9,10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "vectors2=[(1,2), (3,4), (5,6)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(list(zip(*vectors1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(list(zip(*vectors2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini project:** The comprehension below creates a list of 24 Python vectors\n",
    "```\n",
    "from math import sin, cos, pi\n",
    "vs = [(sin(pi*t/6), cos(pi*t/6), 1.0/3) for t in range(0,24)]\n",
    "```\n",
    "What is the sum of the 24 vectors?  Draw all 24 of them tip-to-tail as Arrow3D objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-4.440892098500626e-16, -7.771561172376096e-16, 7.9999999999999964)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import sin, cos, pi\n",
    "vs = [(sin(pi*t/6), cos(pi*t/6), 1.0/3) for t in range(0,24)]\n",
    "\n",
    "running_sum = (0,0,0) #<1>\n",
    "arrows = []\n",
    "for v in vs:\n",
    "    next_sum = add(running_sum, v) #2\n",
    "    arrows.append(Arrow3D(next_sum, running_sum)) \n",
    "    running_sum = next_sum\n",
    "print(running_sum)\n",
    "draw3d(*arrows)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Write a function `scale(scalar,vector)` that returns the input scalar times the input vector.  Specifically, write it so it works on 2D or 3D vectors, or vectors of any number of coordinates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def scale(scalar,v):\n",
    "    return tuple(scalar * coord for coord in v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini project:** The coordinates 3, 4, 12 in any order create a vector of length 13, a whole number. This is unusual because most numbers are not perfect squares, so the square root in the length formula typically returns an irrational number.  Find a different triple of whole numbers that define coordinates of a vector with whole number length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vectors_with_whole_number_length(max_coord=100):\n",
    "    for x in range(1,max_coord):\n",
    "        for y in range(1,x+1):\n",
    "            for z in range(1,y+1):\n",
    "                if length((x,y,z)).is_integer():\n",
    "                    yield (x,y,z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(2, 2, 1),\n",
       " (4, 4, 2),\n",
       " (6, 3, 2),\n",
       " (6, 6, 3),\n",
       " (7, 4, 4),\n",
       " (7, 6, 6),\n",
       " (8, 4, 1),\n",
       " (8, 8, 4),\n",
       " (9, 6, 2),\n",
       " (10, 10, 5),\n",
       " (11, 10, 2),\n",
       " (12, 4, 3),\n",
       " (12, 6, 4),\n",
       " (12, 9, 8),\n",
       " (12, 12, 1),\n",
       " (12, 12, 6),\n",
       " (14, 5, 2),\n",
       " (14, 8, 8),\n",
       " (14, 12, 12),\n",
       " (14, 14, 7),\n",
       " (15, 10, 6),\n",
       " (16, 8, 2),\n",
       " (16, 11, 8),\n",
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       " (86, 53, 46),\n",
       " (86, 59, 38),\n",
       " (86, 70, 5),\n",
       " (86, 72, 48),\n",
       " (86, 76, 52),\n",
       " (86, 77, 70),\n",
       " (86, 86, 43),\n",
       " (87, 26, 6),\n",
       " (87, 46, 42),\n",
       " (87, 60, 40),\n",
       " (87, 62, 6),\n",
       " (87, 66, 42),\n",
       " (87, 68, 24),\n",
       " (87, 72, 4),\n",
       " (87, 76, 36),\n",
       " (87, 78, 6),\n",
       " (87, 84, 4),\n",
       " (87, 84, 60),\n",
       " (87, 84, 80),\n",
       " (87, 86, 66),\n",
       " (88, 16, 10),\n",
       " (88, 24, 12),\n",
       " (88, 28, 11),\n",
       " (88, 29, 8),\n",
       " (88, 33, 24),\n",
       " (88, 39, 12),\n",
       " (88, 41, 40),\n",
       " (88, 44, 11),\n",
       " (88, 54, 24),\n",
       " (88, 55, 16),\n",
       " (88, 56, 28),\n",
       " (88, 56, 46),\n",
       " (88, 56, 53),\n",
       " (88, 64, 34),\n",
       " (88, 64, 43),\n",
       " (88, 72, 69),\n",
       " (88, 76, 13),\n",
       " (88, 77, 4),\n",
       " (88, 80, 16),\n",
       " (88, 80, 70),\n",
       " (88, 84, 24),\n",
       " (88, 84, 63),\n",
       " (88, 88, 44),\n",
       " (89, 18, 6),\n",
       " (89, 42, 42),\n",
       " (89, 52, 20),\n",
       " (89, 62, 58),\n",
       " (89, 68, 64),\n",
       " (89, 82, 22),\n",
       " (89, 88, 88),\n",
       " (90, 10, 9),\n",
       " (90, 18, 15),\n",
       " (90, 22, 21),\n",
       " (90, 27, 14),\n",
       " (90, 30, 5),\n",
       " (90, 45, 22),\n",
       " (90, 45, 30),\n",
       " (90, 50, 3),\n",
       " (90, 51, 18),\n",
       " (90, 52, 36),\n",
       " (90, 54, 3),\n",
       " (90, 54, 47),\n",
       " (90, 55, 18),\n",
       " (90, 57, 10),\n",
       " (90, 60, 20),\n",
       " (90, 60, 36),\n",
       " (90, 63, 34),\n",
       " (90, 65, 30),\n",
       " (90, 70, 15),\n",
       " (90, 72, 40),\n",
       " (90, 75, 54),\n",
       " (90, 81, 50),\n",
       " (90, 82, 75),\n",
       " (90, 90, 21),\n",
       " (90, 90, 31),\n",
       " (90, 90, 45),\n",
       " (91, 48, 36),\n",
       " (91, 52, 52),\n",
       " (91, 58, 26),\n",
       " (91, 62, 14),\n",
       " (91, 68, 28),\n",
       " (91, 78, 42),\n",
       " (91, 78, 78),\n",
       " (92, 11, 8),\n",
       " (92, 13, 4),\n",
       " (92, 34, 28),\n",
       " (92, 36, 21),\n",
       " (92, 40, 31),\n",
       " (92, 40, 40),\n",
       " (92, 44, 2),\n",
       " (92, 44, 25),\n",
       " (92, 56, 8),\n",
       " (92, 60, 6),\n",
       " (92, 71, 56),\n",
       " (92, 74, 44),\n",
       " (92, 75, 60),\n",
       " (92, 76, 49),\n",
       " (92, 79, 44),\n",
       " (92, 84, 57),\n",
       " (92, 86, 4),\n",
       " (92, 89, 16),\n",
       " (92, 90, 60),\n",
       " (92, 91, 56),\n",
       " (92, 92, 46),\n",
       " (93, 24, 24),\n",
       " (93, 36, 16),\n",
       " (93, 42, 14),\n",
       " (93, 44, 36),\n",
       " (93, 66, 34),\n",
       " (93, 72, 36),\n",
       " (93, 74, 6),\n",
       " (93, 80, 24),\n",
       " (93, 88, 36),\n",
       " (93, 92, 24),\n",
       " (94, 26, 17),\n",
       " (94, 28, 28),\n",
       " (94, 31, 2),\n",
       " (94, 42, 3),\n",
       " (94, 46, 37),\n",
       " (94, 53, 26),\n",
       " (94, 56, 32),\n",
       " (94, 58, 11),\n",
       " (94, 59, 2),\n",
       " (94, 64, 8),\n",
       " (94, 66, 63),\n",
       " (94, 70, 67),\n",
       " (94, 81, 42),\n",
       " (94, 83, 50),\n",
       " (94, 87, 54),\n",
       " (94, 90, 15),\n",
       " (94, 94, 47),\n",
       " (95, 26, 10),\n",
       " (95, 40, 20),\n",
       " (95, 44, 8),\n",
       " (95, 60, 12),\n",
       " (95, 90, 6),\n",
       " (96, 12, 7),\n",
       " (96, 18, 8),\n",
       " (96, 21, 12),\n",
       " (96, 24, 3),\n",
       " (96, 27, 16),\n",
       " (96, 29, 12),\n",
       " (96, 32, 24),\n",
       " (96, 37, 36),\n",
       " (96, 38, 24),\n",
       " (96, 42, 16),\n",
       " (96, 44, 27),\n",
       " (96, 48, 12),\n",
       " (96, 48, 19),\n",
       " (96, 48, 32),\n",
       " (96, 48, 44),\n",
       " (96, 51, 8),\n",
       " (96, 58, 48),\n",
       " (96, 60, 53),\n",
       " (96, 64, 12),\n",
       " (96, 66, 48),\n",
       " (96, 72, 22),\n",
       " (96, 72, 27),\n",
       " (96, 72, 35),\n",
       " (96, 72, 50),\n",
       " (96, 72, 64),\n",
       " (96, 75, 28),\n",
       " (96, 78, 24),\n",
       " (96, 78, 40),\n",
       " (96, 80, 3),\n",
       " (96, 84, 77),\n",
       " (96, 88, 27),\n",
       " (96, 88, 66),\n",
       " (96, 90, 72),\n",
       " (96, 90, 80),\n",
       " (96, 92, 3),\n",
       " (96, 92, 33),\n",
       " (96, 96, 8),\n",
       " (96, 96, 48),\n",
       " (96, 96, 92),\n",
       " (97, 14, 14),\n",
       " (97, 40, 4),\n",
       " (97, 54, 30),\n",
       " (97, 64, 56),\n",
       " (97, 82, 74),\n",
       " (97, 84, 48),\n",
       " (97, 94, 58),\n",
       " (97, 96, 12),\n",
       " (98, 14, 1),\n",
       " (98, 20, 20),\n",
       " (98, 28, 4),\n",
       " (98, 35, 14),\n",
       " (98, 39, 18),\n",
       " (98, 42, 9),\n",
       " (98, 55, 50),\n",
       " (98, 56, 16),\n",
       " (98, 56, 56),\n",
       " (98, 62, 41),\n",
       " (98, 69, 42),\n",
       " (98, 70, 25),\n",
       " (98, 70, 61),\n",
       " (98, 71, 22),\n",
       " (98, 73, 14),\n",
       " (98, 74, 7),\n",
       " (98, 75, 30),\n",
       " (98, 78, 21),\n",
       " (98, 78, 69),\n",
       " (98, 84, 36),\n",
       " (98, 84, 84),\n",
       " (98, 86, 35),\n",
       " (98, 91, 86),\n",
       " (98, 98, 49),\n",
       " (99, 16, 12),\n",
       " (99, 22, 18),\n",
       " (99, 30, 18),\n",
       " (99, 36, 28),\n",
       " (99, 44, 12),\n",
       " (99, 54, 38),\n",
       " (99, 66, 2),\n",
       " (99, 66, 22),\n",
       " (99, 72, 12),\n",
       " (99, 72, 52),\n",
       " (99, 88, 12),\n",
       " (99, 90, 18),\n",
       " (99, 90, 70)]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(vectors_with_whole_number_length())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Find a vector in the same direction as $(-1,-1,2)$ but which has length 1.  Hint: find the appropriate scalar to multiply the original vector to change its length appropriately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.449489742783178"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length((-1,-1,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = 1/length((-1,-1,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.4082482904638631, -0.4082482904638631, 0.8164965809277261)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scale(s,(-1,-1,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(scale(s,(-1,-1,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The dot product: measuring alignment of vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the dot product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dot(u,v):\n",
    "    return sum([coord1 * coord2 for coord1,coord2 in zip(u,v)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dot products by example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot((1,0),(0,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot((0,3,0),(0,0,-5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot((3,4),(2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot(scale(2,(3,4)),(2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot((3,4),scale(2,(2,3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot((4,3),(8,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measuring angles with the dot product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import cos,pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5529142706151244"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 * 2 * cos(75 * pi / 180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def angle_between(v1,v2):\n",
    "    return acos(\n",
    "                dot(v1,v2) /\n",
    "                (length(v1) * length(v2))\n",
    "            )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini project:** Find a vector $\\vec{u}$ of length 3 and a vector $\\vec{v}$ of length 7, such that $\\vec{u} \\cdot \\vec{v} = 21$.  Find another pair of vectors $\\vec{u}$ and $\\vec{v}$ such that $\\vec{u} \\cdot \\vec{v} = -21$.  Finally, find three more pairs of vectors of respective lengths 3 and 7 and show that all of their lengths lie between -21 and 21."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot((3,0),(7,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-21"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot((0,3),(0,-7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u = (0.14317567615339055, 2.9965815066101604), v = (4.015170265108397, -5.7339696321300275)\n",
      "length of u: 3.000000, length of v: 7.000000, dot product :-16.607433\n",
      "u = (0.7327707232895235, 2.9091316689159585), v = (-2.8856954383684053, -6.37752003814804)\n",
      "length of u: 3.000000, length of v: 7.000000, dot product :-20.667599\n",
      "u = (-1.191912147595753, 2.753061102194007), v = (-3.513907103757361, 6.054127258834551)\n",
      "length of u: 3.000000, length of v: 7.000000, dot product :20.855651\n"
     ]
    }
   ],
   "source": [
    "from vectors import to_cartesian\n",
    "from random import random\n",
    "from math import pi\n",
    "\n",
    "def random_vector_of_length(l):\n",
    "    return to_cartesian((l, 2*pi*random()))\n",
    "\n",
    "pairs = [(random_vector_of_length(3), random_vector_of_length(7))\n",
    "            for i in range(0,3)]\n",
    "for u,v in pairs:\n",
    "    print(\"u = %s, v = %s\" % (u,v))\n",
    "    print(\"length of u: %f, length of v: %f, dot product :%f\" %\n",
    "                (length(u), length(v), dot(u,v)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Let $\\vec{u}$ and $\\vec{v}$ be vectors, with $|\\vec{u}| = 3.61$ and $|\\vec{v}| = 1.44$.  If the angle between $\\vec{u}$ and $\\vec{v}$ is 101.3 degrees, what is $\\vec{u} ∙ \\vec{v}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0186064362303022"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3.61 * 1.44 * cos(101.3 * pi / 180)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini Project:** Find the angle between $(3,4)$ and $(4,3)$ by converting them to polar coordinates and taking the difference of the angles.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.2837941092083278"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from vectors import to_polar\n",
    "r1,t1 = to_polar((4,3))\n",
    "r2,t2 = to_polar((3,4))\n",
    "t1-t2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2837941092083278"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2-t1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The cross product: measuring oriented area"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the cross product of 3D vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cross(u, v):\n",
    "    ux,uy,uz = u\n",
    "    vx,vy,vz = v\n",
    "    return (uy*vz - uz*vy, uz*vx - ux*vz, ux*vy - uy*vx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Use the Python cross function to compute $(0,0,1) \\times \\vec{v}$ for a few different values of a second vector $\\vec{v}$.  What is the $z$-coordinate of each result, and why?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2, 1, 0)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross((0,0,1),(1,2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, -1, 0)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross((0,0,1),(-1,-1,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 1, 0)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross((0,0,1),(1,-1,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rendering a 3D object in 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining a 3D object with vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "octahedron = [\n",
    "    [(1,0,0), (0,1,0), (0,0,1)],\n",
    "    [(1,0,0), (0,0,-1), (0,1,0)],\n",
    "    [(1,0,0), (0,0,1), (0,-1,0)],\n",
    "    [(1,0,0), (0,-1,0), (0,0,-1)],\n",
    "    [(-1,0,0), (0,0,1), (0,1,0)],\n",
    "    [(-1,0,0), (0,1,0), (0,0,-1)],\n",
    "    [(-1,0,0), (0,-1,0), (0,0,1)],\n",
    "    [(-1,0,0), (0,0,-1), (0,-1,0)],\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vertices(faces):\n",
    "    return list(set([vertex for face in faces for vertex in face]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "def component(v,direction):\n",
    "    return (dot(v,direction) / length(direction))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vector_to_2d(v):\n",
    "    return (component(v,(1,0,0)), component(v,(0,1,0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "def face_to_2d(face):\n",
    "    return [vector_to_2d(vertex) for vertex in face]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Orienting faces and shading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "blues = matplotlib.cm.get_cmap('Blues')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def unit(v):\n",
    "    return scale(1./length(v), v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normal(face):\n",
    "    return(cross(subtract(face[1], face[0]), subtract(face[2], face[0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "from vectors import *\n",
    "from draw2d import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "def render(faces, light=(1,2,3), color_map=blues, lines=None):\n",
    "    polygons = []\n",
    "    for face in faces:\n",
    "        unit_normal = unit(normal(face)) #1\n",
    "        if unit_normal[2] > 0: #2\n",
    "            c = color_map(1 - dot(unit(normal(face)), unit(light))) #3\n",
    "            p = Polygon2D(*face_to_2d(face), fill=c, color=lines) #4\n",
    "            polygons.append(p)\n",
    "    draw2d(*polygons,axes=False, origin=False, grid=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8gSbNWzBm0nS2bt1C1arVuHr1qtGRRBqRYhBpavz48bRu3ZryFSvx9ZBpWDJlNjqSSIVG7zVlwrTZ7Nq1k+CQEC5fvmx0JJEGpBhEmhk5ciRffPEFL70TRNtBkzD7+hodSThBnfqNmDwrjH1//EFgUBDnz583OpJwMikGkSYGDx7Mt99+yysB1fmi/wRMFikFT1KjVl2mz13I4UOHCAwK4uzZs0ZHEk4kxSCcrk+fPnTq1ImKIXVo02c0Piaz0ZFEGqhSrQaz5oUTGxNDQGAQp0+fNjqScBIpBuE0Wmu6d+9O165debNGA1r3GI6Pj5wt68n8g6owZ2Ekx479S2X/AE6cOGF0JOEEUgzCKbTW/Pjjj/Tq1YtKdd6j1c9D8Jbr62QIb1fyZ174cs6cOU1l/wD+/fdfoyOJVJJiEKmmtaZDhw4MGDCAwEYf8GGXAXjJFTkzlIpvvMX8iJVcuHCeSpX9iY2NNTqSSAUpBpEqDoeDtm3bMmzYMELeb0WzTr/INfwzqFdfq8jCyNVcv3aNyv4B/PPPP0ZHEk9IfoPFE3M4HLRp04axY8dS48PPeK9dd7klZAb30suvsGjZahITEvD3D+DQoUNGRxJPQIpBPBG73c7HH3/MlClTqPPx1zT86kcpBQHAcy+8xOIVa7A7HAQEBHLgwAGjI4nHJMUgHltSUhIffvghM2bMoMFnHaj3WUcpBXGHZ8s9R8TKtXj7+BAQGMiePXuMjiQegxSDeCw2m42mTZsSGhrKu207U+vjb4yOJFzUU2WfYcnKdWTOnIWg4GB27txpdCTxiKQYxCNLTEykcePGLFy4kKbtulHtwy+MjiRcXMnSZQhfsZYcOXNRJSSErdu2GR1JPAIpBvFIbt26Rf0GDYiMjOSDTr0JbtLa6EjCTRQvUZKIFWvJly8/1apVY+OmTUZHEg/hlGJQSlVXSv2tlIpRSnW+x/KPlFLxSqm9yY9PUixrqZSKTn60dEYe4Vw3b96kTt26rF61io+69CegcQujIwk3U6RoMSJWrqNw4SLUqlmTNWvXGh1JPECqi0Ep5Q2MAWoA5YGmSqny9xg6T2tdIfkxOXnd3EB34HWgItBdKZUrtZmE81y/fp2aNWuyYf16WncbzDv1mhodSbipAgULsXjFWoqXLEXdOnVYuWqV0ZHEfTjjE0NFIEZrHae1tgJhQL1HXLcasEZrfVFrfQlYA1R3QibhBFevXqV69eps3rKFNr1G8EbNxkZHEm4uf/4CLF6+hqeefob69eqxZEmk0ZHEPTijGIoAx1NMn0ied7dGSqn9SqmFSqlij7muSGeXLl2iSkgIO37/nS/6jsYvpK7RkYSHyJMnLwsjV1P+uRdo3LgRCxcuMjqSuIsziuFeB7Dru6aXAiW11i8Ca4EZj7Hu7YFKtVFKRSmlouLj4584rHi4CxcuEBwczB97/uCr/uN5OaCm0ZGEh8mVOzcLIldR4RU/mjR5n9DQMKMjiRScUQwngGIpposCp1IO0Fpf0FonJk9OAl591HVTvMZErbWf1tovX758Togt7uXcuXMEBAZy8M9DfD14Mi9WCjE6kvBQ2XPkYF74ciq+8RYffNCcGTNmGh1JJHNGMewCyiqlSimlzEAT4I4dh0qpQikm6wKHk5+vBqoqpXIlf+lcNXmeMMDp06cJDAzkn+hovh06lefeDDA6kvBwWbNlY87CSN6q5E+rVh8xefIUoyMJINUXzNdaJyml2nL7Dd0bmKq1/lMp1QuI0lpHAt8opeoCScBF4KPkdS8qpXpzu1wAemmtL6Y2k3h8J0+eJDAoiOPHT9Bu+AzKvvyG0ZFEBpElSxZmz4+gVbN3+fTTT0hITKTtV18aHStDU1rfc5e+S/Pz89NRUVFGx/AY//77L4FBQZw5e452w6dT+sXXjI7klr4Ofh6Ao6cuGJzEPSUkJPBJiyasWbWCIUOH0b7dd0ZH8jhKqd1aa7+HjZMznzO4uLg4KleuzNn483QYPUdKQRjG19eXqbPnU6tufTq0b8eAAQONjpRhSTFkYNHR0VSuXJmLV67SacxcSpavYHQkkcGZzWYmTJtD/Ubv0bnzD/Ts1dvoSBmS3JQ3gzp8+DBBQUHcTLTRaWwYRZ4qZ3QkIQAwmUyMmTQdk8lEj+7dsFqt/NK7l1zaPR1JMWRABw4cIDg4GJtWdBoXRqFSTxsdSYg7+Pj4MGLcZHxMJvr2+QWr1crAAf2lHNKJFEMG88cffxASEoL2NvH92FDyFy9tdCQh7snb25uho8ZjMVsYPGggiYmJjBg+TMohHUgxZCC7du2iatWq+PhmoeOYUPIVLWF0JCEeyMvLi/5DR2Iymxk1cgRWq5WxY0bj5SVfj6YlKYYMYtu2bdSoUQNLtpx0HBtKnoJFjY4kxCNRStG7/2AsFjOjhw/BarUyedJEKYc0JMWQAfz222/UrFmTbHny02F0KLkKFHr4SkK4EKUUXXv2xWQyM2xQP6xWKzOmT8Pb29voaB5JisHDrVu3jjp16pCrYFE6jJ5DjrwFjI4kxBNRStH5556YzWYG9OmJ1Wpl7pzZ+PjI25izyZ+oB1u1ahUNGjQgX9GStB81h2y58xodSYhUa//DT5gtFnp364LNZmNeWChms9noWB5FdtJ5qKVLl1KvXj0KlChD+zGhUgrCo7T9riO9+g0mInwxDRo2IjEx8eEriUcmxeCBFi9eTMOGDSn6VDnajw4lW87cRkcSwuk+++ob+g8ZyYrly6hTtx63bt0yOpLHkGLwMGFhYbz33nuUKv8S342aTZbsOYyOJESaafXp5wwZNZ61a36lZq3a3Lhxw+hIHkGKwYPMnDmT5s2b89RLfnw7fCaZs2Y3OpIQae6Dlh8zctxkftu0kWrVa3Dt2jWjI7k9KQYPMWXKFD766COeffUNvhk6Hd8sWY2OJES6ea/Zh4ydPIMd27dRtWo1rly5YnQktybF4AHGjRvHJ598wvNv+NN28DQsmTIbHUmIdNeg8ftMnD6HqKhdBFepwqVLl4yO5LakGNzciBEj+PLLL6lQqQpfDpyI2dfX6EhCGKZ2vYZMnTOfA/v3ExgURHx8vNGR3JIUgxsbOHAg3333HX5BNfi83zhMZovRkYQwXLUatZkRuoi/Dh8mMCiIs2fPGh3J7UgxuKnevXvzww8/8HrVunzaezQ+JjnBR4j/BIVUY/aCJcTFxuIfEMipU6eMjuRWpBjcjNaan3/+mW7duvFWzYa07jEcb7kkgBD/o3JAEHMXLeX48WNU9g/g+PHjRkdyG1IMbkRrTefOnfnll1+oXK8JH3UdjJdcREyI+3rrncrMj1jBuXNnqewfwNGjR42O5BakGNyE1pp27doxcOBAAht9yAed+0kpCPEIXnv9TeZHrOTSpYtUquxPTEyM0ZFcnhSDG3A4HHz11VeMGDGCkCYf06xTb7kWvRCP4RW/11gYuZob16/j7x/A33//bXQklybvLi7O4XDQpk0bxo0bR40Wn/Ped93k1oZCPIEXK7zM4hVrSLRa8fcP4M8//zQ6ksuSYnBhdrudVq1aMWXKFOq2/paGX3aWUhAiFco/9wLhK9aggYCAQPbt22d0JJckxeCibDYbH3zwATNnzqTB5x2p26a9lIIQTvDMs+WJWLEWk9lMYFAQu3fvNjqSy5FicEFWq5UmTZrcvlLqN12o1eproyMJ4VHKlH2aiBVryZIlK8FVqvD7778bHcmlSDG4mMTERBo3bszixYtp2r47VZt/ZnQkITxSydJliFi5jpw5c1MlJITNW7YYHcllOKUYlFLVlVJ/K6VilFKd77G8vVLqkFJqv1JqnVKqRIpldqXU3uRHpDPyuKtbt25Rv359li5dyoc/9CH4/Y+NjiSERytWvAQRK9dSoEBBalSvzoaNG42O5BJSXQxKKW9gDFADKA80VUqVv2vYH4Cf1vpFYCEwMMWyW1rrCsmPuqnN465u3LhBnTp1WL16Na26DsS/4QdGRxIiQyhcpCjhK9ZStFhxatWsya9r1hgdyXDO+MRQEYjRWsdpra1AGFAv5QCt9Qat9c3kyR1AUSds12Ncu3aNmjVrsmHDBj7pMZS367xvdCQhMpQCBQuxaPkaSpYuQ906dVi+YoXRkQzljGIoAqS8CMmJ5Hn30xpYmWLaVykVpZTaoZSq74Q8buXKlStUq1aNrVu30qb3SF6v3tDoSEJkSPny5WfxsjU8/Ww5GjZoQETEEqMjGcYZxXCvYyj1PQcq9QHgBwxKMbu41toPaAYMV0qVuc+6bZILJMpTrrF+6dIlQkJC2LlrF5/3HYNflTpGRxIiQ8udJw8LI1fz3Asv8e67jVmwYKHRkQzhjGI4ARRLMV0U+J9r3CqlqgA/AXW11on/zddan0r+GQdsBF6+10a01hO11n5aa798+fI5Ibaxzp8/T3BwMHv37aPtgAm8HFDD6EhCCCBnrlwsWLKSl199jaZNmzBnzlyjI6U7ZxTDLqCsUqqUUsoMNAHuOLpIKfUyMIHbpXAuxfxcSilL8vO8wNvAISdkcmnnzp0jKCiIQ4cO8/WgybzwThWjIwkhUsiWPTvzwpfz+ptv06LFh0ybNt3oSOkq1cWgtU4C2gKrgcPAfK31n0qpXkqp/44yGgRkBRbcdVhqOSBKKbUP2AD011p7dDGcPn2agIAA/omO4duhUyn/hr/RkYQQ95Ala1bmLIzkHf9AWrf+mIkTJxkdKd045Q4vWusVwIq75nVL8fye/yXWWm8DXnBGBndw4sQJgoKCOHHyFO1HzKRMhYpGRxJCPEDmzJmZGbaYj5u/x2eftSHRZuXrr74yOlaakzOf08nRo0epXLkyp06fof3IWVIKQriJTJkyMT10IdVq1uabtm0ZMnSY0ZHSnBRDOoiNjcXf35/4CxfpMHoupV541ehIQojHYLFYmDwzjNr1GtCxQ3v69etvdKQ0JcWQxv7++2/8/f25fO06ncaGUrzci0ZHEkI8AbPZzIRpc2jQ+H26dPmRHj17GR0pzchd5NPQoUOHCAoKItFmp+PYMAqXfsboSEKIVPDx8WHMpOmYTCZ69uhOYmIiffv84nGXxJdiSCP79++nSpUq2FF0HBdGwZJljY4khHACb29vRoybjMlspn+/vlitVgYPGuhR5SDFkAb27NlDSEgIXiYL348JJW+xUkZHEkI4kZeXF4NHjMVsMjN0yGCsVisjRwz3mHKQYnCynTt3Uq1aNcyZs9FhzFzyFC5udCQhRBrw8vKi35ARmC0WRo8aQWJiIuPHjcXLy/2/upVicKKtW7dSo0YNsuTMTYfRc8lVUC4iK4QnU0rRs+9ATGYTo4fd/uQwZfIkvL29jY6WKlIMTrJx40Zq165NznwF6TB6LtnzFTQ6khAiHSil6NqjDxazhSED+mC1Wpk5Yzo+Pu779uq+yV3I2rVrqVu3LnkLF6P9qDlky5Pf6EhCiHSklOL7n7rf/kK6d3dsNhtz58zGZDIZHe2JSDGk0sqVK2nQoAEFi5em/ag5ZMmVx+hIQgiDtOv0IxaLhZ5dO2O1Wlkwfx5ms9noWI/N/b8lMVBkZCT169enSOmn6TAmVEpBCMGX37TnlwFDiVwSQf0GDUlISDA60mOTYnhCCxcupFGjRpR45jk6jJ5D5hy5jI4khHARn37RloHDRrNyxXJq16nLrVu3jI70WKQYnkBoaChNmjShzPMV+G7ELCxZcxgdSQjhYlq2bsOwMRNZv24tNWrW4saNG0ZHemRSDI9pxowZfPDBBzzzckW+HT4TS5ZsRkcSQrioZh9+xOgJU9n82yaqVqvOtWvXjI70SKQYHsPkyZNp1aoVz1V8m6+HTsOcKYvRkYQQLq5xk+aMmzKT33dsJ6RqVa5cuWJ0pIeSYnhEY8aM4dNPP+WltwJpO3AyJksmoyMJIdxE/UbvMXlmKHt27yYouAoXL140OtIDSTE8gmHDhtG2bVte9a/K5/3H423xNTqSEMLN1KxTn6mz53PwwH4Cg4KIj483OtJ9STE8xIABA2jfvj0Vg2vyWd8x+JgtRkcSQripqjVqMTNsMf/8/TcBgYGcOXPG6Ej3JMXwAL1796Zz5868Vb0en/QehZeP+52oIoRwLYFVqjJ7wRKOHDmCf0AgJ08Yp/qqAAAgAElEQVSeNDrS/5BiuAetNV27dqVbt25UqtOYVt2G4eUtJ4kLIZyjkn8gYYuXcfLkCSr7B3Ds2DGjI91BiuEuWmu+//57+vTpQ0D9prToMgjl5ldKFEK4njfeeod54SuIjz9HZf8Ajhw5YnSk/yPFkILWmu+++47BgwdT5d0WNP+hL8oDrq0uhHBNr73+BguWrOLy5UtUquxPTEyM0ZEAKYb/43A4+PLLLxk5ciTVm3/C+x16SSkIIdLcy6/6sXjZr9y6eZPKlf3566+/jI4kxQBgt9v59NNPGT9+PLU/+pJGX3f1mFv0CSFc3/MvVmDxijXYkpLw9w/g4MGDhubJ8MWQlJTERx99xNSpU6n/6XfU+/x7KQUhRLorV/55IlauRXl5ERAYyN69ew3LkqGLwWaz0bx5c2bPnk2jLzpR+5N2UgpCCMOUffpZIlasxWLxJTAoiKioKENyZNhisFqtvP/++8yfP5/3v/mJGh+1NTqSEEJQ+qmyRKxcR7Zs2QmuUoUdO3akewanFINSqrpS6m+lVIxSqvM9lluUUvOSl/+ulCqZYtmPyfP/VkpVc0aeh0lISKBRo0aEh4fTvEMPQpq3SY/NCiHEIylRshQRK9eRO3deQqpW5bfNm9N1+6kuBqWUNzAGqAGUB5oqpcrfNaw1cElr/RQwDBiQvG55oAnwHFAdGJv8emnm1q1b1KtXj2XLltHyx74EvtcqLTcnhBBPpGix4kSsXEvBgoWoWaMG6zdsSLdtO+MTQ0UgRmsdp7W2AmFAvbvG1ANmJD9fCASr2zvz6wFhWutErfURICb59dLE2bNnqVq1KmvWrOHjnwdRqX7ztNqUEEKkWqHCRQhfsZaixYpTu1YtZs2enS7bdcZ1HooAx1NMnwBev98YrXWSUuoKkCd5/o671i3ihEz/w+FwUKRIEex2O94mM7MH92D24B5psSmRQVlv3b5DV9mi+QxOIjyN1pqEhARafPghDrudli1bpun2nFEM9zqMRz/imEdZ9/YLKNUGaANQvHjxx8kHgJeXF/nz5+f06dPYbVbs9vtsXYhUup5gAzm6TTiRTrKitcbLx0SDho3TfHvOKIYTQLEU00WBU/cZc0Ip5QPkAC4+4roAaK0nAhMB/Pz87lkeD3Pq1CmWLF1Bwwb1wZQFU+m6KHPWJ3kpIf5Hwv5JAJT9fDqZ8+QxOI3wBFprzmycxZmNM8hboQrLFs4le7a0v3OkM75j2AWUVUqVUkqZuf1lcuRdYyKB/z77NAbWa6118vwmyUctlQLKAjudkOm+6tWpyfIVKyHpJrbYCLTVPe7BKoTIWLTWnF43hTMbZ5DvleqsDp/H62XSZzdlqotBa50EtAVWA4eB+VrrP5VSvZRSdZOHTQHyKKVigPZA5+R1/wTmA4eAVcBXWmt7ajM9TPWqwfz662qUIxFbTASOxKtpvUkhhHhkWmtOrh7P2c2hFKhYh3URobxSMne6bV/d/o+7e/Hz89POOCNwy9btBAYFY8cbU5l6eFlyOiGdyKj+25X0TNvZsitJPDHtcHBi5RjO74yg0JsNWL9oOs8Wyu6U11ZK7dZa+z1sXIY98xngnbffZPNvv+Gj9O1PDgmXjI4khMjAtMPB8WXDOb8zgqKV3mdT+AynlcLjyNDFAPDG637s2L4Fk4/X7XK4dcHoSEKIDEg77BxbMpgLu5dTPPADNi2aTNkC2QzJkuGLAeCVlysQtXM7FosJW2wEjpvxRkcSQmQg2m7n38UDuLh3NSWrfsxv88dTOp9xR0xKMSR74fnn2LPrd3x9M2GLXYLj5jmjIwkhMgBtT+Looj5cOrCOMjXasCVsNCXypv0hqQ8ixZBCuXLPsP+PXWTOkvV2Odw4Y3QkIYQHcyRZOTK/J5f/3MTTdb9ic+gIiuTKZHQsKYa7PfVUGQ7u203W7DmxxkbiuH7P8+2EECJVHDYrR8J6cOWvbZRr2I4ts4dQKIev0bEAKYZ7KlmyBIf27yZn7nxY45Ziv3bC6EhCCA/isCYQF9qVqzE7eeH979k8oz/5slmMjvV/pBjuo2jRohw+sJvceQtii1uG/eoxoyMJITyAPfEWsXO6cC1uDxWadWHTlN7kyWo2OtYdpBgeoGDBghw+sJt8BYtiO7IC+5WjRkcSQrgxe8INYmd35vq/B/Br2Z2Nk7qTK4trlQJIMTxU/vz5OXxgNwWLlsJ2dCX2y3FGRxJCuKGkW9eJmfUDN08c5o3WvVk/rgs5MpmMjnVPUgyPIE+ePPx1IIqiJctiO7oK+6VooyMJIdxI0s2rxMzsxK3T0bzzWT/Wjv6ebL6uWQogxfDIcuTIwaF9uyhZ9jls/67BfvFvoyMJIdyA7cZloqd3IOHcEQK/Gszq4e3JYnHGHQ/SjhTDY8iWLRsH/9jBU+VewnZsLUkXDhkdSQjhwmzXLhIzrT2JF04Q8u0wlg1uSyZzmt7W3imkGB5TlixZ2Be1lWdf8CPp+AaSzh80OpIQwgVZr8YTPa0d1stnqdlxJJH9PyeTyfVLAaQYnkjmzJn5Y+dmXnjlTZJObCIpfr/RkYQQLsR6+SzR09qTdP0i9TqPJfyXT7H4uEcpgBTDE/P19SVq+0ZefcOfpJObSTr3h9GRhBAuIPHSaaKntcd+8wqNu05gXveWmLzd663WvdK6GLPZzPbf1vBGpSokndpG0pnU3zxICOG+Ei6cIHpqOxyJN2nWYwqzuzRzu1IAKYZUM5lMbF6/ksrBNUk68zu207/jjnfFE0KkTkL8v0RPa49OstLil6lM6/QePl7u+RbrnqldjI+PD+tXRxJcvR72s1Eknd4h5SBEBnLr7BGip7VHaQefDpjJpHYN8fZSRsd6YlIMTuLt7c2vyxdTq9572M/tIenUVikHITKAm6djiJ7eHuXtw1eD5zDmqzp4KfctBZBicCovLy+WhofR4L0PscfvI+nkZikHITzYzZN/EzOjI94mX9oNm8vQNtVRbl4KIMXgdEopFoXNoMkHrbGfP0DS8Y1SDkJ4oBvH/yR6Rid8fLPww+h59G9VxSNKAcC1z8t2U0op5s6chMXXwozJY9Hagal4IEpJDwvhCa4f3U/snC6Ys+Wm65gwfnr/HaMjOZUUQxpRSjF90hgsFgsTxwzDhh1T8SpSDkK4uWtxfxA3tyuWnPnpPWE+HRq8bnQkp5NiSGMTRg/F12Jh5ND+2BwOTCVDUMp9zoAUQvx/V2N2ERfaDd88RRgwZT5f1/IzOlKakGJIByOG9MNisTCoX09sR+2YSlRHeUk5COFOrvy9nSPzepIpfwmGzVhIm5CXjI6UZmS/RjoZ2LcHXbv3wXHlKLajK9GOJKMjCSEe0eXDWzgyrweZC5Zm7Oxwjy4FkGJIV717dKF3v8E4rv6L7cgKtMNmdCQhxENcOriBI/N7kqXw00wOW0LLoOeNjpTmUlUMSqncSqk1Sqno5J+57jGmglJqu1LqT6XUfqXU+ymWTVdKHVFK7U1+VEhNHnfQtXMHBg4ZiePaCWxxy9F2q9GRhBD3cXHfGo4u7Eu24s8zc8ESmrzzjNGR0kVqPzF0BtZprcsC65Kn73YTaKG1fg6oDgxXSuVMsbyT1rpC8mNvKvO4hU7tv2bEmAk4bpzCFrdMykEIF3Rhz0r+DR9A9lIvMXdBBA1ef8roSOkmtcVQD5iR/HwGUP/uAVrrf7TW0cnPTwHngHyp3K7b++bLTxk/cSqOm2exxUWikxKMjiSESHZ+11KOLRlMjqf8WBi+hNp+pYyOlK5SWwwFtNanAZJ/5n/QYKVURcAMxKaY3Sd5F9MwpZQllXncymeffMTU6bNw3IyXchDCRZzbsZjjy4aT69k3CQ8PJ+TFYkZHSncPLQal1Fql1MF7POo9zoaUUoWAWUArrbUjefaPwLPAa0Bu4IcHrN9GKRWllIqKj49/nE27tFYtmjEndD464SK22CVo202jIwmRYZ3dOp+TK8eQu3wllkYsJvC5IkZHMsRDi0FrXUVr/fw9HkuAs8lv+P+98Z+712sopbIDy4GuWusdKV77tL4tEZgGVHxAjolaaz+ttV++fJ61J6rZ+41YsDAcbb2cXA43jI4kRIZzZtMcTv06gTwvBLJiyULefqag0ZEMk9pdSZFAy+TnLYEldw9QSpmBcGCm1nrBXcv+KxXF7e8nDqYyj9tq1KAOkZHLwHYdW2wE2nrd6EhCZAhaa06vn87p9VPJ93JVVi9ZwOtPPXCvuMdLbTH0B0KUUtFASPI0Sik/pdTk5DHvAZWBj+5xWOocpdQB4ACQF/gllXncWu2a1VixciUk3Uouh6tGRxLCo2mtObV2Mmc2zSK/X03WRoTxaqk8RscyXKouiaG1vgAE32N+FPBJ8vPZwOz7rB+Umu17omohQaxZ8ytVq1bDGhOBqUw9vCw5jI4lhMfRWnNy1Tjidyyi4Ot1Wb94JuUKy+8ayJnPLikooDKbNm7AGzu22AgciZeNjiSER9EOByeWjyR+xyIKv9WI35bMllJIQYrBRb391hts3fIbPl5giwnHkXDR6EhCeATtcHB86TDO74qkqH8TNkdMp2yBbEbHcilSDC6s4muvsnPHFkw+3thiInDcumB0JCHcmnbYObZkEBf2rKBEcAu2LJxM6XxZjY7lcqQYXFyFl14iaud2LBbz7d1KNz3nHA4h0pO22/l3cX8u7v2V0tVas3XBeErkzWJ0LJckxeAGXnj+Of6I2kmmTJmxxS7BcfOs0ZGEcCvansTRhb25dGA9ZWt9zpZ5oymSK5PRsVyWFIObePbZpzmwN4rMWbNhi43EceO00ZGEcAuOJCtH5vXk8qHNPFvva7aGDqdQDl+jY7k0KQY3Urp0Kf7ct5tsOXJhjV2K4/opoyMJ4dIctkSOhHXnyt/beK5xB7bMHky+bBnqkmxPRIrBzZQoUZxD+3eTM3c+rHFLsV87bnQkIVySw5pA3NyuXI3ZxUtNO7N5el/yZDUbHcstSDG4oSJFinD4wG7y5CuELW459qvHjI4khEuxJ94idk4Xrh3Zy6sfdmXTlF7kyiKl8KikGNxUwYIFOXxgN/kLFcN2ZAX2K0eMjiSES7An3CB21g9cP3aA11v1YMOEn8mRyWR0LLcixeDG8uXLx+EDuylUrDS2o6uwX459+EpCeLCkW9eImfk9N0/+xTuf9mHd2B/J5iul8LikGNxc7ty5Obx/F8VKPo3t6Grsl6KNjiSEIZJuXiFmRkdunYnF/4sB/DqyE1ksqbocXIYlxeABcuTIwZ/7dlLq6eew/bsG+8W/jY4kRLqyXb9E9PQOJMT/S5WvB7Ni2HdkMnsbHcttSTF4iGzZsnFgzw7Kln8J27G1JF04ZHQkIdKF7doFYqa3x3rxFDXaj2DpoK/IZJJSSA0pBg+SJUsW9kVto/xLFUk6voGk8xn2vkcig7BeiSd6WjusV85R5/vRRPT9DIuPlEJqSTF4mEyZMrHn9994ye9tkk5sIil+n9GRhEgT1stniZ7WjqTrl2jcZTwLen6MyVve0pxB/hQ9kMViYefW9fi9GUDSyS0kndtjdCQhnCrx4in+mfod9lvXaNp9EnN+/lBKwYnkT9JDmc1mtm36lbf8q5J0ajtJZ6KMjiSEUyScP070tHZoawItek9l+g9N8fGStzJnkj9ND2Yymfht3Qr8q9Qi6czv2E7/jtba6FhCPLGE+H+JntYebU/ik/4zmNyhMd5eyuhYHkeKwcN5e3uzbtUSqtZsgP1sFEmnt0s5CLd062wc0dPaoxR8NWgWY7+uh5eSUkgLUgwZgLe3NyuXLqR2/fexn/uDpJNbpByEW7l5Opro6R3w8vbhu6FzGfZ5LZSUQpqRYsggvLy8iFwcSsP3W2A/v5+kE79JOQi3cOPEX8RM74i3ORPfjwpjQOuqUgppTIohA1FKsTB0Ok1bfIr9wkGSjm+UchAu7fqxP4mZ2QmfTNn4eewCercIllJIB3IhkQxGKcWc6RPwtViYNmk0WtsxFQ9CKfk/gnAt14/uJ3bOj5iz5aXXhPl0avSm0ZEyDCmGDEgpxdSJozBbzEwYPRSbdmAqEYxScsaocA3X4vYQO7crvjkL0n/KAr6p85rRkTIUKYYMbPyoIfhaLIwY0g+btmMqURXlJeUgjHU1eidxYd3JlKcoQ2cs5LNqLxsdKcOR/QcZ3PDBffm+Sw8cV+KwHV2FdtiNjiQysCt/byMutBuZ8pVg7JwlUgoGkWIQDOjTnW49++G4ehTbkRVoR5LRkUQGdPnQb8SF9SBzwTJMnreElsHPGx0pw0pVMSilciul1iilopN/5rrPOLtSam/yIzLF/FJKqd+T15+nlJKbshqkZ7fO9BkwFMe1Y9iOLEfbbUZHEhnIpQPrObKgN1mLPsvMBUtoWqmc0ZEytNR+YugMrNNalwXWJU/fyy2tdYXkR90U8wcAw5LXvwS0TmUekQpdvm/HkOFjcFw7ie3IMrTdanQkkQFc2PsrRxf1I1vx55m7MJKGbz5tdKQML7XFUA+Ykfx8BlD/UVdUtw9GDgIWPsn6Im20//ZLRo6diOPGaWxxS9H2RKMjCQ92YfcKjkUMJHvpCiwIj6TOa6WNjiRIfTEU0FqfBkj+mf8+43yVUlFKqR1Kqf/e/PMAl7XW/+3QPgEUSWUe4QRff/EJEyZNw3HzHLbYSHRSgtGRhAeK37mEY5FDyFn2NSIillCtQgmjI4lkDz1cVSm1Fih4j0U/PcZ2imutTymlSgPrlVIHgKv3GHff03CVUm2ANgDFixd/jE2LJ9GmdUssFgutWnyALS4SU+k6KJ9MRscSHuLc9kWcXDWWXM++RWT4Qt55tpDRkUQKDy0GrXWV+y1TSp1VShXSWp9WShUCzt3nNU4l/4xTSm0EXgYWATmVUj7JnxqKAqcekGMiMBHAz89PruOQDlp+0ASLxUyzJu9hi12CqXRdlCmz0bGEmzu7JYxTayaR+7nKLA+fzxtlCxgdSdwltbuSIoGWyc9bAkvuHqCUyqWUsiQ/zwu8DRzSty/SswFo/KD1hbGavNuQRYsj0Nar2GIj0LYbRkcSbuzMxlmcWjOJvC8G8evSxVIKLiq1xdAfCFFKRQMhydMopfyUUpOTx5QDopRS+7hdBP211oeSl/0AtFdKxXD7O4cpqcwj0kCDerVZunQp2G5gi4lAW68bHUm4Ga01p9ZN4/SG6eR7uRrrli7k1VJ5jI4l7iNVl8TQWl8Agu8xPwr4JPn5NuCF+6wfB1RMTQaRPmrVqMaqVauoUbMGttgITGXqoszZjY4l3IDWmlNrJnJu63wKvlaL9RFzKFc4h9GxxAPImc/ikYVUCWTdunUohxVrTASOxCtGRxIuTmvNyVVjObd1PoXeqMemyLlSCm5AikE8Fv9Kb/Pbpo14Kzu2mAgcCZeMjiRclHY4OLF8JPE7FlPknXfZEjmbpwvKp0x3IMUgHttbb1Zk+9bN+HiDLTYCR8JFoyMJF6Mddo4vHcr5XZEUD2zG1vBplM6X1ehY4hFJMYgn4vfqK+zcsQWzyef2J4db542OJFyEttv5N2IQF/aspGSVlmxdOIkSebMYHUs8BikG8cQqvPQSUTu3Y7FYsMUuwXEz3uhIwmDansTRxX25tG8NT1X/hG0Lx1M0t5z74m6kGESqPP9cefbt2UmmTJlvl8ONs0ZHEgZxJNk4suAXLh/cyDN1vmTb/NEUyuFrdCzxBKQYRKo9/XRZDuyNIku27FjjInFcP210JJHOHElWjszvyZXDmynf4Fu2zh1GvmwWo2OJJyTFIJyidOlS/Lkviuw5cmONW4rj+kmjI4l04rAlEhfajat/b+fF9zuxZdZA8mSVW6u4MykG4TTFixfn0P4ocuXJjzVuGfZrx42OJNKY3XqL2Dk/cS02ipebd+G3aX3IlUVKwd1JMQinKlKkCIcP7CZP/sLY4pZjv/qv0ZFEGrEn3iR29o9cP7qPii27sWlyD3JkMhkdSziBFINwugIFCvDXgd3kL1wc25GV2K8cMTqScDJ7wnViZ/3AjeN/8lbrXqwf35VsvlIKnkKKQaSJvHnzcnh/FIWLl8Z2dBX2y7FGRxJOknTrGjEzv+fmqX/w/6wfa8d0JoslVZddEy5GikGkmdy5c3N4fxTFSz2D7ehq7Jf+MTqSSKWkG1eImd6RW2fiCP5qECtHdCCT2dvoWMLJpBhEmsqePTt/7ttJ6WdewPbvWuwX/zI6knhCtusXiZ7egYTzx6jWbijLhnxNJpOUgieSYhBpLmvWrBzYs52nn3sZ27F1JF049PCVhEuxXbtA9LQOWC+dok7HkUT2/xKLj5SCp5JiEOkic+bM7N21hecqVCTp+AaS4g8YHUk8IuuVeKKntcN2NZ6GP45j4S+fYvKWtw5PJn+7It1kypSJ3Tt+o8Jr75B08jeSzu01OpJ4iMRLZ4ie1o6k65dp0m0iod1bSilkAPI3LNKVxWLh9y3reO2tQJJObSXp7B6jI4n7SLx4iuhp7bDfusYHvSYz88fm+HjJW0ZGIH/LIt2ZzWa2bfqVtwOqkXR6O0lndhkdSdwl4fxxoqd+h7Yl0LrfdKZ2eh9vL2V0LJFOpBiEIXx8fNi0djmBIbVJOrMT2+kdaK2NjiWAW+eOEj2tHTgcfDFwFuO/bYiXklLISKQYhGG8vb1Zu2oJ1Wo1xH52N0mnt0s5GOzWmVhipndAKS++GTqHEV/WQUkpZDhSDMJQXl5erIhcQJ2GTbCf+4Okk1ukHAxy89Q/RE/vgJePie9HhjHo0+pSChmUFIMwnJeXF0sWzqVx05bYz+8n6cQmKYd0duPEYWJmdMTHkpmuYxfwy0dVpBQyMCkG4RKUUsyfM43mLdtgv/AnScc3oLXD6FgZwvVjB4mZ+T0+mXPQa+JCfm7mb3QkYTC58pVwGUopZk0bj8ViYerEUWhtx1Q8GKXk/y9p5dqRvcTN/Qlz9nz0m7KA7+q+bnQk4QKkGIRLUUoxZcJILBYL40YNxqYdmEpUQSm5/IKzXY3dTVzoz/jmKsjQ6Yv4vMarRkcSLkKKQbiksSMH4etrYdigPsnlUBXlJeXgLFf++Z0j87qTKW8xRs8Kp1WVF42OJFyIfEYXLmvowF/o3LUXjitx2I6uQjuSjI7kES7/tZUjYd3InL8kE8MipRTE/0hVMSilciul1iilopN/5rrHmECl1N4UjwSlVP3kZdOVUkdSLKuQmjzC8/Tr/TM9evfHcfUotiMrpBxS6dKfmzgyryeZCz3FjAVLae7/nNGRhAtK7SeGzsA6rXVZYF3y9B201hu01hW01hWAIOAm8GuKIZ3+W661lquqif/RvesP9B04DMe149iOLEfbbUZHcksX96/j6MJfyFasHHMXLaPRW88YHUm4qNQWQz1gRvLzGUD9h4xvDKzUWt9M5XZFBvNjp+8YOmIsjmsnsR1ZhrZbjY7kVi7sXc2/i/uRvcSLzA9fSt2KZYyOJFxYaouhgNb6NEDyz/wPGd8ECL1rXh+l1H6l1DCllCWVeYQHa/fNF4weNwnHjdPY4pai7YlGR3IL56OWcyxiEDnKvEL4kkiqv1zS6EjCxT20GJRSa5VSB+/xqPc4G1JKFQJeAFanmP0j8CzwGpAb+OEB67dRSkUppaLi4+MfZ9PCg3z1eWsmTZ2J4+Y5bLGR6KQEoyO5tPjfIzi+dCg5y1Zk6dJIgl4oZnQk4QYeeriq1rrK/ZYppc4qpQpprU8nv/Gfe8BLvQeEa63/bwfxf582gESl1DSg4wNyTAQmAvj5+cn1EjKwTz76AIvZTMsPmmGLXYKpTF2UTyajY7mcc9sWcnL1OHKXe5tlEQt58+mCRkcSbiK1u5IigZbJz1sCSx4wtil37UZKLhPU7Yuy1AcOpjKPyCA+bPYeofMXoBMvY4tdgrbJ11YpndkcysnV48jzvD+rl0VIKYjHktpi6A+EKKWigZDkaZRSfkqpyf8NUkqVBIoBm+5af45S6gBwAMgL/JLKPCIDeb9xAxaFR6CtV7HFRqBtN4yOZDitNac3zuT02snkfakK65Ytxq90XqNjCTeTqjOftdYXgOB7zI8CPkkxfRQoco9xQanZvhAN6tZi2fLl1KldG1tMOKYy9VDmbEbHMoTWmtPrpnJ281zyv1KNDZFhlC+S0+hYwg3Jmc/C7dWsFsLqVatRjgRssRE4Eq8aHSndaa059etEzm6eS8GKtdm8fL6UgnhiUgzCI1QJDmDdunUobUsuhytGR0o3WmtOrhzDuW3zKfxmA7YsncvTBbMbHUu4MSkG4TH8K73N5k2b8FF2bDHhOBIuGR0pzWmHg+PLhhP/ezjFKr/HtshZlMmfMXelCeeRYhAe5c03XmP7ti2YvNXtTw63LhgdKc1oh51jkUO4ELWMEkHN2RY+jRJ5sxgdS3gAKQbhcV595WV2/b4Ns8kHW+wSHLfOGx3J6bTdzr/hA7j4xypKV23FtkWTKJo7s9GxhIeQYhAe6cUXX2DPrt/x9bVgi4nAcfNB5166F21P4uiivlzav46yNduwY+E4CueUE/yE80gxCI9Vvvyz7Nuzi0xZsmKLjcRx44zRkVLNkWTjyILeXP5zI+XqtWX7vFHkyyaXGBPOJcUgPFrZsk9xcG8UWbPlwBq3FMf1U0ZHemIOm5Uj87pz5fAWnm/cjq1zhpAnq9noWMIDSTEIj1eqVEn+3B9Fjpx5sMYtw37tpNGRHpvDmkBc6M9c/ed3KjT5ni0zB5Ari5SCSBtSDCJDKFasGIcP7CZXnvzYjizDfu240ZEemd16i9i5P3Etbjd+H3blt2m/kCOTyehYwoNJMYgMo1ChQvx1cA958xfGFrcc+9WjRkd6KHviTWJn/8j1o/t546PubJzUnWy+UgoibUkxiAwlf/78HD6wmwJFSmA7shL7lTijI91X0q3rxMz8nhvH/197dx8dVX3ncfz9CQmDSK0B3K4oImsBmjoAAAu1SURBVHSplmN71Gatre22oCuoZwW7tMUeztJqd0uttRVp0Uq31Za2aF20xecHiNIVEZeKiqUoclxbocRTFJADGYiW8BiUBx9qzCTf/jG/9NwJM5lJ5gnI93XOnMz87u/e+8nv3sx37p07k/V89j9/yvK7pnN0LK+vN3MuJ14YXI8zcOBANrxSxwlD/omW15bSui9e7kgHSbx7gPiD3+OvO+oZdcVNLJ39fY7q3avcsVwP4YXB9UjV1dW8+vJqhgw7lZbXfk/r3k3ljvR3Le/sI147lfd2NXD+Vb9kyazvclSVFwVXOl4YXI91zDHHsG7NKj586sdpeX0ZiTc2lDsSLW+/SXzuNby3ZysXTb2NJ27+NrFKLwqutLwwuB6tX79+vPLSHzn1tE+Q2LqcxJ71ZcvScmAP9XOu4f29O/nCtNn834xvUNXL/0Rd6fle53q8vn378ufVL3DaGWeTaFxBomltyTO8v3839XOm0HKgiS9Pv5P5N17uRcGVje95zgF9+vSh7sUVnHHWZ0lse57E7jUlW3fz3h3UP3A1iXf2MfGG+3ho+iQqK/xP05WP733OBbFYjFUvPMsnzzmXxPY/kNj1UtHX2fzGNurnTKG1+R0umzGHOdMupVeFir5e5zrjhcG5iKqqKl5Y8Ts+M3IMiR0rSez8E2ZWlHW91/QXNs25GmtpZvLMWu6eMp4KeVFw5eeFwbkOKisrWbHsSUaNvpjEztUkdq4qeHH4664G6udOQdbGVbfM49dXjkNeFNwhwguDc2n06tWLZUsWccG/jad110sktv+xYMXh3Z2bic+9BqmCqbc9zC+/cZEXBXdI8cLgXAYVFRU89fgCxo7/Cq1Na0hs+/+8i8O72zYSn3sNFVUxrr9jAT+7bLQXBXfI8cLgXCcksWjBPL70la/RumcticYV3S4O72x9lfra71HZ52huuHshP5o4qsBpnSsM/0Yu57KQxPx59xOLxXhozl1gbVQOHomU++uqt19fy+Z511HVr5qf3/coV1/y6SImdi4/Xhicy4Ekau+/g1ifGPfdeRtmbVSddG5OxeGthj+z5TfT6f3B47il9jGuuPCfS5DYue7zwuBcjiRx7x23EovFuP3Wm2ixVqqG/CtS5u8yOhCvY8vDP6RP/0HMfmgRl51/egkTO9c9Xhic66LZs2YS692b/7npp7RYG1VDRqOKg4vD/k0raZj/Y4467iTu/t/fMnHkaWVI61zX5fXms6QvSlovqU1STSf9xkjaKCku6dpI+1BJqyTVS3pEkv8TW3dYuGXmT/jBf/+Etv0NtLz2NNaWSJm+b8MLNMz/EX0/NJTahU94UXCHlXyvSloHfAF4PlMHJY+zbwcuAEYAl0oaESbPBGaZ2XBgL3B5nnmcK5kZN0znxhk303bgdVoalgDJq5Xeqn+RhgU3cvSgj/Cbx55k/DkfLW9Q57oor8JgZhvMbGOWbmcBcTPbYmbvA/OBsUpevD0KWBj61QLj8snjXKn98AdT+cXNt9H21lZoS4C1sv13t/KBwSN49LdPMfbs4eWO6FyXleJzDCcAWyOPG0PbAGCfmSU6tDt3WJk29Spu/fWdgIG10nfQKSxa/CRjzjy53NGc65ashUHSM5LWpbmNzXEd6T7WaZ20Z8rxX5LqJNU1NTXluGrnSuM7V06m/4ABgLj93lrO/fhJ5Y7kXLdlvSrJzM7Lcx2NwODI4xOB7cAe4FhJleGoob09U457gHsAampqivN1l87l4Y09e2hra6PC/5eCO8yVYg9eDQwPVyD1BiYAiy35vQLPAeNDv0nA4yXI41zReFFwR4J8L1e9RFIj8CngKUlLQ/sgSUsAwtHAlcBSYAOwwMza/7HuNGCKpDjJ9xzuzyePc865/KlY/4SkmGpqaqyurq7cMZxz7rAi6SUzy/iZs3Z+3Ouccy6FFwbnnHMpvDA455xL4YXBOedcCi8MzjnnUnhhcM45l8ILg3POuRReGJxzzqXwwuCccy6FFwbnnHMpDsuvxJDUBLzezdkHkvxm10ON5+oaz9U1nqtrjtRcQ8zsuGydDsvCkA9Jdbl8V0ipea6u8Vxd47m6pqfn8lNJzjnnUnhhcM45l6InFoZ7yh0gA8/VNZ6razxX1/ToXD3uPQbnnHOd64lHDM455zpxRBYGSV+UtF5Sm6SM7+BLGiNpo6S4pGsj7UMlrZJUL+mR8L+qC5Grv6RlYbnLJFWn6TNS0prI7T1J48K0uZIaItNOL1Wu0K81su7FkfZyjtfpkl4M2/sVSV+OTCvoeGXaXyLTY+H3j4fxODky7brQvlHS6HxydCPXFEmvhvF5VtKQyLS027REub4qqSmy/q9Hpk0K271e0qQS55oVybRJ0r7ItKKMl6QHJO2WtC7DdEn6Vcj8iqQzI9MKP1ZmdsTdgI8CpwArgJoMfXoBm4FhQG/gZWBEmLYAmBDu3wV8s0C5bgKuDfevBWZm6d8feBPoGx7PBcYXYbxyygW8naG9bOMFfAQYHu4PAnYAxxZ6vDrbXyJ9rgDuCvcnAI+E+yNC/xgwNCynVwlzjYzsQ99sz9XZNi1Rrq8Cs9PM2x/YEn5Wh/vVpcrVof+3gQdKMF7/ApwJrMsw/ULgaUDA2cCqYo7VEXnEYGYbzGxjlm5nAXEz22Jm7wPzgbGSBIwCFoZ+tcC4AkUbG5aX63LHA0+b2bsFWn8mXc31d+UeLzPbZGb14f52YDeQ9QM83ZB2f+kk70Lg3DA+Y4H5ZtZsZg1APCyvJLnM7LnIPrQSOLFA684rVydGA8vM7E0z2wssA8aUKdelwMMFWndGZvY8yReBmYwFHrSklcCxko6nSGN1RBaGHJ0AbI08bgxtA4B9Zpbo0F4IHzKzHQDh5z9k6T+Bg3fKGeFQcpakWIlz9ZFUJ2ll++ktDqHxknQWyVeBmyPNhRqvTPtL2j5hPPaTHJ9c5i1mrqjLSb7ybJdum5Yy17+H7bNQ0uAuzlvMXIRTbkOB5ZHmYo1XNplyF2WsKvNdQLlIegb4xzSTrjezx3NZRJo266Q971y5LiMs53jgY8DSSPN1wE6ST373ANOAG0uY6yQz2y5pGLBc0lrgQJp+5Rqvh4BJZtYWmrs9XulWkaat4+9ZlH0qi5yXLWkiUAN8LtJ80DY1s83p5i9CrieAh82sWdJkkkdbo3Kct5i52k0AFppZa6StWOOVTUn3rcO2MJjZeXkuohEYHHl8IrCd5PeQHCupMrzqa2/PO5ekXZKON7Md4YlsdyeL+hKwyMxaIsveEe42S5oDTC1lrnCqBjPbImkFcAbwGGUeL0nHAE8B08Nhdvuyuz1eaWTaX9L1aZRUCXyQ5OmBXOYtZi4knUey2H7OzJrb2zNs00I80WXNZWZvRB7eC8yMzPv5DvOuKECmnHJFTAC+FW0o4nhlkyl3UcaqJ59KWg0MV/KKmt4kd4LFlnxH5zmS5/cBJgG5HIHkYnFYXi7LPejcZnhybD+vPw5IewVDMXJJqm4/FSNpIHAO8Gq5xytsu0Ukz78+2mFaIccr7f7SSd7xwPIwPouBCUpetTQUGA78KY8sXcol6QzgbuBiM9sdaU+7TUuY6/jIw4uBDeH+UuD8kK8aOJ/UI+ei5grZTiH5Zu6LkbZijlc2i4H/CFcnnQ3sDy98ijNWxXiHvdw34BKSlbQZ2AUsDe2DgCWRfhcCm0hW/Osj7cNI/uHGgUeBWIFyDQCeBerDz/6hvQa4L9LvZGAbUNFh/uXAWpJPcPOAfqXKBXw6rPvl8PPyQ2G8gIlAC7Amcju9GOOVbn8heWrq4nC/T/j942E8hkXmvT7MtxG4oMD7e7Zcz4S/g/bxWZxtm5Yo18+B9WH9zwGnRua9LIxjHPhaKXOFxz8GftFhvqKNF8kXgTvCvtxI8r2gycDkMF3A7SHzWiJXWxZjrPyTz84551L05FNJzjnn0vDC4JxzLoUXBueccym8MDjnnEvhhcE551wKLwzOOedSeGFwzjmXwguDc865FH8DFAjW971FugQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "render(octahedron, color_map=matplotlib.cm.get_cmap('Blues'), lines=black)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def split(face):\n",
    "    midpoints = [unit(add(face[i], face[(i+1)%len(face)])) for i in range(0,len(face))]\n",
    "    triangles = [(face[i], midpoints[i], midpoints[(i-1)%len(face)]) for i in range(0,len(face))]\n",
    "    return [midpoints] + triangles\n",
    "\n",
    "def rec_split(faces, depth=0):\n",
    "    if depth == 0:\n",
    "        return faces\n",
    "    else:\n",
    "        return rec_split([new_face for face in faces for new_face in split(face)], depth-1)\n",
    "\n",
    "# NICE SPHERE!\n",
    "def sphere_approx(n):\n",
    "    return rec_split(octahedron,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "render(sphere_approx(3), lines='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mini project:** Find pairs of vectors defining each of the 12 edges of the octahedron, and draw all of the edges in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "top = (0,0,1)\n",
    "bottom = (0,0,-1)\n",
    "xy_plane = [(1,0,0),(0,1,0),(-1,0,0),(0,-1,0)]\n",
    "edges = [Segment3D(top,p) for p in xy_plane] +\\\n",
    "            [Segment3D(bottom, p) for p in xy_plane] +\\\n",
    "            [Segment3D(xy_plane[i],xy_plane[(i+1)%4]) for i in range(0,4)] \n",
    "draw3d(*edges)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
