{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://github.com/orlandpm/Math-for-Programmers/tree/master/Chapter%2002"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: matplotlib in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (3.3.3)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.3 in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from matplotlib) (2.4.7)\n",
      "Requirement already satisfied: cycler>=0.10 in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from matplotlib) (2.8.1)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from matplotlib) (1.3.1)\n",
      "Requirement already satisfied: numpy>=1.15 in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from matplotlib) (1.19.4)\n",
      "Requirement already satisfied: pillow>=6.2.0 in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from matplotlib) (8.0.1)\n",
      "Requirement already satisfied: six in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from cycler>=0.10->matplotlib) (1.15.0)\n",
      "Requirement already satisfied: six in /home/yingshaoxo/miniconda3/envs/cling/lib/python3.9/site-packages (from cycler>=0.10->matplotlib) (1.15.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Three type of drawing\n",
    "\n",
    "Point, Segment(line), Polygon\n",
    "\n",
    "That's also how you work with svg if you want to implement a free-drawing whiteboard."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from vector_drawing import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": [
    "draw(Segment((0, 0), (5, 5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x445.5 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vectors = []\n",
    "for i in range(16):\n",
    "    v = i % 4\n",
    "    if  v== 0:\n",
    "        vectors.append((i, i))\n",
    "    elif v == 1: \n",
    "        vectors.append((i, -i))\n",
    "    elif v == 2: \n",
    "        vectors.append((-i, -i))\n",
    "    elif v == 3: \n",
    "        vectors.append((-i, i))\n",
    "draw(Points(*vectors))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x445.5 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vectors = []\n",
    "for i in range(16):\n",
    "    v = i % 4\n",
    "    if  v== 0:\n",
    "        vectors.append((i, i))\n",
    "    elif v == 1: \n",
    "        vectors.append((i, -i))\n",
    "    elif v == 2: \n",
    "        vectors.append((-i, -i))\n",
    "    elif v == 3: \n",
    "        vectors.append((-i, i))\n",
    "draw(Polygon(*vectors))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
      "[100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100]\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": [
    "x = [-11 + i for i in range(1, 10 - (-10) + 2)]\n",
    "print(x)\n",
    "y = list(map(lambda x: x ** 2, x))\n",
    "print(y)\n",
    "\n",
    "draw(Points(*zip(x, y)), nice_aspect_ratio=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2D vector moving"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The secret of moving for a 2d vector graph is to add a vector to all of its vectors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "dino_vectors = [ (6, 4), (3, 1), (1, 2), (-1, 5), (-2, 5), (-3, 4), (-4, 4), (-5, 3), (-5, 2), (-2, 2), (-5, 1), (-4, 0), (-2, 1), (-1, 0), (0, -3), (-1, -4), (1, -4), (2, -3), (1, -2), (3, -1), (5, 1), ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "def add(v1, v2):\n",
    "    return (v1[0] + v2[0], v1[1] + v2[1])\n",
    "\n",
    "dino_vectors2 = [add((-1.5,-2.5), v) for v in dino_vectors]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x403.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Points(*dino_vectors, color=blue),\n",
    "    Polygon(*dino_vectors, color=blue),\n",
    "    Points(*dino_vectors2, color=red),\n",
    "    Polygon(*dino_vectors2, color=red),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get vector length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import sqrt\n",
    "\n",
    "def length(v):\n",
    "    return sqrt(v[0] ** 2 + v[1] ** 2)\n",
    "\n",
    "length((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.linalg.norm([3,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pythagorean theorem:\n",
    "\n",
    "$c = \\sqrt{x^2 + y^2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiplying vector by numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The operation of multiplying a vector by a number is called `scalar multiplication`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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": [
    "a = np.array([(0, 0), (5, 5)])\n",
    "b = a * 0.5\n",
    "draw(\n",
    "    Segment(*a.tolist()), \n",
    "    Segment(*b.tolist(), color=\"red\")\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vector subtraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the number line, there are only two directions from zero: positive and negative. \n",
    "\n",
    "In the plane, there are many directions (infinitely many, in fact), so we can’t say that one of v and -v is positive while the other is negative. What we can say is that for any vector v, the opposite vector -v will have the same length, but it will point in the opposite direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0],\n",
       "       [-5, -5]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([(0, 0), (5, 5)])\n",
    "b = -a\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([4,4])\n",
    "b = np.array([1,1])\n",
    "a - b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2.8\n",
    "\n",
    "Write a function translate(translation, vectors) that takes a translation vector and a list of input vectors, and returns a list of the input vectors all translated by the translation vector. \n",
    "\n",
    "For instance, translate ((1,1), [(0,0), (0,1,), (–3,–3)]) should return [(1,1),(1,2),(–2, –2)] .\n",
    "\n",
    "Solution:\n",
    "```python\n",
    "def translate(translation, vectors):\n",
    "    return [translation + v for v in vectors]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you know why the position change in Unity is called `translate`.\n",
    "\n",
    "Because all those modifacation was based on vectors.\n",
    "\n",
    "```c#\n",
    "// Move the object upward in world space 1 unit/second.\n",
    "transform.Translate(Vector3.up * Time.deltaTime, Space.World);\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2.11—Mini Project \n",
    "\n",
    "Write a Python function using vector addition to show 100 simultaneous and non-overlapping copies of the dinosaur. \n",
    "\n",
    "This shows the power of computer graphics; imagine how tedious it would be to specify all 2,100 coordinate pairs by hand!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "dino_vectors = [ (6, 4), (3, 1), (1, 2), (-1, 5), (-2, 5), (-3, 4), (-4, 4), (-5, 3), (-5, 2), (-2, 2), (-5, 1), (-4, 0), (-2, 1), (-1, 0), (0, -3), (-1, -4), (1, -4), (2, -3), (1, -2), (3, -1), (5, 1), ]\n",
    "dinosaur = np.array(dino_vectors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x365.538 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    Points(*dinosaur.tolist(), color=red),\n",
    "    Polygon(*dinosaur.tolist(), color=red),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "side = np.max(dinosaur) - np.min(dinosaur) + 4\n",
    "side"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "dinosaurs = []\n",
    "c = 0\n",
    "r = 0\n",
    "for _ in range(100):\n",
    "    new = dinosaur.copy()\n",
    "    if c == 10:\n",
    "        r += 1\n",
    "        c = 0\n",
    "    new = new + np.array([c*side, r * side])\n",
    "    dinosaurs += [\n",
    "        Polygon(*new.tolist(), color=red),\n",
    "    ]\n",
    "    c += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x426.667 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw(\n",
    "    *dinosaurs,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
