padawan.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# JEDI 2018 - Atelier 3B\n",
    "> Pré-requis :\n",
    "- quelques (restes de) notions d'algèbre linéaire ;\n",
    "- quelques (restes de) notions de géométrie dans l'espace ;\n",
    "- savoir écrire et lire des fonctions en Python.\n",
    "\n",
    "> Objectifs :\n",
    "- découvrir la programmation orientée objet ;\n",
    "- lire et enrichir le code source d'une bibliothèque écrite par d'autres ;\n",
    "- découvrir la synthèse d'images par l'algorithme de lancer de rayon ;\n",
    "- découvrir la géométrie de construction de solides ;\n",
    "- manipuler des arbres comme structure de données représentant des combinaisons booléennes d'objets solides simples ;\n",
    "- écrire quelques classes et méthodes et observer le découpage d'un gros projet en plusieurs classes simples grâce au principe d'encapsulation ;\n",
    "- se confronter aux problèmes de précision et de stabilité du calcul en nombres flottants.\n",
    "\n",
    "> Extensions possibles (non traitées ici) :\n",
    "- améliorer la mise en œuvre du lancer de rayon en évitant les calculs d'intersection inutiles par l'emploi de structures de données appropriées pour décrire la scène ;\n",
    "- enrichir le modèle en ajoutant la gestion de la réfraction ;\n",
    "- améliorer le réalisme du rendu en gérant les ombres douces et la profondeur de champ ;\n",
    "- enrichir les matériaux en ajoutant la gestion des textures.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "# Initiation à la programmation orientée objet en Python 3\n",
    "\n",
    "L'objectif de cet atelier de travaux pratique est de vous initier à la programmation orientée objet en Python en mettant en pratique les éléments du langage présentés lors de l'atelier 3A. Pour cela, nous allons étudier et enrichir le code source d'un projet libre de moteur de lancer de rayon appelé *pyRT* (prononcer *pirate* avec un accent anglais)\n",
    "[![pyRT](img/logo.png)](https://github.com/martinchristen/pyRT)\n",
    "\n",
    "Pour paraphraser ses auteurs :\n",
    "\n",
    "> PyRT est un générateur d'images/moteur de lancer de rayon pour Python 3.5. Ce projet est développé avec les objectifs suivants :\n",
    "* ajouter les graphismes 2D aux carnets jupyter\n",
    "* ajouter le lancer de rayon aux carnets jupyter\n",
    "* enseigner le lancer de rayon\n",
    "* (...)\n",
    ">\n",
    "> pyRT est en cours de développement. Tout est encore en version (pré-)alpha !\n",
    ">\n",
    "> pyRT **n'a aucune autre dépendance**, mais il est recommandé d'installer les modules suivants: pillow, numpy, jupyter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. À la découverte de pyRT\n",
    "\n",
    "Le [code source](/tree/pyrt/) de la dernière version de *pyRT* est fourni avec l'énoncé. Il est constitué d'environ 3000 lignes de Python orientée objet. Il n'est pas question de tout lire mais plutôt de s'y référer lorsque le texte vous y invite. Une partie non négligeable de l'atelier consiste à s'aproprier le fonctionnement de *pyRT*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Des vecteurs, des matrices et des images\n",
    "\n",
    "Le module `pyrt.math` et ses sous-modules, définis dans le répertoire [pyrt/math](/tree/pyrt/math/), proposent toute sorte de classes et de fonctions pour manipuler des vecteurs de 2 à 4 nombres (`Vec2`, `Vec3`, `Vec4`) pour représenter des points et des vecteurs de l'espace et des matrices 4x4 (`Mat4`) pour représenter les transformations affines.\n",
    "\n",
    "Prenez le temps de parcourir la définition de `Vec3` dans [pyrt/math/vec3.py](/edit/pyrt/math/vec3.py) et de comprendre comment celle-ci est utilisée dans [pyrt/math/vecops.py](/edit/pyrt/math/vecops.py) pour définir des fonctions comme `dot3`, `normalize3`, `min3` ou encore `reflect3`.\n",
    "\n",
    "Voici à titre d'exemple une fonction qui teste si un point $P$ de l'espace 3D appartient au plan orthogonal au vecteur $\\overrightarrow{V}$ et qui passe par le point $O$. Cette fonction se contente de tester si \n",
    "$(P-O)\\cdot\\overrightarrow{V} = 0$. Pour le test à zéro, il convient de prendre en compte les problèmes d'arrondis. La bibliothèque `pyrt.math` fournit la constante `G_EPSILON`.\n",
    "\n",
    "Le module `pyrt.utils.pretty` défini dans [pyrt/utils/pretty.py](/edit/pyrt/utils/pretty.py) permet un affichage plus agréable des vecteurs est des matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "Test d'apartenance au plan passant par $O=\\begin{pmatrix}0.0\\\\0.0\\\\1.0\\end{pmatrix}$ orthogonal à $\\overrightarrow{V}=\\begin{pmatrix}1.0\\\\1.0\\\\1.0\\end{pmatrix}$ :\n",
       "\n",
       "> $\\begin{pmatrix}0.0\\\\0.0\\\\0.0\\end{pmatrix}$ False, $\\begin{pmatrix}1.0\\\\0.0\\\\0.0\\end{pmatrix}$ True, $\\begin{pmatrix}0.0\\\\1.0\\\\0.0\\end{pmatrix}$ True, $\\begin{pmatrix}0.0\\\\0.0\\\\1.0\\end{pmatrix}$ True, $\\begin{pmatrix}3.0\\\\-3.0\\\\1.0\\end{pmatrix}$ True, $\\begin{pmatrix}3.0\\\\-3.0\\\\2.0\\end{pmatrix}$ False, $\\begin{pmatrix}2.0\\\\-3.0\\\\2.0\\end{pmatrix}$ True"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import fabs\n",
    "from pyrt.math import Vec3, dot3, G_EPSILON\n",
    "from pyrt.utils.pretty import *\n",
    "\n",
    "def isZero(x):\n",
    "    return fabs(x) < G_EPSILON\n",
    "\n",
    "def on_plane(P, O, V):\n",
    "    \"\"\"teste si le point P appartient au plan\n",
    "       orthogonal à V et qui passe par O.\"\"\"\n",
    "    return isZero(dot3(P-O, V))\n",
    "\n",
    "O = Vec3(0, 0, 1)\n",
    "V = Vec3(1, 1, 1)\n",
    "\n",
    "s = \"Test d'apartenance au plan passant par $O=%s$ orthogonal à $\\overrightarrow{V}=%s$ :\\n\\n> \" % (tolatex(O),tolatex(V))\n",
    "l=[Vec3(0,0,0),Vec3(1,0,0),Vec3(0,1,0),Vec3(0,0,1),Vec3(3,-3,1),Vec3(3,-3,2),Vec3(2,-3,2)]\n",
    "show(s + tomd([(P, on_plane(P, O, V)) for P in l]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Des images\n",
    "\n",
    "Le moteur de lancer de rayon synthétise une image à partir d'une scène tridimensionnelle. La classe `RGBImage` définie dans [pyrt/renderer/rgbimage.py](/edit/pyrt/renderer/rgbimage.py) permet de créer des images 2D d'une taille donnée, de dessiner dessus (points, lignes, cercles, rectangles) et d'afficher ces images dans jupyter et/ou de les sauvegarder dans un fichier.\n",
    "\n",
    "Voici quelques exemples d'utilisation de cette classe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyrt.renderer import RGBImage\n",
    "from pyrt.math import Vec2, Vec3\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "width,height = 320,240\n",
    "image = RGBImage(width, height)\n",
    "\n",
    "for i in range(2000):\n",
    "    point = Vec2(random.randint(0, width-1), random.randint(0, height-1))\n",
    "    color = Vec3(random.uniform(0, 1), random.uniform(0, 1), random.uniform(0, 1))\n",
    "    image.drawPoint(point, color, 3)\n",
    "\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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Cy4JLZuUiDF1kzhQ0RvDxppKRNG460jPSzfXiukYRP9osZ4gNU38x/wujaAahekFgKVLZxoPk/ddMIzj50oJfx4crL4KX/PWb9X7mVynAQuGMbebF+xK9PDEQM0YetDVh7HVhI/p//FTv6tMeLhzRh+ncn9haJcC7f29hoFcOTXat1LenOnb7pE3R/9VivgU5SnAaPryuZUIcXJXerZZbhMJKr3lTBSDKX3SEjN+podeKd7rx3DcEFrIO9lRGSjSN0QZuWFcQ0vIO5yul2H9/iSlF6QDS+HvksOtEZVAeqEiMJ5ZWTz5JybJO1ctjJ7EAoDFO7oDfThKH5Kuw71XecTPIYkrmEiv0Mb5/aKqiFgaYyzqvYcV1+vD2IRv/fzTkCZsxpqiN30ruaWpqFwoJ0UGIrDMQpjhP339PrHBT1/Zjgnx4fCnEBJyzXowg2fbPTEOnCTWlBZiVvqi0lrTt90jFjDASkEvKN1ItnSU0NKlM8U//tnz0AuMstEfTZGkN4oUYv1yWtHpdVVg09c27FmpIXotZ2a2yklr3TmjLxu9gAG++6efNh7hxC0dPGf4maRLS2PsOkyaP3tBZ7iE1HSi4VlS8v7owTMWricrnhlYfXibH8a1M2ws5A1f/0Q6eoEYC+3ht7T4AySjiCg/jTG234iPIyy8ewlIhiNmnplLXhkrfSXGxkGXTsXzk61gYi3OpCtpjQGM7debW8J+a0wVOmHsN1eJOXuhQIZTzHPgNH0VKSYsNoxWDEdoIUjOxjBRktWHt+kr6abQVED0xrVcqRIS/UyMce/RV05aFj01rc8lLophowmH2C8dPHNkwxhIQ07NMHFpWWB8r9KZ8JgDh6Nrs98S6JXyC6qjqzSG84gOno0mLFWJsY5TCoZp8ycKmU7+DzdTZAS4KHoV6cR+4KXxL+YrJy2T28a4Onz1HMytrW8pxSgOo2xdSn72i2/O6MVnA6/py5+4VpnQkiCF10D+tYyKO3BNlzqQw0+NoxeO9AznNF5FeJhHsWMto4iZuJLjOgBgxTMDBMOCGQIt+adfDI/tEQ9JrBzm4bRCVX6/1RUHYF2F0yslMcb2+7Mzti0FGHzrCc4ZYq2/US/DeGyWHCDt7R6jF589/W+erz4uTJIfDnW/GJ595ODZsa7LkW2AdCy5PRvJKN1+m0KvFKZXaunxF4qNFKMshTqyMawkrpwelUK3hG0Sjc+kTdAMl/BTZAdetnctADyr7ITf47z3vtk3xS2Mn352xvg3JBhmWrGfwsdLx5Jiwu/uPyj/VMhD6zkyDgIJP0mIkpqwG8CCT1X7xv7/1axDIUUxnzw92NrEo5lKw3jp8ReCaZphLJXDcLjC+41wSziKMI2Niw0rVRFCL9u7Fv/TD3jPvqPTFMyhDCEyrjupdzXJcDqRComljeM6+I4RTq+iuCRDxjEeitKFMKoDhxBy7h/+L7nt9NvmdFHl4Ij+jAdO6jlqsZ1ioItQ0304Or2JpK8E0GiN9QM7ISSZwT+Q56z9ptyOFZn4lYovzqx9vZ9JMMxc/8lVivcev2mn2Mg5G8mjAawnrgLvT/jjo2lhhvME0ok6hKdxIKkrvaRcly6q/CuztPSi7VKDbz2hxM+Dg/uz+XAjFJJ2LkG1r8UTInMSy5XYFPari8kzh2SFXmLW0c5VC2H9VpjYDB4c3P/WE48wiuwjzPBby+dJE65FlV6RiN7oqSxF+dfxwLnoiJqQxLpv9k3iH+edxvub85essrTMvBdzzmDSziRCby2fl/mKOH6m5wnn8d5EJNeV0IKocxumQbwIua44RJaf6cn8BZ8V6eF0IimBdH6GPdS4yBkKW0/LT1P96NXTVyV8co4nM5u+WLgHWG/9JnqqqJKCTrS6Ha0pM48h/kpM9I1yT/xGZbkqZ71N0ZkUYSgllEEvlo3ky+9+Br/0W3BDZzjRjAjMcI0mbIyim9JpxBGuvY3rYQoFGKevChQmWaF3+5fme3R6i3HRS5fOPP7CK/D+DLOayslO85u+gX1sKTqQKtUshn0AbuJ4NJ1eseE9uitdTxJWISO0sJreaWRUjQmtQPkA/Lc3/b7cLp/eHf29SrtX0itViTFnIHQiE87cjWRMkIoo+rYHdtVIb9JeJchek2Mlop0BbtCPE5hGaywYGLIlurzdWPYJZ2C4LhPWG702ehNl9TKoiY1hN4CVT1VLE4UvI71yOzrGQh3TGB7tWynnNvzpPvXxkdm8t8Y6loLh+BP6b3tgF7NnRXweHD8XKz1sXjAwZMw5h2Bsy9CkYLjG8VgKvWuWdDPpjTtKHNJH0dDAxvBUABiZe4tH72ixoo3XKAJjfadxgQ4lp5Wa4WyBtE5vnuvWqPLTOlhjIbRgmMBY/ykqMH42fgR+Z68RY2ZEvX7hvYkYts1DysCwR8oqRQM4f01rUGN4vA08MvcWsMzRKfwzCBnR9RiqYcOYk4hO3beUc4awQu9XZjk8e73DVHL9n5DEGpl7C23FZTaAA43XKCPDv9P3f5WduJknzAcznCKQxgwnMuG1Bz+y9uBH8B5Bb+UD0MLXyq5UhmawUFMC6al6XCStWFBR8s+PDd0oDyUzWrHOMK24DOsjoqMzrKALk9h7GxFITwVT20YwDAA7+ntPPus4/W21N4BtYULE5wkKVTKsW03qhFa6QNrY2evxALTo9lt7fYNSGR6b0C8Yxt+fYLjrxS8DgGB4wcDQiuwh9PCiLmXPgZNONB557OtviON7tozELYNgGKeyxLbO9vqF94q6u3SpurRliC6fdY3ivdGf6sAfp2FTc8dvECp/Aa0JK3KsWdKtfJEjc28RDAPAjv7ebyUujY6rlI1bOIIucZIoSN83+yYlHb1s71pi6iJmOOkqPOHS6b3pmL+rpSQFCjNc4IRhdSQWEU5j0X1OThpe1CX/6X89cNKJ4p/xvce+/oZCr8cl+Pr7bf9J2SOQ1lNZumIZsrTiWNksJ3pteawM6atWRhnWxLKF03vnfF850ntpC/A1W/pyHD7lMX62LBjGzeAxW15tODhuIE3LI5A2hs1JHycfRfRzz1KoZBM2P15UFPe1K/9c2S8Z/vRj1bgyGePgSp+TEAdpPslyDNbOVQv10R1nrj5ZbmMXwgyHBNLGR41ynlFqlK3RKwFWRu1K79VzWnnsN/VCs7QiTqG13WE/UQCDiWEAWLOkO/PQyyi5ZRpmDsYYYNAGWmKAAVVl9UEtvgzjPFYIw8bFNGTTybZ8sQ1gpcmQNH6WDNc+0d8b4OirQxtCaFxQPZwWLxegpnIimKN3CElEjSSLnU5xtZKd3n3nawrDQjkD6UqFZ5sJdXbrt8xA2uDAxl8a+mdbkQfS0XHlyObJNowVB5bCVpw0kDZG0cAzYf43aIzxjA6cOXdVrwNDDBOOGz+D7sC2Iq5Z0r3imYHZez6GDxZ1Qq8ECwaGXNmoRaIwelFd3VjvYRKS3cLRtX3fBv7DVpx+fPnK2fF7+2k9APDKxJc2Xf/ycKJiFGjCbhP69UQ0aPXD1lvTs2WkKHqlbAVz6naSHcK773wN75e1POkYaaJLKQ+9KX6nbj+tR/7L88YmagLARIQgo5e9c76vf/1ytaRmoYtFYMw8g43hiHJ6xJm+hBW4TMe3Se8Kjksvh71XHrok4tmcVNoA6QltYA7AgFogxl/3nu99cXy7eG6NMkJ73YfXyG1iaqGMpY2N4fCWsC0XDch7f2Z6JD2fW2OmFHN7633jT3KPSG8lZphbYzO48gxRomvvlnCKBxSOt4GZxcI3Th96CQDDH/8aNHzpBmPb+I4f3YYZtsnYHk7XGFZkRBeqvo7FW96e8Prf0PaWPzhy6rH/f+c7D3kWzi4CvAnIzR+mpxPig43nFDsDMS6qJTzuwDTARAJweFGXgFZXozEGkxVf9+E1nJn9gmFjz3BEE8YObHtUgvErUIllS6H37z/1ObGxeZFhyhpHNnRtjHkkol0vwZGfCUdPQYMEuLJAxhun1O/JgzGnaWBjOHoUzUTXG1opG72KmDD7ceXdkxQdY1eGEz3g2x9gW7V2soKmqCiGJcAvDpkfmPSBbWMbi3d087nF4Om1TUk72+i1nVCREScOS4Fdwd7X1VUQwJyiKDeuskJ3HsYRGQYA+WglPxMmbi/uRvreZ+cSJ6GtUla427apo31we77yB0K/ik4RH6EoYzlCCoDlxHCK+Bn8AFaqMlGPiWfYNYtkOQbrjh/dhvdnZph5PwmG+Y1VUeF0em9YdrRtjQ4CZnHdcHIiDsYKL0wJAE91jQT49ALZ62jspSxfSiKa00ss+of1zmH5QBaOiNs1t3envMmLt7xtpGjzouPEP/4VwUIvcTxxlcVb3o7le7GkX921u5jfJ5xukqZhMgNfzG5e44wIIbmzKYa8c9XCnoncchbxEX1LgmFsxYJhYr0O+jdubu/4Uu+Y2+99du7H/+pFse2XH16/8F7YNmHPqq1XV65KKSUuiot05rpPKcfUS68sgwLt7af1lFAwvsZHYrl2Z7kO0hBu3BmGrHx2vg8D24qJG6LcycefXELFru6LdeiDnNf0vet6EjhiyKDRu3vdd3av+47HCVPo+peHFWKdfJhjwonSV0KeDhwyxKoRhjznpQmx4puwZGz/JWP7l8I/AsDgraeLl06L6ekTDwUzq7ZeTf+K6bfl8SeX6IdtXnTcx70W2THOT/CjV0qnV2ws3vK2d+9xdClW3CAfniJ+Nmj7HV7U9dAXrxTbn/vaw3EHSFYabx6YFWL9tOeMQ/QB9BoAQqMXn63s4Q/GwEg4TfQ3ortq69XYPabMPEZsOC00i8EwGq8TxklnFOKiOgEsvVfnKKn9AseBnbJWHiIMWSipLUfhVj+bjWQ80PK0JxeMXgzT/+Z55Ri5Z/Tis20fWaf30k8+4DTVQYiYEhhl7KeKhNY2hpKsGPuwnwnnH1kZlMSKKFlTOSQrb/ETB909ZxzCzyLEgyjpt4u/KhiPlf/JCUcKv9UxFjuNg6iN9II2SRivHa2Lie5o30rpIe/uPyhNmCNbY3LzouOKZRgrPJBObb8gACZ+MwLXYfUQxpKOrvFfnWAm2KuMgW1HGs8pdi76309Vnm304rPf96s5xmwWJk0f/7R50XH681Z0iTUrK6fgp5tapJCgp6nFdu0Y+zWGa5zeQDlwfnoVcWzZdoARaRu6HG7pOQwimzX88a9t+c8XKH8Se2wYv/zJHQDQ/cSfAOLHRpoyGlkcj5/boJjwvx4zbuze0XKICQvZGCjTivW+JT9lsF+wrUoJGr0yiVXCU2r8Opx0tKAKXWP8zLm68VqCYfnLghNaAmClNzjDmjVMy1VSWZVJLKdskN4iIBjOtiyWR0JLSWUVBHDPlpHa1xOziQmzThQnsg2UflHl96KSYaHFW96OOAvXL052qo4etV/B2MZwIwAGgKuXL5Lb6egFWwit0Jvu8uEyru+DX+ZHV65JsmbJIZgYtxuTW0K7LvyqYFiRqNnKzFsnc/6Ng2P9UnmeD+7XGaOE07XH0uEZ6TwyAFx70zdQGGm90RuLXlvaTB9lueeMQ0ox5rx0tGDYtpyllM2XjC7KWfndW1NmHvPu/oNie/q2e1K4SmkMu0qmsrLZLxhDaKP91vtgCz/p9PKTzGBfBbpSxhtIFAYzjB93yIwqsYwMez9+BWvG0IMSYCFj1fQeCyFFfOr8ldD149zf243phfQAq8vKNih4pqUAs+eMQ370egjfN3k/9QIYU+I2Q/bwIk73kpOU/HOiGTbNcl1FmekF/rrQTXFdIZ3eukqiyMiw8SHD2Ij4ddo4GCti05fuQwq3XyH8eY0jRrPVxspV8gjdu2lL7OIYNAHgzrDfcHpto6/4MpqwsTw6w8v2rg1ZvwozrJtweHsYu0qeZ5GGr+aVR/hu5KEXyhlKmUjleC+WntYiFBhSOj2ExUM37uqS24fgwPh+6NIPFrq5e6TytOUktJjjOup6rvK4A3ee/frRG26/QoQJw8SyiTLjPqT3fmK92PCrtQqx2/dtiBhF37irq3/2JvnP7wz4n+2wAhvDNpIVerPZ7/Z9G9yejVS4wqcWheSuQmQseUgNJlzXI4q+cVfXdcfdJf55F4k4uQ3mysZwCVLoxU2MDM9eGQuhnex3xTMDBea0oieuQuxXqGfLiLyx+ox/JZC+4/xTzn3659J75Ya3lDHSby13PgNhj4oG9i6/qX9sJgaRvqo8oTxAD7NnnL6RWZjoIqJogt7UEl9uZ7aB6w2e+XJqDAfq+E0731puXkdaVyVpEjCntp+CJXEV8aebu0f0CQ/lyEYvnpyUSPKneRqw7Xfj/H76yTQ1Krzp66cDw4/xDx6GdfrtxQw/e+77sQkv27vW2MPEFzZhpgio7nj7Wn0ag5irJO3XSZhn43WPYDyB4XqjPzmskum9KWYX4u+0Mx3YQ0z7dSJWUdfSdQeWjr88tucy71PxZWRYTA9WdtrQvbl7hF6PcrRvJaAI02+gpYRZL8aNu7oAzn/jV1e6njOdao+cpSYksRqafI6beTbqwPBj4p/HySvPicv87Lnvx+loeqQ0U5XdSLZs8M3dI5X0Klo7cAWE9amIi+r7T3zPwye+52GoKZuFG/YcevPM6b981jXTmj51IVwKvYr9cqCt9FL6JAeGH/soVD9qKETCh/VmMOG6gVcMnPAgCqAX78T3PAxnPhxQrsjK6b1gGuvuGUKXk4iO2/rF9BLUuUa/I4Pr5HbPlhH9zM+9/tBHTxpj+I7zT7nuiVd3XfhV8TK8JWyTzXVtxzstRglHnCoFxjfu6gr/iQkX86PFagYb0xnjIXRD4+dAGZu+tmj52J7LxD/Xqyj31vs8IVICaZ0KW+zqJL1Ohw9Rurl7RG8A87u4okj/FDV6L6Bv020gRyGua1TgmGchGl2vcqnCbZZjey77o38aW2/gudfH19z47Jzv3fXTs+TLKC1hOPKt/2TtF3+y9ot4P4GuUwNYKAXDAPDGr65UMKYHckWUH70Rm8E2esEV4NIU0omqN31To2vTH/3TBRJjIRFOY4ZjSUEXYjR3dY32rVSq+PRt90TB+J93/0DZk5RhY7EL8V6hMYA94udi+4Q5UugdOucond646BrvME6oGq9110/PEhhHMWG9rp99yhJmR7FrAxgsVuyBMa5pmxcdl4fhWL84Qt7jOmh6oekOLBWSvho65yhlT/4GqpDtU0SxYqWWf+imr519ythzlWwMe8TPioxmFc7GP+/+gYJxRIbjohuiSnrBA+CSm8FMYfs10pu6AHrXXeW8hUCGdXoBAHcpRV++Q0oPp4U8OBF1T96r6AzbimT7CJUKaQZz6IVAB25iFE3Qm9l46QEJemG8h5EY6dW1fd8GG8Ye8bMib4zpOhaL4ejohkj/IoihOFOhsR1IHhksmt7wItFyus/i04UzrNTpm7tH8CBKvWbIqhMeP+uK6MZS/AkSRhWFLphCIXognY8DNzGKnrd+a730EqLj5xCGdXr1YwiGPcRZvILG2EYUrnXKHXNlmL6QsXjhD1vh5LFc6YXOmMxQmcHSc874Zb30KrruB6/ecf4pys5rP/gCbgMfGH6MU2YOvUKiluDas33fhiteHNsOj5+NEpDYjBftP2g8QNHN3SP48xqHalWafC2WK8UPm7FCs9DlN4PLpNd1RP61H3wBv6z0YT69UrjGXPHiCeyiAQSsQUlHqktOGafX5pnyTuo+jJ2WppcfMLt+Uk4ey6nRq6gTHJhQmfS6SjzAge/DfHqVeYUe84ejyGmly7ED/k3bAzCwF/AyXf2zNw3stS5EUq/fSnmEzVieDowbJGWasNLohVLpdVr4ytWHwX2g1eWzrsH2+8jcN12RDmwuCjMc7VuJ7feBV9X1qB/5d98wvp0gVjk/v0hRnjZqVCC9ADCtoSloWvog552rFgKq7nXRi1fJ8pPiw7qw/droXbyj22lpO1HPki5PS4tuMCsa2Ltc+nD/7E0lzFvSFY6ukH8buNhctJHeAwXQGyI8oxCXXzHhuIMKH5n7Jn5JW3G65/fJmibNU7FQZb/irhHvSeBnlInoWPRCrKGUhUTReti8c9VC2yyFGvU/L1BH8zpJGRctP51H4koX7v419jBxIurwmNOpRukZwcDOYay48bPxBoaENh0yFlpHFyxLWzXRfnVVfopYcePls66J21GcTeVEzkQi2nh7nRQEcCGpLOOKVnh2vtxZGr1OGSxlXQ4lkOY0fSuF7Rd3/zKtOORRYFjMx4hW3r3KVS8rFetxbUZFySlME7U/zzLIifTmJUtO+PYD8mVzP8vg4H59FIdR6dbZsUkf7AEFJLfKl7hFby6ZsI5XxDs25sDGEJSjulJZNtcllqQrzX7DJT/RwFHr5M7o9otlrHnYjWOZsFB47Qox4UD7teUL4v7eTRjI4f1MeqEMK91hbk/49gNvXrJEvmyu8RplHB8qRnTEvZBxjWhCRiuGeG5cSEI0RESOIHq0Ym4DextyOtFFMtLb2fYrdGzPZdnsF8uWfdm+b8Oc4c/Il+mGQPDlZ8J+9svM0kfUNFH1jWwwDRk/ciW6CZf2O9Ixch3LYZTNjb3FTF8VKNtNELco3aOSps0YevBw71US0RCSI4rmVhZjziVjU4LnvHS0EnM20X6ZGSwhkcfCltL/y3X9wz4f1tV+FekYzxn+zJ6eR8W2fJhQjcJzlThrSjvZL42uouiPSlInMxCGDJZVlCGSCXPMtsMaup0kwo1vP61nzvBnKpt/hdgvM+zP2dAlNA0AhAnjvbQhW/70itOFnWJjG7ecx3M2xX4HB/ffAWMOTMxwxnksxX7DyxA+9VdijE0YAPb0PCprfC3dTkwTVujV7ZduL9g+WroHjk4b+sZdvX9wrc6wEIdkoZFnT+069xWxveKZgZFnTw0vnJPf4ii6tLGTUsRMBqf4mRBzun9SSYwxw1JGkguxXyxMb2U7v67OcO58YMxS0sRSGyR76Obukf7gZmb0lTdEnZaetqfnUZygBgvJ6aSs2qFLb/oWy63UOMA2E9alMyaQxibcde4rHBMOxxVH0Xoqq3YvYsrjEW0n//xx/PLYnstC4o5E6+Yo0hkWym+/ehStBM9+oXJ+xVmRQ3LYhb6J1ktbAcD1Lw9jNvb0PHr9y8MEHt6Ly3hLD/WNvzJ5CuOqCQM5wlcSrWV6A7askKcl5ZeYB4fLfN0PXq18lzIKOnzaYGr7VVJBt5/Ws6fnUTkU5Lt7R+WfLpo9XXmvGBqh/BN/8njSt3wYhTyzKAw+RqdXFLVAekF3YH4gzVEtjxEuNoOVTZV5rBRrPtNSfBiO9A9jevkSDD/+pLrHVXqOTdJbJq66pgLA0DfuwrsCv91aUojYhOWTskuTTEH/4VPny52K/S5dOpNzKqUB7KT89ArpXTIK0hvn90uvc+Ln0k8+UH2QpudfVd91/cvDJZutUWMOfLj3qojfa9LBlRx99KTPPff6Q+VnsJ499/0RzxaYx8ogwbDk9pWHLpF/0iuJbax1uoI1UeMhNGa4iYG0MqijWB8GgJ4tI4svUOnltH51uTaA67JfLBFOY3qBPeISU714yxJ9J63bT+s5Go499JcHlPIw316grCtyND2Qbpb86HVVCfQKKcyc+rlvA8Dtp/XwZy+5ZrBsJ280vSABFs0zxXUjMtxmpJUxWNh+Jb3MBjAWf3qw8m3m6fi1CdcHQa+UE8YcESdsOr2gO3C677WWidpFMSwVWKrwdVLLoRcsFAnqOCTbVsbinCHuKry1yDCQI2JjGGezsum51x/CDWB9eFa9WnrDP+KX5z77c4Bfp75ozl5fJ4kwTUluYTnN7KsEXpzhRuhyLGa5Ggd4eFGX8SkNERnOlpEujWEZP5vohR++d+p57/zaI35+7f2Xcg4rp+kL5KhJAmOhCX9a9ynDTrsw/JWDohsk81BKpVcpYlK6Roah1iyXgi4coTe1im362iRJi9IS7oBWLq2ptmcjRUxoKcTWktASqqtJrNO754xDTotC+6lkeit/x69/eVj+c7qQ9xubqAkOrETREX24lsYwmGb85w+n9V8NvQA/fG/8R2QURa8i1ygMo4g7kDL8CBauinqTyIdzwrznjEMKMHNeOjqPFesXwoUZHNyf7tKl0VvgfP3O0FQAwK6rLxkRt3NYKgPDeFyhMZxOh7Hx5HoZzntnPP/sMbdGkW0cZVH0Bqq1X0WsyC0Ww3U1hoWMkXN0jG0nHLz19AkvU9ovlo3e8DVlmXJt+rZy0hjAtAlDoxgm5jDo4bSQoC6EZOIMg7eePnjr6bZkYVwTFjrx8Nh5SvPeQHpb+9XlkDtpEMO0bBgD4rCSZ86RAl3DfmS/Ht2/TDHpdXquipNa782gcYArTRiSMVyLCIylFEqZbIuTY3Rt9iuEzcTbhEvLWikK/8Ybbb/pnszg3HuRguF0Jlw5P1ZgHKtjiXO2FPY7Y+jBN2aM1+kS6G3Tznk0AWCOCUOavHTtz6ST7DnxbHsXvnu0/QqFmHBRIyWFon+bjbZfrLjPVQEPBxaKwnC6xnD4WhwKmbZ/rqfN0PqtfR2StumbUyrATBMGE8MeGGdIaOVfZcbVfoU8TFiujIXj53qVgt7o9tsxMxmg0oGdGAYvK649KR1XxB1zst9YXUo5lZreVroMAPNNAwpmGEeSdS315nQngW0vd7x9LX6J7ZcZP6cYxZEhco7e+vV+Hno5MjswP5AGgMO9V4WH0zrDTbRiInhm2i8dSPu1U1JL/7Ji0dsxuat0YiWxKhmGGFasf+uBDGc2Yc5dchWuwcb7eddPz5LbHumr8FEc+neUgt5WNlkBVgykoQxnk3J//OxXSLEaUY9td3LgqHXcIiZQNnoj2m/+DFa6URxAO7BrEw5ihNMb5/dHbBLX0hIm6GVKqa+cUVb5e4/0sDlRj1EbPBOqCKGdGsNSRit2xRi/LNyH+f1G/L5fXGv/688uk9vi3jJXw0qnpCmrPE3f/Bms6KM4wHUgRwjD4BhRx0prpTZh+p54j9xQ7pVg2DZG0sl+A1PQ6VJWQm3T10nVAHs0hoX0cBocrThFkzguw/ymL1/yFv3lBx7D+7EP49xVzmZwukavULqmr1AnDeEQYjmwN8MQjHEUhhO1D2l6FXHsV78tCsNx3ck1Bd10ejtSU/iHOtVXXTZimVNnwmsP9t5wpCvvhlPwTN8cpWb/j998SmxI73VqzskQmg9wanQhF73SgbM1gHEKuuY2cIgPg8WKge3GccPpwEDaiV5ato+PbxeuzZJerKSRYQbjzUxvJ8ktiRXIMIRhbGSYj7Hiut4Mu9Jrs18OulKiThvpdZJTBst4e1OnrDo1ck5hv+AUQksFxtJSBLF0XB1SqxRuXWNpzmeng2fvT62U/NoPvgBoQhLwwkIMMB1C5w+bISW92H5zdiDJELoggMHkvZkxNhovs4b5Mcz8yAS93uiChd53nl71H848X+50ApigN+TeMpXfeFuAVUVkGKq6iG3129slXBn2oBeOAOz30bCM9ALAO0+vAgAnhisB7jDjFaqdXigQYIjNsJBrdfe2Cz7DfvR+6YPfIq7OX7ZKL6d8qLcrwHT8XIvxQpZGbwcD/P8B8Q/LKBYl2OQAAAAASUVORK5CYII=\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image = RGBImage(width, height)\n",
    "\n",
    "for i in range(20):\n",
    "    center = Vec2(random.randint(0, width-1), random.randint(0, height-1))\n",
    "    radius = random.randint(3, width//2)\n",
    "    color = Vec3(random.uniform(0, 1), random.uniform(0, 1), random.uniform(0, 1))\n",
    "    image.drawCircle(center, radius, color, 3)\n",
    "    \n",
    "image.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image = RGBImage(width, height)\n",
    "\n",
    "A = Vec2(5,5)\n",
    "B = Vec2(width-6, 5)\n",
    "C = Vec2(width/2, height-6)\n",
    "P = A\n",
    "for i in range(10*width*height):\n",
    "    P=(P + random.choice([A, B, C]))/2\n",
    "    image.drawPoint(Vec2(round(P.x),round(P.y)), Vec3(1,1,1), 1)\n",
    "    \n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Des scènes 3D et du lancer de rayon\n",
    "\n",
    "L'algorithme du lancer de rayon, que l'on peut attribuer à Appel 1968 et Whitted 1979, repose sur le principe décrit sur la figure suivante :\n",
    "\n",
    "<img style=\"display: block; width: 70%; margin-left: auto; margin-right: auto\" src=\"img/rtdiag.png\">\n",
    "<div style=\"text-align: center\">*diagramme de principe du lancer de rayon (CC-BY-SA Henrik for [CommonsWiki](https://en.wikipedia.org/wiki/File:Ray_trace_diagram.svg))*</div>\n",
    "\n",
    "Une scène 3D est modélisée par un certain nombre d'objets positionnés dans l'espace (ici une sphère), un certain nombre de sources de lumière et d'un observateur représenté par une caméra qui enregistre l'image de la scène.\n",
    "\n",
    "L'algorithme reconstitue le trajet inverse de la lumière depuis l'œil de l'observateur, à travers chacun des pixels de l'image, vers les sources de lumière. Pour déterminer la couleur d'un pixel, on suit le rayon de l'œil de l'observateur, à travers le centre du pixel, jusqu'au premier objet de la scène intersecté. Puis on détermine la couleur de cet objet en ce point à partir du matériau utilisé et en déterminant quelles sources lumineuses sont visibles de ce point. Enfin, si le matériau est réfléchissant, on lance récursivement des rayons depuis le point pour déterminer la couleur de ce qui s'y reflète.\n",
    "\n",
    "Dans *pyRT* :\n",
    "* la classe `Scene` de [pyrt/scene/scene.py](/edit/pyrt/scene/scene.py) décrit la scène ;\n",
    "* la classe `PointLight` de [pyrt/light/pointlight.py](/edit/pyrt/light/pointlight.py) décrit l'unique type de source de lumière ;\n",
    "* la classe `Camera` de [pyrt/camera/camera.py](/edit/pyrt/camera/camera.py) décrit une caméra abstraite ;\n",
    "* la classe `Shape` de [pyrt/geometry/shape.py](/edit/pyrt/geometry/shape.py) décrit les objets composant la scène (en pratique pour l'instant seules les méthodes `hit` et `hitShadow` sont utilisées) ;\n",
    "* la classe `PhongMaterial` de [pyrt/material/phongmaterial.py](/edit/pyrt/material/phongmaterial.py) décrit le modèle de matériaux de Phong qui permet de connaître la couleur d'un point d'un objet en fonction de sa couleur, de l'angle d'incidence du rayon par rapport à la normale à la surface en ce point et des angles de réflexion des différentes sources de lumière ;\n",
    "* la classe `SimpleRT` de [pyrt/renderer/simplert.py](/edit/pyrt/renderer/simplert.py) propose une première mise en œuvre de l'algorithme de lancer de rayon.\n",
    "\n",
    "La version actuelle de *pyRT* ne propose que deux types d'objets pour décrire une scène :\n",
    "* la classe `Sphere` de [pyrt/geometry/sphere.py](/edit/pyrt/geometry/sphere.py) décrit une sphère de centre, rayon et matériau donnés ;\n",
    "* la classe `Triangle` de [pyrt/geometry/triangle.py](/edit/pyrt/geometry/triangle.py) décrit un triangle, dont chaque sommet de classe `Vertex` est donné et porte sa propre couleur, son propre matériau et son propre vecteur normal.\n",
    "\n",
    "Voici un premier exemple complet d'utilisation de ces classes pour définir une scène et la dessiner à l'aide de `SimpleRT` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Creating Renderer: Simple Raytracer\n",
      "# Shadow Enabled\n",
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 6.71076512336731s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 39096\n",
      "RAYS/s: 17270.161877137194\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pyrt.math import Vec3\n",
    "from pyrt.scene import Scene\n",
    "from pyrt.light import PointLight\n",
    "from pyrt.geometry import Triangle, Sphere, Vertex\n",
    "from pyrt.material import PhongMaterial\n",
    "from pyrt.camera import PerspectiveCamera\n",
    "from pyrt.renderer import SimpleRT\n",
    "from pyrt.utils.colors import color\n",
    "\n",
    "# Dimensions de l'image produite\n",
    "width = 320\n",
    "height = 240\n",
    "\n",
    "# Crée une scène\n",
    "scene = Scene()\n",
    "\n",
    "# Ajoute un sol carré blanc\n",
    "A = Vertex(position=(-5, -5, 0))\n",
    "B = Vertex(position=( 5, -5, 0))\n",
    "C = Vertex(position=( 5,  5, 0))\n",
    "D = Vertex(position=(-5,  5, 0))\n",
    "\n",
    "scene.add(Triangle(A,B,C, material=PhongMaterial(Vec3(1,1,1))))\n",
    "scene.add(Triangle(A,C,D, material=PhongMaterial(Vec3(1,1,1))))\n",
    "\n",
    "# Ajoute une sphère orange\n",
    "scene.add(Sphere(Vec3(0,0,3), 3, PhongMaterial(Vec3(color[\"orange\"]))))\n",
    "\n",
    "# Crée une caméra perspective avec un angle de vue de 45°\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "\n",
    "# Positionne la caméra en (0,-10,10) pointée sur (0,0,2) la verticale étant donnée par le vecteur z\n",
    "camera.setView(Vec3(0.,-10.,10.), Vec3(0.,0.,2.), Vec3(0.,0.,1.))\n",
    "\n",
    "# Ajoute la caméra à la scène\n",
    "scene.setCamera(camera)\n",
    "\n",
    "# Ajoute une source de lumière ponctuelle en (5,-10,15)\n",
    "scene.addLight(PointLight(Vec3(5,-10,15)))\n",
    "\n",
    "# Crée un lanceur de rayon avec ombrage\n",
    "engine = SimpleRT(shadow=True)\n",
    "\n",
    "# Dessine la scène\n",
    "image = engine.render(scene)\n",
    "\n",
    "# Affiche l'image \n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "**Q1** Créez une scène utilisant plusieures sphères (par exemple un empilement de sphères). Attention toutefois à ne pas mettre trop d'objets dans la scène car le moteur de lancer de rayon n'est pas très véloce...\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 27.660160064697266s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 48975\n",
      "RAYS/s: 4547.153729617312\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "camera.setView(Vec3(3.,-6.,5.), Vec3(0.,0.,1.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "scene.addLight(PointLight(Vec3(5,-10,15)))\n",
    "\n",
    "scene.add(Triangle(A,B,C, material=PhongMaterial(Vec3(1,1,1))))\n",
    "scene.add(Triangle(A,C,D, material=PhongMaterial(Vec3(1,1,1))))\n",
    "\n",
    "def randommat():\n",
    "    \"\"\"Une couleur aléatoire pour égayer votre scène\"\"\"\n",
    "    return PhongMaterial(Vec3(random.choice(list(color.values()))))\n",
    "\n",
    "# TODO : ajouter vos sphères ci-dessous\n",
    "\n",
    "\n",
    "\n",
    "    \n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Ajouter des objets non bornés : des plans et des cylindres\n",
    "\n",
    "Il est temps maintenant d'ouvrir le capot et de commencer à enrichir pyRT.\n",
    "\n",
    "La classe `Shape` de [pyrt/geometry/shape.py](/edit/pyrt/geometry/shape.py) décrit les objets composant la scène. En pratique, pour être utilisé avec le moteur de lancer de rayon comme objet géométrique, un objet Python doit fournir les deux méthodes `hit` et `hitShadow` dont le comportement attendu est le suivant :\n",
    "* `hitShadow(self, ray)` teste si le rayon `ray` intersecte l'objet (renvoie True ou False) ;\n",
    "* `hit(self, ray, hitrecord)` teste si le rayon `ray` intersecte l'objet, avant l'instant `hitrecord.t` lorsque celui-ci est défini, et met à jour les informations de collision dans l'objet `hitrecord`.\n",
    "\n",
    "Les classes `Ray` représentant les rayons et `HitRecord` représentant les points d'intersection avec un objet sont définis dans le module `pyrt.math.ray` à consulter dans [pyrt/math/ray.py](/edit/pyrt/math/ray.py).\n",
    "\n",
    "Un rayon d'origine $C$ et de vecteur de direction $\\overrightarrow{D}$ décrit la demi-droite paramétrée $P(t)=C+t\\overrightarrow{D}$ pour $t>0$. Ce rayon est représenté par l'instance `r=Ray(C,D)` qui possède les attributs suivants :\n",
    "* `r.start` : le point $C$ ;\n",
    "* `r.direction` : le vecteur $\\overrightarrow{D}$ ;\n",
    "* `r.invdir` : le vecteur inverse multiplicatif de $\\overrightarrow{D}$, *i.e.* $\\begin{pmatrix}1/D_x\\\\1/D_y\\\\1/D_z\\end{pmatrix}$.\n",
    "\n",
    "Une instance de la classe `HitRecord` représente une intersection entre un rayon $P(t)$ et un objet $X$ de la scène. Ses principaux attributs sont :\n",
    "* `hitrecord.t` : l'instant $t$ de collision entre le rayon et l'objet ;\n",
    "* `hitrecord.obj` : l'objet $X$ rencontré par le rayon ;\n",
    "* `hitrecord.point` : le point $P(t)$ où a lieu la collision ;\n",
    "* `hitrecord.material` : le matériau au point de collision ;\n",
    "* `hitrecord.normal` et `hitrecord.normal_g` : la normale à l'objet au point de collision.\n",
    "\n",
    "\n",
    "Compléter le code ci-dessous pour ajouter des objets plans infinis et des objets cylindre infini d'axe $z$ et de rayon 1. Lorsque c'est nécessaire, on pourra utiliser le solveur d'équation du second degré décrit dans [pyrt/math/solver2.py](/edit/pyrt/math/solver2.py).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Plans infinis\n",
    "\n",
    "La classe `Plane` représente un plan donné par un point $O$ et un vecteur orthogonal $\\overrightarrow{V}$. Le constructeur `__init__` stocke ces deux valeurs dans des attributs après avoir normalisé le vecteur. Les méthodes `hit` et `hitShadow` testent la collision en cherchant l'instant $t$ tel que $(P(t)-O)\\cdot\\overrightarrow{V}=0$.\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "**Q2** Complétez le code ci-dessous et vérifiez que l'exemple donne bien le résultat attendu. La méthode `hittime` cherche l'instant de la collision et retourne ce temps $t$ ou `None` s'il n'y a pas collision.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyrt.geometry import Shape\n",
    "from pyrt.math import normalize\n",
    "\n",
    "class Plane(Shape):\n",
    "    def __init__(self, point, vector, material = PhongMaterial()):\n",
    "        \"\"\"Défini un plan orthogonal à [vector] et qui passe par [point] de matériau [material]\"\"\"\n",
    "        self.point = point\n",
    "        self.vector = normalize(vector)\n",
    "        self.material = material\n",
    "    \n",
    "    def hittime(self,ray):\n",
    "        \"\"\"Instant de collision entre [ray] et le plan ou None si non défini\"\"\"\n",
    "        # TODO : tester la collision et retourner l'instant\n",
    "       \n",
    "    \n",
    "    \n",
    "        \n",
    "    def hit(self, ray, hitrecord):\n",
    "        t=self.hittime(ray)\n",
    "        if t and t > 0:\n",
    "            if hitrecord.t and hitrecord.t < t:\n",
    "                return False\n",
    "            else:\n",
    "                hitrecord.t = t\n",
    "                hitrecord.point = ray.start + t * ray.direction\n",
    "                hitrecord.normal_g = self.vector\n",
    "                hitrecord.normal = hitrecord.normal_g\n",
    "                hitrecord.material = self.material\n",
    "                hitrecord.color = Vec3(1,1,1)\n",
    "                return True\n",
    "        else:\n",
    "            return False\n",
    "        \n",
    "    def hitShadow(self, ray):\n",
    "        t=self.hittime(ray)\n",
    "        return t and t > 0\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si le code ci-dessus est correct, la scène ci-dessous devrait faire apparaître un plan gris, une demi-sphère bleu et une sphère verte. La sphère rouge est cachée par le plan. En cas de difficultés, n'hésitez pas à ajouter une cellule et à faire des tests en appelant directement `hittime` pour un plan et un rayon connus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 7.129427909851074s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 66711\n",
      "RAYS/s: 20129.385108404553\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
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Cr2QFM8T4RTtutPn94EBiPugel2HHscaCJR9GAczjPo+JdsHBhil036vOIWxOUbxTEomWSgtecNXYnhLnt4YL3LODmju4bsUejAp9Pd97feOIoxWbxTUZlPovsQ2udW1LSss31Hf8umqdG2+bWGE8lAz44cm+8ADAHLJAKDMDcBkfmQXwU0gMcOgZdkVgkunAUQiLZZJRjE2vdw0yeZw42foFYc0BfLrRt75/kHXASYi2wFuTqHBIF2QQk8hUdFwddQXKmwob64CgPwP0BXSWAVtG+HxOGCmPVHpDzHCwLVKf6YBFOCAJoseEJTE1cQh8yqHtcCyDbpXzA+WhjHGFP5CtyHZ3bzkizC4t2wJlCRlZN+Rz7BZg0U8iJXMnyErxaOqMIWGcvY68tmsw/3cUoWQ4Kcn2HNUtySXLkOxGdrpH7gcSIsPIsuk7QPzHUgAwGsnPYaBRdi96sd2oCfFAEKBoxgDn15AsuzIuuTZPOFyxPDIRIodZtFWfsHRCwPBQHThD0E3ps8A3lLK5TBemeE5ejsf4AZKm7V3kt5CdCu5rfXXQ6+ogO+GFX3gAchk0drHYzhJr5XiTCLND9TSmAsR5v9bks2EE4AYdmYmo1IM0kO+zckvEfD4M2VGsOwlK6v0VmKNNXNrGHdmuBzXHqz2ZXsSoyLMqlis/i1pYyZ11PQOiMDJsekD6ywaEYAGkgwjEmH4CrZvLGDm0eMQYyuznIqjoSsQYRI9XNZhB3IaprH28s5C+QWxiHJ4dOinwEo1ktMFvxL22kpG+5rjVlWYLE8DkKzJMjMBVAlv5UwiC1e96XULNoUmAtTdYAWkkVbcEwb0GAbX7+VtgAS9EYx5qpi3WZDBKi5JbvlaGB3OIeXOTWwyruAxLORXd4Av6JXf+YpcyBqYRwo8n9JNYVxG3RJSvAkd3gbDdEF0IByIlDcKDQQ4ACnuCQ80YliSLLrE7qcHzUOjmTjzVDyDsesGu8kd5PSZR9gctyQ7vcTn6l5Ezegf968dhSbmeOBJ4IFooIGHoE2OnbluWQddm1Dg2cit06S5ZI5bVWEKj2rJnQNqGcZQCGc9xnRBbggHAQdNFACYFNr0hAGZYaABzMoNQbJZrYG8ZgPs8zl4EYjtDwNjbG4rjokwOZYFt/Jikf+SOj337cDyS96GTp4HI790bYg80a6VZLzrnnvcG5hLcgu3K8pvO7Szlbcuqc5AMo/kZNgqn3rn277uNnVF4UGpg8IDojL/gUJERAWIZhsQUCEiAPJbRDBvwXurDwD5KMSGOTQ06ul9LBHsmBXw0XslonzCyNsmCTwP13HH1wI8/OJ3vyYeZpLhmI95KuU0mdskuZXRIq+N5NCNuXUPmMvdhLPZ9GvI9IGJ0Fs0gQCgeN7I6DDQAIB6FNrzdIm0kWIut/1hJ8KiS0ymzqJN3MtFMENWTkSdFFv30WmOhdkeKfHaC+JN2fsdiC7iM8DNDB/H4SbQnc1hA5YL6u15dYjzOM0ktgbpIk/RRHeDSRFQ2A0GPcPkGEYzZDUgIS+BVki8HBo4hTYJMXJ/2MPYPalHAxsh2fs9Qz4jMW9EPqRxs9mtZJjEBpl7gLX8Do+GE0gufAm9Izfvt5FmorgG271E+JTd4qQzNKTN2VbJKuHQwcf3jPoP1wY8aPz8uVgAUBQyjPoeBqG6gx62MiNLppBRJNB9V4GxmRZCJhL0dLBHcqDD/AL8kjtnGr+13PJ2APAF0QX9lx/41UiAJnS1cQq9NKuTotqgumeHboqo2vJE1Uv/zm8gHlAdAA+IClAhHgCU6WKiAlQAiIC/9K+f0gHadMI8tnfc+Y5bXnqLmU9CgAHB0YgBwwAAA4IWW+V9bDW3LMUWY7S3Ikl6hQjboWlfk0HADI5bczp23Do0objklfnaqzfILt4Yrg3m+RlZYoPAeeejUmpt4a2HedWSOW6QoG4xdL/om96IeAB1QAOt+ZCK9FTPrijSq5BRAeBXfsdDgIigAPF1P/jpMrLZjO66ym3kPFwbUKEBmBXRzCT5DCOS6QyDIdkk0sytiU0WY51zG5G29Jp7E/nHDvk2I/EWwK74cEfqftHBvI+cl8A3uI1BoCsBHuiCfu1H7o5epHAHhYIMAESjPvAUXROwzVfa09Jbjt9J6b39G16L6oB4ANTf6ABApJ80Bea+W6TBZoJcpUweCYSgCAhAffl3vB9AAeIbfuiJyf2Kvbt3Gc+Y83BtUAcFKADWpjyGAbkEPZLRCiQJmINc2vRmQ3pDksG8BQB7DwOZYBCMT+XMKnFwD0MIMNEFOfmFCUS98N77SCu87+1v996fGtc1eYZiLMuZ7ABqGuDbvvaVqK5wkmzzZPfKCbPOqtyGEWdUWnURFbgNZOnWkzn4Kz/8pNjO5wIMAM+47RnqykEdEP3JJNQTSArNMSIfNWpddZNJ/AqAPB2EYMrB23B/DH050fa7xegyiqND/2gzp0cCrZBht4KS9GMMePbozT/+G65FMvIE2ONq/we+Z/I5n8azEtsqBa4oj8X5qy//d6iugDroDy8AOMklFl6dMOt+HyjWFaVrAfRIrkkfAQcEpTuQRqHN8y7US779fQjwxh+9eXxccxgGzqIJFfiTSQCsuooHpSEtwqTpJUR7dz/n0rwB/GtodhsCHQZ7s6KQYj4l0ceVR+njYzG2wgtB8swAa/mN/gzobJ7xnb/1W/b96dPj5eAsJLOG6khh1rmiXFQ97yt+FNUVxCMqLbksvKDAaS/yWxQai0KKRUmq3ImwMl8TCHf+m6eND00eniuI+4XOn/H8p6qjwiPiQSm7loNF2B6dFmHzFhFG8otWV0dqHGhvYhs8KfZOACEsYQtGrmyunUieYQAahuGC7v3pt2Yujx80WpesXFaBTyuw3SW3vLn5d175c176/epwA6qjXSdk1JN/4ACBgMxtAYSDERKnMVpb0fR4iQCVfcAFdwL5Zzrt7QGEhAOA0jS8+FsfBKK7fuKzIocdOwVXkHAcHr0ABKXv5WdP8/FU5v4kGADRqLEWWw0qmVczQO0t3kCxZto+913czOBrMgAgT0u5iSZz1O6plQn9lRjrFx9gECufaaCLj12k5FeGnEhnUksp3/XAA+Jdf2JhpITV7BWLZyOcncgsZX4qji6/5Uv+JaorqI6IerBKhT1eq58sWwC2N2t1VWw4XTWdS9fQSFsiAiAA3POTny2PMH78sXMZ+z/pOU/SIqwOyltTycsqwUixll7kvjkLrye//gpK2Svmb71g2xwc+sfEWjxBEQBIyYU4wOYOJE6e3/nqt4fNay2jwKhUDrD5otqF4UTJOHJYknYrKiyPWVCeijMuf9YXfy+qo0EoNPMZ4XULhKBv3hnATIYi9+pQSDGabjCgaSTUWI/qgrnHRy+GQr6/HgkRAF/4ze98079/1vjM5Fm4grifcb5gEdZ93lFLe/hAyLJsuLU3BhvYjKKi0VVzxsRtWYft/QwgJo/N7qwagz86FZzDiCB586DpAtubB/kJJMMF3f+ad1ZcnBSosW9DU/Pgu989weSpZLZZPysVdZbM1mbLU1Wf88LvRp02G+E1Y7UghFf3DoVaCkX1pNUTUlYuq7dBEyfR1i3UYQQi+o1X3Boe9fhERicb+D/hc25UVw54QHlvA9/YwCLstFcIr/caqHG4YRQV0R5lRIrHJ5A5H/K2SQI8Xvl8QRcfu/bA6347c3nKLSXB+O73vAdgFWhLSJsHbWG0VGEX53xVhmcA+Ozb/ikeHqPp9VZToZ1giY5USYYDDi3qmMU41ko4cC5gVO/Nr3x+A7SB3fg5N5pEWhmGxwA7koNcGkYY6/1aYtEeSGQbQKAsjyx+4OHgs90QAJulV+beI06eH3j9A9DXUncjARQwWUZgtfYWRw5LlizsUF5Z9Zlf8F2orhiiPCPgORAeuAK+o2ZAnnIhQr1NOCAh6ETTpdao80sAnmYxG2ZxJd8rrwtR5NV6UGgwB0aIiC/4hje/5VWfnzojr2xcxDa4RHpAUKgfkaVESxQbunzgrxH7oGeDMbnnd/AG+ncy2G0dk1NtASRv+x1hxyuFBQDh2km57Hn4nTc8mD77FjP9Ct/wve9//2mktZCoGreiwmzMhvIuVU9/wXeqUHvFOg2TLU8MU4Wq6wmsvx36e8o83RYAgN76sy8cn5R3rtFS0eSTn/Z4dUWpo0Kll6UoMSnmK7BLCPxXcCfBOiw2rM6GUuzeQvguc9TBXUdgAPaem6O7vsPv/sq7M2ff0fChhx8GWJHSvtnvKog2SG6m1bjqac/7x3jQM73HEN1R2iz6tzqvFjBHeYtxm8O4pLk5Cbr31S8KTs0742ipfzU++WmfhMfwLn95oz94ubQ+QPQOUMOH/HlFL5EO6fXfTv7RfDNLrdymlF/7zOcLes8bfzdzyn0NH37kkWAfK3E7xy1bWFpeAFs5hBOfgnTtU2/9++pwA+KRb0g4ZOeKUA5ZeYwJTY4xCaUY24+/e+vtxQofABAM973mJcEJeucdLfWvyeM/4xPHDIPuDJvTRXHeKI46psPgNgKAxSdGCG70L6M3vf6mP0zt5NfO+up5o+F9d743epoL2dGd/2ivW6Z0FroN5ZD6U09VQfgnlG+e8uxvU4cbfGULjGc/eJ2F+QE/XSWWYwCA/h0h4A6w2eZVDu4zaR6ljMA9XjTbAN5btG8JdK8ZERDMxJKxW17+hre/9stSJ5u7LGzX/vziYHxQkdKzqahAzwvxQYHbYHrJHqOsEv6IbnWGeEW7RAPtKg5dKA83HC0SAEfXXQ00XAzvv/uh9IkuYpF5YOiC7pzEOFtYtKOC8m5VNbWBA6oj8D2Ao4Z6shfdqikSN6KjudnVMQwA9uex7QorHZcI+JY8QOTb5RhjfjgN928ZCzJaJkgGuy1OhTABbUZ8ZMVHP/DRx970WCBQpIbDgIRICPo/BUAAin9QRdkDRH4VrKI5BwoOcAwzny1B5LrHbJpeuhge/rX3l8Tqa/jB3/s9gBk6uQy6RTFnlNdV9auVPk+65e8qdQXVcXxrke362oElt2HkejwPZDZAZJMihXYlwVvhACIUgHALs2veMOdD9I7XvTx5+unrIO2xN3784YaDOig88JgWongYge36ev1h5G8edwHA3wBxBrztHUv2T+eEOL7iytH7gTc9nDzvzGnPNvzQH/xBuI++mfB8IDemsfm2hRGe+Mxv1l3f6L2BdrVGbCFksJ0cZ5LdYPeWWbUfc1uogQ5R9wvdV4PFQxsN97/h68Ynnbsgoyvz8Z/6ccywf6eh6RLrIxLoumGtCYADmMO/RvwvT+G/0QXPFzRcDB988wcy57eo4e9/+MN+QQGo5Zj1o7e0vLmqprbEIeNz02f9TXX8i3apM/AsilhuhWLeCAMRtp/ckGFbzlgGUsxC5BUKORUC65oEJIvmHA60Gg2PvutXv1Ge64vvuGN8ASbtvvf+pjqyDrsRaYhi7F8A/oqJHLUEWB545k8VrNlggg29ZtRquHbxobf8z4bT7GVHdyrrgHraZLgGwjmI5n1QXbFdX2vufhTiwRvRiwXgpcr2fho0zfxxLED3I9jmI4fIPxNiHlQB7pcMgHiIy0a0T6lhTXbjW+DwNuHcYQBiG7GBPfspt1x9z32KCPUKLd0lVmg6w8SrVBSi7AwDf7HoU5Mb7tjFK0T/eCOznV8SC54HAqLhgj703x+Zar+44Yc/8hGAU8tsQ3lZ1czaWT4xNwB4wmd+gzrcIB+skV4viaEIW7GNTO2Ms99AigGCQneErg/sFbpoYLf907UbBEA0XHzatZ+KXolau/d3rprF0qN7hsGqsT0zl5Hw8Y+TCZDfPCDOKLZ7lz5HFkvSQHRt+L17P9jlTGfaUScksFlQm+W0pjbiUOhT7saeqA4sv9KReOxYSwe5n612GidV2hPe+FvgD6L+PRHz6bb6LB7ZaEQbWZD1skpWMPIUmLfGZ0njuZdme+7TngMAV3/3PjhqHVZARIPB2CQaVn551gx4Eg0A7Ya5qPbqoDlWlM/gCE9ELtgIF1ptBF1t+JGPfhQSn+8ixk6bEtfUljjEfWa4Bc6f+vS/Ye7RD+9YsCPPKLrBCPE7hJA1M+jBBt1Xb0jHEigHZKWi+mPLXq354Id/uuBktQhfu3F4VfQitNnbHryqjoqfuqns3cJuFYdNTcy5xld02JOMfv9gfN43eDosDY8OH37n73c8u/l2xDGrGwS1ksMWh5FPuVvO2fdHlA+1gtHHRvZludPrYpPn5QQbwd7OOpLtQIoBpBqL/SOvCwHWZHC/6WmW0dP4/N2JUOR0OtitT38O6Iz6qFCRUWBOpwkJByTFz50FocbgNjS35lKAHVlwRnIznDHSOTN9+P5toasN//CP/ghqAC4tT8Upa9JSO3Io9Im7VXkmnIMmn/IZfx2594vj3i8oMfIc3rEQCq/o/cZ0GLiK9x8ZSQahU+Iw/be+LE9cA16RdO0mDH+/q4vd++BVPCp1GD2+w6pxbD7JP0U/mQiO3v7fzvQONFwbPvKuD8fcN2HFClxQvkRVpHbk0O4Tc0t6JpwnmshWeuwlrHY9Xv2USdBdUtNLI+vPz64C/jUCbm07zkJ1ASAQb73qyKkxV8lnRpndWH13v/plj8IJsXfOdrTHPKNrEXvu058DAG974F53AxOiXSxNCtE8MQsQ3E83AD+nRMswHy+fgkwaxDgzDbRlbq3FAIa1GIYQiTzJJRHiPjG3pGfCOeefbiLbIqpUCIshswjmw8VwcUMNCQLyjJFrzIsrPS+ZPJP9zQHel5hocSQDwyzRdYckvlH8EzC9xgFgQYYB4NZnPFdv3PvgVbMEBsVSLY0xGDW2A3Bof7YwagLd//3A/1r0+Psa/tGf/InZ8orXFdVeoG6A0pQ9/uavUofHoLpifwkFzMTIAQD99Rvo3XIUTZ45heavXzuVIDNnO5fCh+alx3J9g3WQJyH+mlMnDmBvrhuAiIZrn3583WSTXva2374Xj7zwA81VNEctx/Vifx/7FKtn3fRMW3iP+NHsjRv+3z/9U/cmrEwAWUxjteSOHAp94m5p55x/usl0w3SEx9/8VUqJW/bVQSx4DpY9ywc4GzjlrO80w4yuOd4cxsAk+yXu3+jpSlm2phVb3xd78cTj60uu00J27+9clXPF8osKAIjg2U9+1mSQs8AY/1gDvPCAU4tDzCfulvBMOmebTDcsixBEe/zNLxdrJ4NnbqA3hxQRXuVDC0mGzVGhY3YCY3mu6BwjFyB1srZXyXfr0EB08cQr/7nw4mzZts8w/smf/Rlv9mG1RXVHPuVuOee0/0Srsubl0T7xSV/Kq6+O/KDJxI37Jp22wuvft+Al0pBleCzFAGOMw3MMTiLBsjVvSIgXPdAAMNDFo0/6C3fmrtf52JYxPobdm6VZLRTVNUGtEdJGc7sg8XF3i/TQzrsiyLEr4h/UC+Z4zYi09QSxbhrcIBaAHItmf12vh7nBDjvz4XlXw3mPTklOnZL7xzxdZqAwwT5ju/322zfL8LEkeZ6sjTgU+sTckp4J54kmUw3r4jQaRzWwkKPScklmWaN8+IZcsyGXZ8QYtpNPvEe9GkS/Ga8ajLE54tn3jph9zKnNn80vAi2xqOOEtlmGj6KzZGwpVlcAtYzSZRAtMSIgdKtsCYDMymcLqH8HEtgJWdNePBonYBgA+JdvEbz5pBBjGJPM3ytg/81fJLnsik/H6K9eu0SLTgifxLbJMP6/j33ML5gNc8ytyjPnP9WqqPliFt3pJ9z0InX8S7GHbxy43xsdhbYjz+OH1wGI/jAAj2kBuBKv9+s6xuBtycHZhgtmMeZ1lN4NOxd08ec3f9xb6sNu2rbGcDqFhoIO7cin3G3CP9tkum1vm7MjNE8lt31dMmuOwTyiDj0R5u4sgUyk/Zt+US7hAH2br8aVzLoFLasOYfAWYLns1v0AH0efPFVeswFSiMWqfwAC0Ms5LlUWvU07Mr5TrC43ozMF6qKULv0VcMfttwMe9XoBRP3ARZtz2hTarCdA5IErPjq3lHKCYfcUAK8QRhiDRzKMISOA0WWh+CaJQuLV/2YQCy7XONZm7RhfZbPu+NNEwxl2uu4ugKYXuLdrV+GSXvBMgFqKiWlkyMEue+bf/uAObfDwDfDvPTLq6/d+QUhmkmT7HjFeAxJX6cJLEM22Pgv9iGQaNdmtv42mkRZmtS9Rp+Wzxkzn0Mov37cgCv05JJMVV964D2mMIULyaLCqdAja59Y0lA+tIKDh8o1jbdCOMS4XHoKqsfNBNGmGVSJAcvLL/+nfKxPaa7iVc0hxhoFrJa6W1THGECEZ5BVOq68tE1mxG8HigSxN78A/NHIJU+i777knekon/JQeFxyFKrZLQGnWiKdkDb0mc7ZgA9cSuFsFzWxwmmHwk+eRFEOAMURIlmUFuEloeQ92VsyJ8GDuSaLhrnvuAYAX6a7EOdvd2cHn1JVb4YNdqsAw+2guO6Vp0ze8mBlgO/HrBrH4Nj/d4yWwtwpKbqcYhvEdvymMIfaJy/x5yPvHvZcT2l4KPZgbajmFvkt8+s8R5rt84S3/JK8AdkSB5+xgTUrX3Ne8XJBA9wlR6U+5kV8UIozgBrEIBIU8/sUMg1joYYiVuAYZNYQY602MD1gXXQDBLZ+a6ROLFJoGfcrjqHf6UvbiDfN8V0J185eq5GPZEWy8aBoqXA6esxDq8kt2x+23/+a7iX/79wjmQakH8fhY95O47sYjc8eCeJ4Ob/g3G5kSBOBZXORLKG/3tfX26nqXOXO7L4UfDzf4zMm0WL8BbhqJhgsaHn3k/h+zgQqvWJeHSzfbnTFoO34m20JlWk0AfL0OGk9bOcOP/bTb8HCDUkdQRxz/eLe9f9DeADz+JVHwbwm2Nxt5uDLGKKD1MIYYyeBVTZwlibTAoguC3sFNIw0XNHzskfv/bfF1mrCFwL7z7rvjFTU3osEpOpjmD2wB3seNa62c4U+46UX6WRz8OA79IA77U2bBTfzej5iFz6/zbyQUSyb9WwXRh9ZxHBPh6Q6w2yIhv673a7oJ5k4GogHo4uF3/EjxFdqQVX+Al1wyONkQh/oU+vpBNG9VF+5xn/7F4le87VpouwTa/Zo1hAwz3hZRD2nw7/stev6GrSs/V5cy21M36ILr/Zo+8AA0PPyOHy4JuQmrFFuvaY/4zfILeYB3UPNW+wF83BNfgnhEVKAO/sN0Rr9mFt7PgI5br0sMsV4xRDAGGGmy2E79paPjz+Hdv+Sl0EREw8Nv/6HKa5Pe+QLW54Pd6wbVbJwiBd5BbbDmj9dfefKXe0/kAPlUHYwz7OXPQnvtWwAfYygjGUCW58+SRAoNEl0QvV96+Dd/cCrQ2Vtl53iG/BYsvsDRMONuRTbzqn3iU/7a6AfNEgwH2osBsSJ5BoGxK+dXFP+PfmzsxyXykRjduM8bdhT6oft+oPoqnN1nb4mRrTYFtjcR7gA32PxLZiM8/qlfI6aRxj9K6A9lsboKKYYwowZW4lQf2L1zH4/gg0LBOy+X9tB96L5/lT7Jluu0zY9jY5Y6c3xrV+AlbOb1SjX/5Kd9vbunHzDSDZ54rh1EMRafAhxzO/XJJG+be70A9NDV7+fi0usx67qd8FPaOsRV3EXeFXhFm3Oxytt+yjO+Mf44Do9hGGfUACCSavBJBg9mGH867HvZ9TX/EMBDV79vEqSK69Ppg7fEx3fNUa7mIS7zB94BLrfmK9XQMGhy42d9cyx/Zmg9jMH0nAFCkiH4QCCkP0Dvm8K16KRqPl2LfBBLDmDGNFIyZIVrkwJzwx3gUmu7TLWtssREKgngpmd+m8AYZN9Yv/VJlhsQ9mDTH4Yp5S3DucSpJuBGrdcM01Qo3AEutPkS2u6f4LbcucE/1yTbarptcZCWmBuwajWfN8+0AzxtPVW03L8KxR7OSf+2JgVtK4LUxzyZ1STkM+eZdgWetkXpLQdsrmcP54km2VbTbYuDzAq+mLV3o+cttNwBzlkHGqs8R3+LJQjv45z2n2hV0LYizuz43axpJGz+VNMOcNKWoLc7ulsgPOk/1Wq6bU2c0jA9gnQbtp59J9MOcNw6yGmJZyFpfd1meyad0/4TrQra1oWqCFQfqdO0U5epph3giHWnt11OOyrzWcnyRPPKUBu1His9doBDm5sMl7j513xZvGeod/mx5ZzT/hOtCtq2BNyAdZxq2gF21ld4e6G7ZVleeRB7onl9tFNap8UeO8DGFhfeepx6Se6pOtVJ57T/dMPiCO2RF7Mlppp2gAG60nsydFdmu8oz4TzRJNuqIsi8yJ2t9x3FO8Cr0ruCQ8RnS5rc4D/RsDJIuTXH6nxvRJb5Y999XVab/FtuAd0Ts53wrHXONSloWBGnIkpdGIIOU02ufXbv17sCtw9H5R3yaM0kcz6WZ6HJ2SbTbSvjbNEKvgWuawVuIXPSoSucM8ncYL6ddM7651qVta0OeCLzkC04qesX4BPQe0J0T83tmpo8EWFGzBWsKv2+fu9G6k9vjfSdkPxFOtIxn3K3pHPWf6JhTYS5u2i1LmNd16MCr03vOdS2OMR8SuIko6Wdc02mWlXEybXpT3GV2Erznop0vSnwTHrniOdKcK6ebEd85rklnaeaTLetCbJ1Q4TrTYEXpXchAruhu8LY9RLQ7iNbABDNt4ngugK4M73L87mSJq/DbadEen4WXey3LZBT+fZ1BHDeFqK3D9iriHm+bUnzRp+EW9I56z/RsLh5oXWkfLo3HDvs6wXg6tw4U7uwup6Y+VFtPnJhhEKfuGfWOe5f0KoiznTLDiCbEJXDWtcFwAvRuzhpp0b3lLl0A7FlFBVo90mT58q9X36A16d3I1Vh7Yqd5I4+cc8p/1yrsraNYZe3QKAvP8AZ2yi9p5PrmbWhwwyfiFvaM+lf0Ko0yLywHY3AS7MvOcDN13gLiK4JfM/amEOjT8It6Zz1n25bE+GUJo7wMgPcnDyfKaKlTYoDTjbMty10KNlL0jPrnGxS1rA64Cns0gJ8ZvQu1mSJqrC2yaHQJ+KW9kz6TzWZbj4j4KJ2aQHO2Gr0zm2yParramMOjT4JtwbniYaVEZotH718KulyAlyBaC7KVujdAtUza0OHGT5xz6xzsklZw7poLbFEMMSq4JcQ4OYru00h3YLwbkGTI25pz6T/VJPp5q3RSq0y4CUEOGMdlPmM6N0Uuh25XWBcev1cui3oOLW+bAC3IbpCujsLuY5p8wbRncft2efSNTul0ULLywZwg52Q3kWobkA0Q2BXdKu5LRfbBmiryJn2WESoJ/dyqQA+bYZ8lrR3qppZGzokfMrdIp5Z54mGlRHarDy0VOHLA3CH5DkzcNXFzoX2mqqZtSUOhT6h25RzrlVZw4poLYFGkTh/lhWXB+AGW1WWN0Dvnk7H/QuaTEeYF7Bsr5GYlwTgrSfPawUvKi+L31w1szZ0SPiUu8Wdp/xzDSsjLGqXBOAGW1Xu4kdwCnpnD3FtK51Ou0U8s865VmUNq2P2sMsAcIP8zirfjiZvc+C6vrbaIeFT6xn3L2hSFKRH2Em7DACnrCF5Liqfcl6f3l7fL6n4pU1GVTNry33K3SLOZU1ybeuD9LKzB7jhgi2aJK+UUV/2Ia7QIeFTEicZcMo/2aq4bYnNjHL2AKes1zdhw8e93LkRyBWHuNqaZFpNNixxCH3SblWeySZlrUpDJV1bdnHeAK8gv+1Byp23Q++aneEu6HbiNrGnGvomqpdKrc8b4JSlrlZReW+ZnXDePr3b6Ayvwe38bvBafWC7mzMGeO6l6iqzqcjT7M2PcBJ6T9UZ7p5RZ51zrcoaVsestDMGOGW95LfKeXFQC4bKt05vHs4tZdTxJmWtiuL0CKvtEgJcZK2gRgujsRpRL+C/CvVGAS+LU9pkVJUJWNK23KfcLeJc1mSieVOccjtXgHvJ7Ny/buhRjPoqQt2F3gaqS6vqaxt90m4NzrmGlc2rLBr0XAFe1Brlt0qT4zteUagLImf825pkWpXUljhMHkDSc8o53qS4YXXMiTam0VkCXHvCtbIcLZzP5ETYVfrDVc4NAruc8FawnXWr8oz7FzQpjTM77FkCnLKisz95njw/o5a7LQ7bxTk8vB4ZdUVtq0PELevZ5j/RvDVO3i4VwFW2kPw2CnXUugp1Z3o7DUSfAN3FuF0iu57c0fkBXJQPp8qb5LcK9fLCbkJd1XNbl97StHkBWa5yCz2nnJOtihtWBMza+QHcxRqZTEXoXrhKRl0eoai8uEm+1WRtPnJ5kIhb1jPZpKxVUZz6sJcc4Pny63t0k9/yo4p6bi6jLm6Sr6qoTTgU+pS7xf3LmuSazwgl7cwArs2fp51X6/0unDx3kdloYceMurQqcWCT57gEus3cpnc/K8cO7MwAXs4Wl996mx+lUWanImTKl6iarIUyJqtQbOM2seMOn4dUiMsMcJXSTkeYUzhTP5cX6ioBz1hDsj2599WS6tBzyjnZqrhhUahs5HMCuH/+HPeYp7T1f7nNZtRLlwMUgx2rzUeu8inZV86/uNV0kMpo5wRwu21wSLlrR6jQumjyCejd0mjWTG7TB9H4ebi0AJ9GaTcsv5vS5MnjmVMLsAq6M0ezOn2Dnz3A8/PnmRdyE/Lb+m1yEk3OV82sLXEAqEC3jdsuCfZ0zDMCeOWMsxxLyBcW7mWmqEZjNu0oZQ2Upso7JNWJ3XXMq6s8401qGhaFioU9G4CrbPrSr5MVRwvnfBMvkTxXAdnWv61tsozwLoduF27T2UIu1OUEOGoz8+dNaHI/qzqd2gM4WVKdcCj0KXeL+5c1SbZtCnLeAC+UVxdmLy0B53SJVxvQOuFw9D6gVWnnAXD7+W1jVHlO24W+pHJ7j1fPpTRVvhK9S6A7h9tOY1rnAXCVnTzhrAu44ZknmLyYS3aJZ9aWOIQHdoZjWpcQ4KhNEDhVKKqXZ7X7zFPXSSaYvETFcea0Kq1N73Q5dLtwmz0gV3nGAC+eW56K1dKdFYuqbJQvXLFL3KEqVptvW+VTsq+cf1mTXPOCOGcM8LR16usumD8XunXifKIwtfeCsGdEbyGTs9Cdz21xhDMAuOpizJTlU+XPfb4O1pTf+KGUHnwbvZP7qqC3n/A2o9sl0z4DgOdb+ae5z17WZbXaWuV3WmZr/fcR6ZqGUbsuAG6x+qS68/7LjkQ0iMlvuSbPn0WrnU+qPJhV6V0A3Y7cypbnCnDj2XfqAFe37avJC88Sd5Hf6eDXx4h02KS4VS6CCHWuAE9b97Glvpq8qWHq5eaZFh7TqqhNOBT6lLvNbJJsnohzqQAu7+sumAP34LwPq03WkmknYyWct0nvcvNJSw5KXyqAu1lfCOvFttCtj+wvJ78p/2TEtMtG6F0S3SpurW0d4AWl0uxgxh7mjR+aGF3dRIMJzlsKl5bfsuMJq5akt4rGNnTbuLW2dYBPa33pWuL7PnBbUJMDl4Rzrfwu0Sv2Xdegtw+6TXpwPQG82GhztVuzdR/TkvXFzav2BSW0zEF0HGyqbR29W51S0m3OEuBZvamVre88U/1OZ16IKqpr99V2bKXJ8/L0zkV3BrfWzhLgmTZHapZCrvIwom4L5s9VoC4pv0vTu1zaPBPdVFf58gDckhaexDY5zzQ/qe4vv10Hpesc8nuvzPDnoJvi1trlAbi7VbN0CTS5JHzx3tvKM/HnnE4veqtonNPXLWx7fQO8vaGpSGVhjC47nT8oPa88s9M5yXOVYJ7XrNL1DfDStj1NLj+SOSMFpc418psLn91Rr1Grpeltk+vrBuClWeobbbGjnXlsXXrF3eV3uiq/t4II5Rq+GrrarhuAe1hdJhYP0UrmZRmUzpTPld987VnMCdd/rjYNcOs36gyZWaa7u3Afut6WOM02tSmI0yy/J6N3FXR1g00DvISdF0sdRrD6dYCrLl3tdW4Au2Ev8bar0zsnZw6aX3cA97UOSXX7vhu/szsfxUR1af6cKs/Enz92lbfyZu30zpwWvsw39J90sGdW/PW/C1I7bZ1VSu6ksryDzUieJ4NAPY3N9KZE+/wAXvvTvcx4VbMVkr/2F0SXYa2aJqXyGw1WcCTVAr7MtHDYcNT2/ACOWstHcmPjVSfR5IU6wNymslGncen2Axjvt9OCyjZ6S7rKlwTg69lOOCzXZVirbfgqUzVTfrdAb/ko1w7witZRSM93Wrh8/01VwinrNe9vsR69U01UScTLbYV/yeZRzUWS6r625rBZ7bh0ZahS+Z10OJN1HbsCn9ROMuCctYU6wB3z5+Xkt47eyUMoP54mf227Al8WW30IetHvnrbgM+W3cmdlPeQpzzZ/azvAJ7BmwPp+BPv0iqtiLpw/F0VbflnlavTS9QLw0pnq9jLhuVZ+Rouee9vCrPraomNxW1uhF/Y+sGdrjU5dfpt3Y8OCF7bLwqx5+4rvt2bX0u//AxeYLujlfKdbAAAAAElFTkSuQmCC\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"red\", \"blue\", \"green\"]]\n",
    "\n",
    "scene.add(Plane(Vec3(0,0,0), Vec3(0,0,1), mat[0]))\n",
    "\n",
    "for i in range(3):\n",
    "    scene.add(Sphere(Vec3(3*i-3,0,2*(i-1)), 1.5, mat[i+1]))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(0.,-10.,3.), Vec3(0.,0.,0.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(5,-10,15)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Cylindres infinis\n",
    "\n",
    "La classe `Cylinder` représente un cylindre infini d'axe $z$, donné par un point $O$ et un rayon $r$ et dont l'équation implicite de la surface est donnée par la formule :\n",
    "$$(x-O_x)^2 + (y-O_y)^2 = r^2$$\n",
    "\n",
    "Pour résoudre cette équation implicite appliquée au point paramétré $P(t)$ d'un rayon, on utilisera la fonction `solve2` définie dans [pyrt/math/solver2.py](/edit/pyrt/math/solver2.py). \n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "**Q3**\n",
    "Écrire le code de la classe `Cylinder` en s'inspirant de ce qui a été fait pour `Plane` et vérifier que l'exemple donne le résultat attendu.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyrt.math.solver2 import solve2\n",
    "\n",
    "class Cylinder:\n",
    "    # TODO : tout est à écrire !\n",
    "    def __init__(self, point, radius, material = PhongMaterial()):\n",
    "        \"\"\"Défini un cylindre d'axe z passant par [point], de rayon [radius] et de matériau [material]\"\"\"\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si le code ci-dessus est correct, la scène ci-dessous devrait faire apparaître un plan gris et trois cylindres rouge, bleu et vert. En cas de difficultés, n'hésitez pas à ajouter une cellule et à faire des tests en appelant directement `hittime` pour un plan et un rayon connus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 7.8851001262664795s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 59860\n",
      "RAYS/s: 17331.42227893398\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"red\", \"blue\", \"green\"]]\n",
    "\n",
    "scene.add(Plane(Vec3(0,0,0), Vec3(0,0,1), mat[0]))\n",
    "\n",
    "for i in range(3):\n",
    "    scene.add(Cylinder(Vec3(3*i-3,0,2*(i-1)), 1, mat[i+1]))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(0.,-10.,3.), Vec3(0.,0.,3.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(5,-10,10)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Modélisation volumique (CSG)\n",
    "\n",
    "Maintenant que nous avons une compréhension plus fine du fonctionnement de pyRT et des objets géométriques qui composent une scène, nous allons enrichir le modèle d'objets en ajoutant des outils de modélisation géométrique des solides : la modélisation volumique ou CSG (constructive solid geometry).\n",
    "\n",
    "La modélisation volumique permet de construire des objets aux géométries complexes en combinant des objets élémentaires simples (typiquement la boule unité, le cylindre et la tranche épaisse de plan) à l'aide de transformations affines de l'espace et de combinaison booléennes de volumes (union, intersection, soustraction). Dans ce modèle, un objet est décrit par un arbre dont les feuilles sont des objets élémentaires et dont les nœuds portent des transformations affines ou des opérations booléennes. L'interaction des rayons avec ces objets est résolue par un parcours récursif de l'arbre, de la racine vers les feuilles (pour lesquelles l'interaction avec des rayons est simple à résoudre). La figure ci-dessous illustre un exemple de modélisation CSG d'une pièce trouée où on a représenté l'objet obtenu en chaque nœud :\n",
    "\n",
    "<img style=\"display: block; width: 70%; margin-left: auto; margin-right: auto\" src=\"img/csgtree.png\">\n",
    "<div style=\"text-align: center\">*exemple de modélisation d'objet CSG (CC-BY-SA Zottie for [CommonsWiki](https://commons.wikimedia.org/wiki/File:Csg_tree.png))*</div>\n",
    "\n",
    "Notre objectif est de représenter cette même pièce avec pyRT en lui ajoutant une classe abstraite `CSGShape` qui hérite de `Shape` et en mettant en œuvre des classes pour représenter les feuilles et les nœuds des arbres CSG."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 La classe CSGShape\n",
    "\n",
    "La classe `CSGShape` enrichit la classe `Shape` des méthodes nécessaires à la gestion récursives des solides. C'est la classe `CSGShape` qui se charge une fois pour toute de proposer les méthodes `hit` et `hitShadow` au moteur de lancer de rayon, nous n'aurons plus besoin de nous en préoccuper par la suite pour les classes qui héritent de `CSGShape`.\n",
    "\n",
    "Pour pouvoir combiner des solides, nous avons besoin de connaître non seulement le point d'intersection avec un rayon mais aussi l'ensemble trié des intervalles de l'objet traversés par le rayon (y compris pour $t\\leqslant 0$). Il est aussi nécessaire de pouvoir identifier les points situés à la surface et à l'intérieur du volume de l'objet. Enfin, une dernière méthode permet de remplir un instance de `HitRecord` à partir d'un rayon et d'un instant de collision."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from abc import abstractmethod\n",
    "from math import isinf\n",
    "\n",
    "class CSGShape(Shape):\n",
    "    @abstractmethod\n",
    "    def hits(self, ray):\n",
    "        \"\"\"calcule la liste triée des intervalles de temps (t_debut, t_fin) où le rayon [ray] intersecte le volume\"\"\"\n",
    "        pass\n",
    "    \n",
    "    @abstractmethod\n",
    "    def inside(self, point):\n",
    "        \"\"\"teste si le point [point] est situé à l'intérieur du volume défini par l'objet [self]\"\"\"\n",
    "        pass\n",
    "    \n",
    "    @abstractmethod\n",
    "    def onsurface(self, point):\n",
    "        \"\"\"teste si le point [point] est situé à la surface du volume défini par l'objet [self]\"\"\"\n",
    "        pass\n",
    "    \n",
    "    @abstractmethod\n",
    "    def fillhitrecord(self, ray, t, hitrecord):\n",
    "        \"\"\"rempli les champs de [hitrecord] pour une collision avec [ray] à l'instant [t]\"\"\"\n",
    "        assert self.onsurface(ray.start+t*ray.direction)\n",
    "        pass\n",
    "    \n",
    "    def hitShadow(self, ray):\n",
    "        for (tb, te) in self.hits(ray):\n",
    "            if tb > 0 and not (isinf(tb)):\n",
    "                return True\n",
    "        return False\n",
    "    \n",
    "    def hit(self, ray, hitrecord):\n",
    "        t=0\n",
    "        for (tb, te) in self.hits(ray):\n",
    "            if tb > 0 and not (isinf(tb)):\n",
    "                t=tb\n",
    "                break\n",
    "        if t > 0:\n",
    "            if hitrecord.t and hitrecord.t < t:\n",
    "                return False\n",
    "            else:\n",
    "                self.fillhitrecord(ray, t, hitrecord)\n",
    "                return True\n",
    "        else:\n",
    "            return False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Des objets élémentaires\n",
    "\n",
    "Les feuilles d'un arbre CSG sont des objets élémentaires. Nous allons en créer de 3 sortes :\n",
    "* `CSGBall` la boule unité de volume $x^2+y^2+z^2 \\leqslant 1$ ;\n",
    "* `CSGCylinder` le cylindre plein de volume $x^2+y^2 \\leqslant 1$ ;\n",
    "* `CSGSlice` la tranche épaisse de plan de volume $z^2 \\leqslant 1$.\n",
    "\n",
    "À titre d'exemple voici le code de `CSGCylinder`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "inf = float('inf')\n",
    "\n",
    "class CSGCylinder(CSGShape):\n",
    "    def __init__(self, material=PhongMaterial()):\n",
    "        \"\"\"Le cylindre infini d'axe z passant en 0\"\"\"\n",
    "        self.name = \"Cylindre\"\n",
    "        self.material = material\n",
    "    \n",
    "    def hits(self, ray):\n",
    "        if isZero(ray.direction[0]) and isZero(ray.direction[1]):\n",
    "            # premier cas : si ray.direction est colinéaire à z\n",
    "            if self.inside(ray.start):\n",
    "                return [(-inf,inf)]\n",
    "            else:\n",
    "                return []\n",
    "        else:\n",
    "            # cas général : résoudre l'équation du second degré\n",
    "            xd=ray.direction[0]\n",
    "            yd=ray.direction[1]\n",
    "            xc=ray.start[0]\n",
    "            yc=ray.start[1]\n",
    "            a=xd*xd+yd*yd\n",
    "            b=2*(xc*xd+yc*yd)\n",
    "            c=xc*xc+yc*yc-1\n",
    "            l=solve2(a,b,c)\n",
    "            if l:\n",
    "                if type(l) is tuple:\n",
    "                    return [l]\n",
    "                else:\n",
    "                    return [(l,l)]\n",
    "            else:\n",
    "                return []\n",
    "    \n",
    "    def inside(self, point):\n",
    "        return point[0]*point[0]+point[1]*point[1] <= 1+G_EPSILON\n",
    "    \n",
    "    def onsurface(self, point):\n",
    "        return isZero(point[0]*point[0]+point[1]*point[1]-1)\n",
    "    \n",
    "    def fillhitrecord(self, ray, t, hitrecord):\n",
    "        hitrecord.t = t\n",
    "        hitrecord.point = ray.start + t * ray.direction\n",
    "        hitrecord.normal_g = Vec3(hitrecord.point[0],hitrecord.point[1],0)\n",
    "        hitrecord.normal = hitrecord.normal_g\n",
    "        hitrecord.material = self.material\n",
    "        hitrecord.color = Vec3(1,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 4.445464134216309s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 45098\n",
      "RAYS/s: 27420.75884984941\n",
      "##################################################\n"
     ]
    },
    {
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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"red\"]]\n",
    "\n",
    "scene.add(Plane(Vec3(0,0,0), Vec3(0,0,1), mat[0]))\n",
    "\n",
    "scene.add(CSGCylinder(mat[1]))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(0.,-10.,3.), Vec3(0.,0.,3.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(5,-10,10)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "**Q4** Complétez en ajoutant `CSGBall` et `CSGSlice`.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CSGBall(CSGShape):\n",
    "    def __init__(self, material=PhongMaterial()):\n",
    "        \"\"\"La boule de rayon 1 centrée en 0\"\"\"\n",
    "        # TODO : compléter\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 5.169564962387085s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 53440\n",
      "RAYS/s: 25193.60931676168\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"green\"]]\n",
    "\n",
    "scene.add(Plane(Vec3(0,0,-1), Vec3(0,0,1), mat[0]))\n",
    "\n",
    "scene.add(CSGBall(mat[1]))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(0.,-6.,2.), Vec3(0.,0.,1.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(2,-10,5)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CSGSlice(CSGShape):\n",
    "    def __init__(self, material=PhongMaterial()):\n",
    "        \"\"\"La tranche d'épaisseur 2 en z centrée en 0\"\"\"\n",
    "        # TODO : compléter\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 4.1874918937683105s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 53440\n",
      "RAYS/s: 31102.149760294207\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"blue\"]]\n",
    "\n",
    "scene.add(CSGSlice(mat[1]))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(0.,-6.,2.), Vec3(0.,0.,1.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(2,-10,5)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Des transformations affines\n",
    "\n",
    "Dans la représentation en arbre des objets volumiques, on ajoute des transformations affines de l'espace, représentées par des nœuds à un unique fils. L'objet fils subit la transformation décrite par une matrice $M$ pour engendrer l'objet père.\n",
    "\n",
    "La classe `CSGTransform` applique une transformation affine de l'espace, donnée sous la forme d'une matrice $M$ sur un objet CSG. Pour chacune des 4 méthodes associées à `CSGShape` il s'agit :\n",
    "* de traduire les coordonnées des points $P$ de l'espace du fils en coordonnées $M\\times P$ de l'espace du père;\n",
    "* de traduire les coordonnées des points $Q$ de l'espace du père en coordonnées $M^{-1}\\times Q$ de l'espace du fils.\n",
    "* ce sont les méthodes de l'objet transformé qui se chargent du gros du travail.\n",
    "\n",
    "On utilise les coordonnées homogènes (dimension 4) pour représenter les transformations affines de l'espace tridimensionnel.\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "**Q5** Prenez le temps de comprendre la méthode `hits` puis complétez les 3 méthodes manquantes.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyrt.math.matops import *\n",
    "from pyrt.math import Ray\n",
    "\n",
    "def inray(ray, invmat):\n",
    "    \"\"\"Transforme un rayon extérieur en un rayon intérieur\"\"\"\n",
    "    instart = invmat*ray.start\n",
    "    indirection = invmat*(ray.start+ray.direction)-instart\n",
    "    return Ray(instart, indirection)\n",
    "\n",
    "class CSGTransform(CSGShape):\n",
    "    def __init__(self, insider, matrix, name=\"Affine transform\"):\n",
    "        \"\"\"l'objet [insider] auquel on a appliqué la transformation affine [matrix]\"\"\"\n",
    "        self.insider=insider\n",
    "        self.matrix=matrix\n",
    "        self.invmat=inverse4(matrix)\n",
    "        self.name=name\n",
    "    \n",
    "    def hits(self, ray):\n",
    "        return self.insider.hits(inray(ray, self.invmat))\n",
    "    \n",
    "    # TODO: complétez\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "\n",
    "def CSGTranslate(insider,x,y,z): return CSGTransform(insider, createTranslation4(x,y,z), name=\"Translation(%s,%s,%s)\" % (str(x),str(y),str(z)))\n",
    "def CSGScale(insider,x,y,z): return CSGTransform(insider, createScale4(x,y,z), name=\"Scale(%s,%s,%s)\" % (str(x),str(y),str(z)))\n",
    "def CSGRotationX(insider,d): return CSGTransform(insider, createRotationX4(deg2rad(d)), name=\"RotationX(%s)\" % str(d))\n",
    "def CSGRotationY(insider,d): return CSGTransform(insider, createRotationY4(deg2rad(d)), name=\"RotationY(%s)\" % str(d))\n",
    "def CSGRotationZ(insider,d): return CSGTransform(insider, createRotationZ4(deg2rad(d)), name=\"RotationZ(%s)\" % str(d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 12.862857103347778s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 22896\n",
      "RAYS/s: 7750.688606658968\n",
      "##################################################\n"
     ]
    },
    {
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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"green\", \"red\", \"blue\", \"orange\"]]\n",
    "\n",
    "scene.add(CSGScale(CSGRotationX(CSGCylinder(mat[1]),90),0.5,0.5,0.5))\n",
    "scene.add(CSGScale(CSGCylinder(mat[2]),0.5,0.5,0.5))\n",
    "scene.add(CSGScale(CSGRotationY(CSGCylinder(mat[3]),90),0.5,0.5,0.5))\n",
    "scene.add(CSGScale(CSGBall(mat[4]),1.2,1.2,1.2))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(3.,-10.,3.), Vec3(0.,0.,0.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(5,-10,10)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 Des opérations booléennes\n",
    "\n",
    "Les classes `CSGUnion`, `CSGSubstract`, `CSGIntersection` réalisent des opérations booléennes entre deux objets. Le cœur algorithmique de ces classes réside dans l'écriture de la méthode `hits` qui combine les listes triées d'intervalles retournées par les méthodes `hits` de chacun des objets.\n",
    "\n",
    "À titre d'exemple, voici le code de `CSGIntersection`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def interlist(xs,ys):\n",
    "    \"\"\"calcule l'intersection de deux listes triées d'intervalles disjoints\"\"\"\n",
    "    zs=[]\n",
    "    while xs and ys:\n",
    "        (a,b)=xs[0]\n",
    "        (c,d)=ys[0]\n",
    "        if a < c:\n",
    "            if b < c:\n",
    "                xs.pop(0)\n",
    "            elif b < d:\n",
    "                zs.append((c,b))\n",
    "                xs.pop(0)\n",
    "            else:\n",
    "                zs.append((c,d))\n",
    "                ys.pop(0)\n",
    "        else:\n",
    "            if d < a:\n",
    "                ys.pop(0)\n",
    "            elif d < b:\n",
    "                zs.append((a,d))\n",
    "                ys.pop(0)\n",
    "            else:\n",
    "                zs.append((a,b))\n",
    "                xs.pop(0)\n",
    "    return zs \n",
    "\n",
    "class CSGIntersection(CSGShape):\n",
    "    def __init__(self, left, right):\n",
    "        self.left=left\n",
    "        self.right=right\n",
    "        self.name='Intersection'\n",
    "    \n",
    "    def hits(self, ray):\n",
    "        return interlist(self.left.hits(ray),self.right.hits(ray))\n",
    "        \n",
    "    def inside(self, point):\n",
    "        return self.left.inside(point) and self.right.inside(point)\n",
    "        \n",
    "    def onsurface(self, point):\n",
    "        return self.inside(point) and (self.left.onsurface(point) or self.right.onsurface(point))\n",
    "        \n",
    "    def fillhitrecord(self, ray, t, hitrecord):\n",
    "        point = ray.start+t*ray.direction\n",
    "        if self.left.onsurface(point):\n",
    "            self.left.fillhitrecord(ray, t, hitrecord)\n",
    "        else:\n",
    "            self.right.fillhitrecord(ray, t, hitrecord)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 14.273316144943237s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 29637\n",
      "RAYS/s: 7457.061759099941\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"green\", \"red\", \"blue\", \"orange\"]]\n",
    "\n",
    "sliceZ=CSGSlice(mat[1])\n",
    "sliceY=CSGRotationX(CSGSlice(mat[2]),90)\n",
    "sliceX=CSGRotationY(CSGSlice(mat[3]),90)\n",
    "objA=CSGIntersection(sliceY,sliceZ)\n",
    "objB=CSGIntersection(sliceX,objA)\n",
    "objC=CSGIntersection(CSGScale(CSGBall(mat[4]),1.2,1.2,1.2),objB)\n",
    "scene.add(CSGRotationX(CSGRotationZ(CSGScale(objC,3,3,3),20),-20))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(4.,-10.,3.), Vec3(0.,0.,0.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(5,-10,10)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\">\n",
    "**Q6** Complétez en écrivant le code de `CSGUnion` et `CSGSubstract`.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "class CSGUnion(CSGShape):\n",
    "    # TODO ALL    \n",
    "\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 16.635058164596558s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 48504\n",
      "RAYS/s: 7532.525510892251\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"green\", \"red\", \"blue\", \"orange\"]]\n",
    "\n",
    "sliceZ=CSGSlice(mat[1])\n",
    "sliceY=CSGRotationX(CSGSlice(mat[2]),90)\n",
    "sliceX=CSGRotationY(CSGSlice(mat[3]),90)\n",
    "objA=CSGIntersection(sliceY,sliceZ)\n",
    "objB=CSGIntersection(sliceX,objA)\n",
    "objC=CSGUnion(objB,CSGCylinder(mat[4]))\n",
    "scene.add(CSGRotationX(CSGRotationZ(CSGScale(objC,3,3,3),20),-20))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(4.,-10.,3.), Vec3(0.,0.,0.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(5,-10,10)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "class CSGSubstract(CSGShape):\n",
    "    # TODO ALL\n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 17.325556993484497s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 41935\n",
      "RAYS/s: 6853.170726035062\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"green\", \"red\", \"blue\", \"orange\"]]\n",
    "\n",
    "sliceZ=CSGSlice(mat[1])\n",
    "sliceY=CSGRotationX(CSGSlice(mat[2]),90)\n",
    "sliceX=CSGRotationY(CSGSlice(mat[3]),90)\n",
    "objA=CSGIntersection(sliceY,sliceZ)\n",
    "objB=CSGIntersection(sliceX,objA)\n",
    "objC=CSGSubstract(objB,CSGTranslate(CSGBall(mat[4]),0.5,-0.5,0.5))\n",
    "scene.add(CSGRotationX(CSGRotationZ(CSGScale(objC,3,3,3),20),-20))\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 45)\n",
    "camera.setView(Vec3(4.,-10.,3.), Vec3(0.,0.,0.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(0,-10,10)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Pour conclure avec CSG\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "**Q7** Il est temps maintenant de modéliser l'objet représenté sur la figure et de le mettre en scène. À vous de jouer !\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# RENDER STATISTICS###############################\n",
      "TIME FOR RENDERING: 18.811153173446655s\n",
      "NUMBER OF PRIMARY RAYS: 76800\n",
      "NUMBER OF SECONDARY RAYS: 0\n",
      "NUMBER OF SHADOW RAYS: 58656\n",
      "RAYS/s: 7200.834459803678\n",
      "##################################################\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img 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XRBuudWSLPIjD98/HA0+/s9PBNlvGpI/7Q3x7uvEVvx2aVXafOWOzi6Ezlk47cMUxUsgjAGGkrBBxFvzn7w6XZKimcW7diU/P+gjzDuX3vmZITZ7n0EjsMQP6YVxFPcEOgD0ue1HXDbKPhmr3mEfa0xAvvboE4ZDY26ySZtt8hzn0iH8cQjA3uReqPsh2wxmJJ0Phg25JArEWwsWX9VyfCBy28163tPX/t9Zfza0hu9TqMBVsHjKMozGsgfXMqNOZzMaAx955P6eNTF0gAnE1HC5tD/umIxapM1XbG/L25bp9BV9H0Q8XuXOZcWpcmYyQAsWX13ccjUbk1rNsN+i28QyYfqp1BhNjZFEDdAIipLnhv1OakSJtKf9jejn7InGcz98gmtjmkUnGfVHb3556KvzLOz7E/fQDPgM173pQmZWAmD+4q+4/JqQadkyf/YlP53xoWV3f65Hn2bvRgW2TJj+WmqMcgI3iBrO2waCEA3TvzSJdM6uNPmYD77KH1vcU+Cinx+7ZWd3NdewcOofB4+Eiqi0Mpg8f/FXxQItBI40jjvZZvFrlj3Rqw+1V6MptMfsHi79Y3ZfgML2UiIyhWCG7wwntJlXi9XgB0efIOdv32ductijCSB8/O4WZ62HwsIpH7DngeQ4PcSIFeC+JEUuR8w8/6mv5RVS7aQsrPqpQDeFZ8KM04hGkk2e3RC0CWcyCMPm0jVx2NPFxu2sa9iDFbZm4eT3OU1FJlsaeSY5aX/Q/Ke+HubL8mdIJykNy8X82VTzZY3AAFRgw7j+eY2RBxLFHWDrbYOEtF7gNh02dL2VKxfcJX+3hZPem15S0ZbGoWT+km9G7a0RuO0OsJntHwb/ePm9XxzqJ9z7UYEBYPzASTQiPQMsO71IX8M7DNBlo9qNBkPf3K1r6MWf9PKJ57t4mItapXEyA+Yv+VbyRi5wTQfYLZIW+lh/9VINwtoHtvjvuQ8X2zP523rgLze2J5fsgyfNtU/43PYj23Q4Oj/cFTUdXGo5RxtcPuk8mA/rTp/BDASAwnVp4S23zaIWAIz5S79d0b7O0K5vPSqwx98NA4b59l62VjMxsb9LMJhOJB0G0H4olpb1ar8c4uDV5RPfaYapXCxkP2rlr5AEfPjMNIa91Hn+sm+3/EztjGC1eEcBoAJHmAsgjLowdwSA2F4ZAbdL26skkDoMGI3pslGPd7jaiF28z14+4e12tXaE2VwHItJc521LjQHMXxa+VTD/IJQVL/rQQaGnK05fn/zDqq9rjPrPim4KABg/cDI1TAd4hBl2tpdwiBGsZBRaTEL0h+G7aZeOfLxXG3c4/kiXjXur7HImjXeekPAl6gxbFX3XFgBo/vLvQVha3wFe9Kez/LpF9ZHGp1y3QjTL1eFWq31gqMCG8QMn9W99ON4WtGHaayH2JvgrnoAqhwF3AwHCvn7pyMcwPBu6izovHbvA2Rq5Gh+A0IXG85f/QLSqTuDvrHjqNZ99vfwYZY1BaODU659Om6UCCzSFxti+4/q3PpyXT113FwHrp51mb631lxj7zDLKpc1CxMwUMk8C8ed3HGVeXTLyUfTU5DY7vZeOOduZRm4ojty9/qbVQLiYWdTu+vxRRo2KpDpQ+RG/s2KJeXHP5be95uLXiw0Jm4Yzmb6LPR52+9VN+w8qcJGwu/atuxPA+v7T7V7pb08iEg67W9WdCeGafrGvf37HUT6aXTLikbCmXnPJAWeGzB/2puFEVzdWZ16Tv4Iq0lh0d+34ALio8YIVP2zRJsJ3nb1uaXbm2zF+dusRQ/y460OzTrtpZaglf7V/owJjcNtiZDtEMtm39nYAGwZeDyS3GCYmtBvNvrDzlVGOSUSgLzX+s6P98ksjTxMJaJTJBz2comY6zhfcffhxIxEdg+JjE5BrPH/FdfU+fffpJYXScCWmuCbTxuJYY4fMpRWDCpxTeZ/q1DW3Adgw8IYo8FpjfVLaMpqJpBRRJP/r5rH+Mi/X15MXfgGhxCzpgjw5tSiEfXuCx2tpC8kJ4/IMZk4bSV6c6BiEgsbzV1wvlco33feK9nqcvAhHHP+x7Dt3fHDm6X/jvk5Z9Y3Rp1J2gDGpb82t9koPd8lHuPZDXAfiTyz7+3EBFB7UmCweJpHUz9EaTcUcqnXzRA9+hKszXkva8lA5EM/vH3UZ6hTtn7/ihvotVmevfOakr9tvoqgtbXb290c0Alu49uCeZtRrbgWwfuCMENAKHcuwZBzNoqQUAIvI6TrY5g1iP9Tko2U8bOZPQcseqeyig8j3LmtDscxp0y1SjMYLVt5UvcFAtfaefOHrxCrFWqsDslJEBW5Nldh9a25ZP3BGclEHQsfSK2TnL2tsX2YOw3Wws0zYrdHOFyfqBLKPvsrENldERvUAaeMjjaXe8Yrmr/xR/Ub72eCLg9NnhIUJqxetkjOET08IJpPP0V0zSuFX82iPCowlL2ybM2Zs1bv1+4pz2IU4RB3Llhq4opLDcF65ixmzoW9Zc3z6ygdnBF0hz/pEodgVyk/rV1HR/np+PviiWLf9Pf2UmSBDOMiFCt2YlZiQARmqbRHtA3cFhX99a29xHbW0Y5n2ipM+p/gKAttfZcgFQ5fY18+hRHaeQwc4XlfcqfaFUVfcLpo3kn3HOH1rwaof12ybor3udkwCYebph5hMpdTdRTThtxBkZQBwlV7FAUAjcMeUwkDf2lsBrO8/oxDN8o4l0mgmI6eMwy7wupS6buhbdonD2ZiQTov2FEKxqxw+o4ZMJewV4ebDLHjm72o2z88HX6q3lxpk1xU+e7SNSqk1if+VCBW4lrMPau5sMtsv+Bt527OmuLgj9a29ZX3/GVYrVGkAoKBx7HA8We4AV5bkBwWA7Gnh4nAXonKncfnpOec88/f5B/dz/aINe2ecepB0NPTK3dPgS6l1G1n7/oqm0ACw5IVtQLqb8JtnNXc0ucn+q3e3v25w++sGXz5toFgJAdPW3hIlwECaUfuTQ3FSGufDSNJjlvVUnr5CZYUunXaViRUlaXZNRu0WqaIde6lBcSvc+n3bAbHeMKVUoQLnuP1oZ1N8HZ/TjxmMl04tOwxg2tpbo15rSYO0b9mWw1GvVYgHX2deYaEwNj+qPOu9J+1f8Gwh/BpSewGU7B08aaaXNaxQGCsKg95KDSqwxQRhg91/muHbsZHu6vzia/pfOGVasappa2+11ZQ0cKmqEKzssNjHXbRM3EvEi670aBGKC1XFAslyY+9P6jZfYi+V7J03IzqqIG6IX3sxIMfoCJZHBY6I9hR22Z7Yk+MXeOGkGocLGqSBDjUOIwqYJWOjIJ+k0yI+l0JxfDgQx6d8FaLOMr+Y/lJLewdOmO6GEpIWBY3jgAz4BmkQrkYFLuKSWJE229iQisPbTuzbNm9qXsW0tbdVRTMkO6xQtBCHMz/zEqkrZIouYn5tKEZaHmt8zuqfVm2pX85obW//8YOuRVyjMWT3OGwlnPl/1vTuL7uvoQIHZBYNYORtq2ODONgBmbEyM54/Yao7NRyYtk44nGsMsbcm0pYdhigBxDzFyJnH/DQUpxpn5WAwn7PmH6u22AMfOvjQsw8P0yV7px07YI+ATbnFUo3rArJSjQqcwuKnl1a88EFOvmBmfu74yWTPgQSTp627PdLDa5zF0iRscmpshdXuaBKH4riVcbbMSWMgaosbacvrIRz65jnmRW5v3zH9ib2pxpm3Mot2x6oIfRCHRAWOEEHYBrli2hwbF/bCLcdNQtDX/u5fd3saHuOAHGW/scOF7JqjZSPxSqE4Oi64FQl1ECpPQrEJv2t/XrWtHvjwwXCf9JCz5nh7ydk79ZXTmBnNgr21Gqd59fD8qfcRVOACIQgHHQppc+kFb547cfMxExFpjP51d0RqxZJEymWBtCKdri7pOhRnGp+z7hdVm+jBDx8cJggADnrDofY65wZNPWralFf0wdjrNpo5nd6Gxm4SblKpRgVOkT3h0XevlflznDZH+TNLI8Cbj55gavBJdf+6O3yETAMyu0y14DCqHUYpnfY1AHFhFooL3siMmqtD34P/5RDR2w8vZpw6Cw2acmSf+aDcdJ+4CX8xTNBYiB1rLI+JfObP1sm1aP6coAKXYfkjyZ8hdEAhFJvlNr1ygq/NhOL+9XdGga4m8FbGYURxMo66DNukKJ12i0BKU6OxK3/L+v9Xt4GiB/j4D0mTD5/KIYrHLxKNm1GLhMZpjh9vRiVCBS7ggzADB9y7LpU2ChEyXNnAaMoA3nTUeF+nCcX96+9M89UqaUWgL+bSELluW+l0GvALGXW8ijI/XLk0LXIP+bH3CZpqnKviSBUFYbu6ZvxZM417+GfdJ1GBK4mDcIW0XiJwWEBMbnzFeFkngfrX35XEukqH/Vr9nJyVtJVOp9VWhWK/irds+KeaLXP3pbfaTyN+2Vvxme0VbH77NEMTUo3dtapohvzZa8xNvOmXG+R6NX/OUYHLyCB84O/Wx0GRhVCRroVJYOOR42TNBOpff7cXJvWw5HBFOi3CeDmdrg/FzplM47du+OeqzeLD792X3hrukTQfCwCBg4qRvaFdzeQ4Iwa64qRaZgGaPFehAley5IVtIgiHvSr1KNY1nrRabjwicRj96+8JzuRxmFMD6xyODyp1oTirJ8pfw/xlrlu5TE66OIzQISYK9obLyDnLqBOfuVJjgX6jdxEVuDUMjPnDRisOxE5p3pT2cmJvmGXD4dFTewjo33CPlDZy2EsrJOfM2A5DMaKMOs+cwQC/ZeOvKg3OuPuy28I4lkmhmyGFtm1MMuq4sTUan/VPm+SfQCmiAteRBWGxCyLRVYTgzF5TtOGw1OGBDfe2djiOzNLYPJ2uCsVpYSlzdvXDf2JJEn4991x2W/hE5BNmtl3Zqow6T6Qzjbv6i+13qMBtwcDY/9gUp83mV5Qqh+Jgb3gLwPrDxshqCRjYcE+InG4Hr0+eW6fTFYV1GTUzwG/d9OsuNs49l4s43LTesgzCSUYtUus4IYg1Flyj+XMFKnALZBAO/ydFLg47if1kFIeNL+vnJA7TwIZ7Eg/z5LnS6op0ujIUy3pk5f5Ak8HV4ddz78LbCeYROcFbL3OaUQurCxqDwXz2r7Z09/fa31CBW+MeuMPj/3Oz9DOx1/4Kk4Us2kyum32grN99N1rqcJRd51bXp9OFUJykrc0ko37r5t8MfVuZKzSiU0RVGXWTRTOzI4zgmmVPDr1h+yoqcFs4EzH+oS0IMmb2ht+V9oawLBjYuMifgQnS1gTe6nS6dSiO01Yxc5nrW4Vfw71X3kFkLGWfRUP8TDNqf4SJTjUBzGffvLWdNSpQgdskSqQL9joBOLc3vCXtXXdoEoQxsPG+VNoKh9MSZpizqy1DcbXG5265pTdbKoq6EbaxpYzaNdn6LPmKht9aVOB28Yn0hEe21KXKqb32tS/wlBxelDkshrWEqEn8bB2K84w6TluT+Osn2wy/9hM9tJblIFYehJuhsXl/2Lz4o99o+O0AFbgDhIxAVarcnr2GdYeknWHpcGWX2JY0kZSUQjHLvm4ho2661xWftiNEaK0IwmwaXuoP2xeyPg2/LVGBO8An0hMe3dpuRzcKygUSh2G/AMHG2yBbfTpdCMXNyNjajPrcrbcV29ZR+IVZU9wHzoNwMrglMmqA+Y9ueT5sNaUNVODO8In0xMe2tmmvL09xJdJh2xlGSVrfceW0pBSKqzLqZknjYvs6x6zKPo63KhRXZNTNqPfLwFc1/LaBCtwx0f4u7eWyvcXkuQYCDWy8z6a+UTrdLFht9v26UNyiY3zu83f2ZLMc+ubD4sRYRuM4FBczasaC28VDBTUGt4cK3DE+kZ74+HNOpKyjG/a/tvbEPJEe3PQ75si0OPA2I2OrQ3FdRu0bX2ro9as6z5/lUcJfwhEHZJM2R3k1+48WmvG15Rp+20IF7gbjMIMnPfE8UDdMVadvfI+cHJQ27wxu+p2rw44zicCLipGtNBS3yqh7Fumybq0IxSIg5wNd5iCz4K4XNeh2gQrcJf770CY9+TwSe5M9sZ0dk4D0xBLBWGEr8Q4jiGfTaf+OT+hZLpJ00MPhgPlt2+4tNvSGDsPvQWccGndra0Kx/Znm1YKvLV/c0dr3Z1Tg7hGWlO1t3feNniHtvhPUvQMgJNJ+VbGEbpXcwmF2JYXFe0FI2EVorQrF2ZznLHq5l43Zn1CBu8d3hicv3tZq3laQ+WJuWj97TFSaOgw3gmVmYBeAGVGhe4E6h9/2wqKhNhsAMOv0g30mXBphFjKXgvBbfhfZ+3UNv52gAg8J3xme/NQ2IIlqnJVUQO7pNARQertSXKGLrGH8iUMSHeIqu+Q7TgxSh7N2AOg8f45HmJNQXMyr4yAsUHs7RQUeKr4zbB12tJWhEuw3kSB6PuuaGaNkgQvCKA1omWLfGS45LM/0Sod7wYxTZxUHpcQ9DHWh+K3370APW7P/oQL3AJ+qdkYceF0hEWjkmFFhJgCRw3JAS4wkd+jw2178faftzZl+8szKQam6UGwLz31wp2sUA/iGht/OUYF7gO8MT1qSdYaLz1MkkLTXz0nkn5b++LbnkqVLA1o+fe7Y4aqmtc/giTPE+ekoCLcKxdF1Vxp7h4IK3BvCgJZzuFIP8t9gGNlrn47uSqYdP2AcjuHMYe7S4Qra7AAPvHp61JstDVDVhWLG2x6Jxuu/qeG3K1TgnhEGtKzD/uxQdKIoTZtt4M2iMaj/+MGoHmBw0+9hlQ2D0umZoW4dbj8g9x8/yImxIhTnATkPxW9/LKrwmyueanvlSoQK3EsShyMl3IkiIBU1+pIh57OZN3koPNzlWc5hcda3E4ff/tIDXX9G84XdydCUENX9rA7Fb3/Cfn5NnoeOCtxj/O1Kk5dsMxHXXayRj1elaXPkcyjJMW4OweGumHr0tL5jpgVRxSnfNCA3ZShGbHha7bc0/A4BFbj3eF1ELl0cr6LE55K9tCn+diUAA5t+H5/g7cLhzpjyir4pR/WZuJpFVN8xD2E5HdMSofgdTzUgWq/2DhEVuPe4AS0RbFoGXpE2+xL//+ajwjeVOrwx6MLh9j/LpMOnTD7CfWNoU0bUwrWTJiwXLrpyi7xj2QhZ+bfV3iGj3xo1XMwZM9aE3c3+Cxl8jEXrwCtmBYBJj4UnRRn/1kx+tVM/SO+Wi7+91x0LzI93bH84aYKbpJ+O3IhwHCG7nD/ekMsbyOYO9rRXVGiXipYlIsK7nh7tOhJ25d9RgYeMRuDhIpwcNldoycCbhdk6ewkgbH7lxKT+gY1/qInDleeW6qNvGEyOT/A2XXQPF1RFiXScTsdjWk2gye96erRfg0Ht7Qkq8DAiHS6eKHIKuxKSTofZKhMlZyk7e+QppZLDjFqDvYQILzKZ2XyjQkU6LW9mEFdBc2gwoPb2DhV4eAmP71j8fLtpc1ZoXm85OgvCm/4ge7zCYU6Cqe/6tgjBYSwKqJJZ9GmrAnIypnXeswfIlXxnxZJON6NShQo87ASHn3y+3bQZkb1EVSEYUlcEh8OoldPOzVk7guVm5OwIEEdgaW+rRPrda8a4hspfSm9QgXcFweEnnmsrbfb2UmR1KQjfDwAcR92ywy3yZ7OIzXdDVi6lFSlxoW8cj0s3wU1+97qxcpUMfPdpDb+9RAXeRfhzSxOecOPJdWmzszephQpxjGWAtQUibQ7yoaXD76O+EEWjmirz6iSdlo+qO39jehnZ99TeXqMC7zqCw49v7ThtdlJvPSYNwoObHyj3foGKLnEdYt40FHMkbakz7E4Un79l3Pmbg71mlWrvcKAC71KCw49tbTNtBpAG4oKDQbjS0HRIp9/ZrPymbM5raiMC5/a+57nxSZVQe4cNFXhX4254wPjHtox/dCvQOm2uh4GBzf8BAMK8rEvcegQrVFetLmcvZN8YjPdumyBrMj++r/YOGyrwbsA/hQfg8Y9ubZk2J2ydm2bRAHLzomy4zUEs4P0jp7nKWg1oZTK/94WJ+QrU3mFFBd49RA4/srl12lzxnhdmYPODwlgk6XQ0Ot0mLbLoKAK/7+XJ73tpUtQgAMD3n17awRqVzlGBdxvCYYx/eHP0Xr297t1Mx+iyjWI6/TPMbtkwG4T9OloNaL1v+5S4EZYfqL3DT6sOljLMzBkzFu7P8Pwxk0o9YOlpuNNg3IOb8tpWT5xLIZrb2xuc8bb8PCzzVWcrC2U/2bHOd2LdnY/+Wm57A8UH0CcbKiu6Vu3dJYzc3Q3Y31nywrY5B45lAoBxD28G8PzcSQCKfkX3CRVhZgIxOxkZTOyHu7mDI/b7R06zDjMYTCAzlk2gDzSm1i+r9u4yVODdz5IXt80+cCyR9WvcQ5ufnzvZvenDb3aXXxlrGwAyixLgzUPkcEud3z9yWnTJZ+38vrZrVy6trVXpJdoH3iNY+uI2dgkrA+Me2jTuoU019o59YGNeCQMDWx/xX+Ed+sBhPKpZfzNDJ2NcZn6OJ9XeXY0KvKfgHYYTadxDm8c9tDm3l0p/tLBoMNZ+k6f8cuC2TgVXU7/wD9XeXY4OYu1xmHTa4P88246b4u0d84co/HL8cvX4o9zdTuKeCdtrtuNY726sSup3FFLzllm0yc3V3t2CCrwnIh1GSbNsiSg0rh73ivgxOqnG7x7xTFVF5SvBKCsRXLdyWfFTKLsATaH3REw6LTPqOHfl7F+COf3btBdMcTNOqpvZ/FHVhZLq1Fnt3b1oBN5zmX3gWGRJbTt/sGfHHu76zSbimiBKLr4SgPNHrqmosHUWbaZU3T0BFXhPp6gxKv5yJlKuHnuYk05e1AHx4AAC4fyRa4v1VN5PIYqvV3v3DFTgvQDjMGrO/sasHjNbGouyyQDoPaPWlaqsC8Kq7h6FCrzX0L7Gzx54SLjcMc6cxSOj7c/3jt6QVVBeQ5tfXKjsSlTgvQnvsKHK5GcPOEhIG84gm4Vkj9ZMvPeATVkdoW71dk9GBd77SDRGNsj0zOgZ0T0HscwI11JXXo/J3Hxh46O9bLQyPKjAezG5yQCeGdXvTvlG3WCXPvu/uPzTmzsDmy9u1m/Z3stQgfcRRo3pBzUIDWts+G4iyB6vg1/aqomxoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoiiKoijKsPP/AeSuMhbqqnOuAAAAAElFTkSuQmCC\"></img>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scene = Scene()\n",
    "\n",
    "mat = [PhongMaterial(color=Vec3(color[i])) for i in [\"neutral 8\", \"green\", \"red\", \"blue\", \"orange\"]]\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "camera = PerspectiveCamera(width, height, 50)\n",
    "camera.setView(Vec3(3.,-10.,3.), Vec3(0.,0.,0.), Vec3(0.,0.,1.))\n",
    "scene.setCamera(camera)\n",
    "\n",
    "scene.addLight(PointLight(Vec3(5,-10,10)))\n",
    "scene.addLight(PointLight(Vec3(0,0,10)))\n",
    "scene.addLight(PointLight(Vec3(0,10,0)))\n",
    "scene.addLight(PointLight(Vec3(10,0,0)))\n",
    "image = engine.render(scene)\n",
    "image.display()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"text-align: right; font-size: 80%\"><a href=\"http://www.univ-orleans.fr/lifo/Members/Nicolas.Ollinger/\" style=\"text-decoration: none; color: black\">N.O.</a>, le 31 mai 2018</div>"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}