{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 8 : Application : Etude de la chute d'une balle lachée par un cycliste en mouvement"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ":download:`Télécharger le pdf <./chute_balle_cycliste.pdf>` |\n",
    ":download:`Télécharger le notebook <./chute_balle_cycliste.ipynb>`,\n",
    ":download:`le fichier csv <./chute_balle.csv>` et \n",
    ":download:`la video <./cycliste.avi>` |\n",
    ":download:`Lancer le notebook sur binder (lent) <https://mybinder.org/v2/gl/pyspc%2Fpyspc-formation/master?filepath=etape_08%2Fchute_balle_cycliste%2Fchute_balle_cycliste.ipynb>`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "def charge_fichier_csv(cheminfichier, delimiter=\";\",N=0):\n",
    "    with open(cheminfichier, 'r', encoding='utf-8') as f :\n",
    "        rfichier = csv.reader(f, delimiter=delimiter)\n",
    "        tab=[]\n",
    "        index_row=0\n",
    "        for row in rfichier:            \n",
    "            if index_row < N:\n",
    "                index_row = index_row+1\n",
    "            else : \n",
    "                for i in range (len(row)): \n",
    "                    if len(tab) <= i:\n",
    "                        X = []       \n",
    "                        tab.append(X) \n",
    "                    try:\n",
    "                        tab[i].append(float(row[i].replace(\",\",'.')))    \n",
    "                    except ValueError:\n",
    "                        print('erreur:contenu de cellule non numérique')\n",
    "                        continue\n",
    "            \n",
    "    return tab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_polynome_deg2(u,v):\n",
    "    u=np.array(u)\n",
    "    v=np.array(v)\n",
    "    coeff=np.polyfit(u,v,2)\n",
    "    vmodel=coeff[0]*u**2+coeff[1]*u+coeff[2]\n",
    "    return vmodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def derivee(t,u):\n",
    "    du=[]\n",
    "    for i in range (len(u)-1):\n",
    "        dui=(u[i+1]-u[i])/(t[i+1]-t[i])\n",
    "        du.append(dui)\n",
    "    return du"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def graphvect(x,y,ymodel,vx,vy):\n",
    "    fig = plt.figure(1,figsize=(10,12))\n",
    "    plt.plot(x,y,'r+',label='y=f(x)')\n",
    "    plt.plot(x,ymodel,'g-',label='modèle polynôme de degré 2')\n",
    "    plt.xlim(0,max(x)+0.5)\n",
    "    plt.ylim(0,max(y)+0.5)\n",
    "    plt.grid()\n",
    "    plt.xlabel(\"x(m)\")\n",
    "    plt.ylabel(\"y(m)\")\n",
    "    plt.legend()\n",
    "    for i in range (len (vx)) :\n",
    "        plt.arrow(x[i],y[i],0.03*vx[i],0.03*vy[i],fc='b',\n",
    "                  ec='b',head_width=0.02,\n",
    "                  length_includes_head=True)\n",
    "    plt.title(\"Modélisation et tracé des vecteurs vitesse instantanée\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.76, 0.8, 0.84, 0.88, 0.92, 0.96, 1.0, 1.04, 1.08, 1.12, 1.16, 1.2, 1.24, 1.28, 1.32, 1.36]\n",
      "[0.00865710739046, 0.106770991149, 0.204884874908, 0.302998758666, 0.398226939961, 0.493455121256, 0.588683302551, 0.675254376456, 0.767596855287, 0.857053631656, 0.946510408024, 1.03019577946, 1.11676685337, 1.19756652235, 1.27836619132, 1.36205156277]\n",
      "[1.98247759242, 1.97093478256, 1.94496346039, 1.89590651851, 1.83530676678, 1.7545070978, 1.66216461897, 1.55827933028, 1.43707982682, 1.29568040611, 1.15139528293, 0.984024540049, 0.807996689776, 0.605997517332, 0.403998344888, 0.187570660127]\n",
      "[1.97254171 1.96885614 1.94560635 1.90279235 1.84252803 1.7638334\n",
      " 1.66670847 1.56241984 1.43438997 1.29383467 1.13701536 0.97558948\n",
      " 0.7936194  0.61003832 0.41318878 0.19532115]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tableau = charge_fichier_csv(\"chute_balle.csv\",delimiter=\";\",N=1)\n",
    "t=tableau[0]\n",
    "print(t)\n",
    "x=tableau[1]\n",
    "print(x)\n",
    "y=tableau[2]\n",
    "print(y)\n",
    "ymodel=model_polynome_deg2(x,y)\n",
    "print(ymodel)\n",
    "vx=derivee(t,x)\n",
    "vy=derivee(t,y)\n",
    "graphvect(x,y,ymodel,vx,vy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Format de la Cellule Texte Brut",
  "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}