SPLINES_LATEX.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Code pstricks/tikz & matplotlib & Splines cubiques**\n",
    "\n",
    "La fonction comprend 5 éléments, donnés sous forme de listes :\n",
    "* celle de l'axe des x : min, max, pasprincipal, passecondaire ;\n",
    "* celle de l'axe des y : min, max, pasprincipal, passecondaire ;\n",
    "* la liste des abcsisses des points de la courbe ;\n",
    "* la liste des ordonnées des points de la courbe ;\n",
    "* la liste des pentes des tangentes aux points de la courbe.\n",
    "\n",
    "Les commandes suivantes sont utilisées dans le code pstricks (la grille doit être paramétrée pour \"coller\" aux bords !)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```latex\n",
    "\\usepackage{multido}\n",
    "\\usepackage{fp}\n",
    "\n",
    "\\newcommand\\defgrille[8]{%\n",
    "    \\def\\xmin{#1}\\def\\xmax{#2}\\def\\ymin{#5}\\def\\ymax{#6}%\n",
    "    \\def\\pasx{#3}\\def\\passx{#4}\\def\\pasy{#7}\\def\\passy{#8}%\n",
    "    \\FPeval{nbsx}{clip((\\xmax-\\xmin)/(\\passx)+1)}\\FPeval{nbsy}{clip((\\ymax-\\ymin)/(\\passy)+1)}%\n",
    "    \\FPeval{nbx}{clip((\\xmax-\\xmin)/(\\pasx)+1)}\\FPeval{nby}{clip((\\ymax-\\ymin)/(\\pasy)+1)}%\n",
    "}\n",
    "\n",
    "\\newcommand\\grilles[1]{%\n",
    "    \\multido{\\n=\\xmin+\\passx}{\\nbsx}{\\psline[#1](\\n,\\ymin)(\\n,\\ymax)}%\n",
    "    \\multido{\\n=\\ymin+\\passy}{\\nbsy}{\\psline[#1](\\xmin,\\n)(\\xmax,\\n)}\n",
    "}\n",
    "\n",
    "\\newcommand\\grillep[1]{%\n",
    "    \\multido{\\n=\\xmin+\\pasx}{\\nbx}{\\psline[#1](\\n,\\ymin)(\\n,\\ymax)}\n",
    "    \\multido{\\n=\\ymin+\\pasy}{\\nby}{\\psline[#1](\\xmin,\\n)(\\xmax,\\n)}\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (1.20.1)\n",
      "Requirement already satisfied: matplotlib in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (3.3.4)\n",
      "Requirement already satisfied: numpy>=1.15 in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (from matplotlib) (1.20.1)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (from matplotlib) (2.8.1)\n",
      "Requirement already satisfied: pillow>=6.2.0 in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (from matplotlib) (8.1.2)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (from matplotlib) (1.3.1)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.3 in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (from matplotlib) (2.4.7)\n",
      "Requirement already satisfied: six in c:\\users\\cpierquet\\miniconda3\\lib\\site-packages (from cycler>=0.10->matplotlib) (1.15.0)\n"
     ]
    }
   ],
   "source": [
    "#packages numpy et matplotlib au cas où !\n",
    "!pip install numpy\n",
    "!pip install matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#générateur code pstricks\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "#code pour les splines\n",
    "def splinepstricks(xa,ya,ypa,xb,yb,ypb):\n",
    "    A = np.array([[xa**3,xa**2,xa,1],[3*xa**2,2*xa,1,0],[xb**3,xb**2,xb,1],[3*xb**2,2*xb,1,0]])\n",
    "    B = np.array([ya,ypa,yb,ypb])\n",
    "    sol = np.linalg.solve(A,B)\n",
    "    print(f\"{round(sol[0],4)}*x^3+{round(sol[1],4)}*x^2+{round(sol[2],4)}*x+{round(sol[3],4)}\"+\"}\")\n",
    "\n",
    "#code pour les lignes de la grille\n",
    "def defgrillepstricks(X,Y):\n",
    "    xa, xb = X[0], X[1]\n",
    "    ya, yb = Y[0], Y[1]\n",
    "    pasx, passx = X[2], X[3]\n",
    "    pasy, passy = Y[2], Y[3]\n",
    "    chaine = \"\\\\defgrille{\"+str(xa)+\"}{\"+str(xb)+\"}{\"+str(pasx)+\"}{\"+str(passx)+\"}{\"+str(ya)+\"}{\"+str(yb)+\"}{\"+str(pasy)+\"}{\"+str(passy)+\"}\"\n",
    "    print(chaine)\n",
    "\n",
    "#code pour l'environnement pspicture\n",
    "def begpspicture(X,Y):\n",
    "    deb = \"\\\\begin{pspicture}(\"+str(X[0])+\",\"+str(Y[0])+\")(\"+str(X[1])+\",\"+str(Y[1])+\")\"\n",
    "    print(deb)\n",
    "    grilles = \"    \\\\grilles{linewidth=0.3pt,linecolor=orange!50}\"\n",
    "    grillep = \"    \\\\grillep{linewidth=0.6pt,linecolor=orange!50}\"\n",
    "    print(grilles)\n",
    "    print(grillep)\n",
    "\n",
    "#code pour les axes\n",
    "def axespstricks(X,Y):\n",
    "    axe = \"    \\\\psaxes[linewidth=1pt,Dx=\"+str(X[2])+\",Dy=\"+str(Y[2])+\"]{->}(0,0)(\"+str(X[0])+\",\"+str(Y[0])+\")(\"+str(X[1])+\",\"+str(Y[1])+\")\"\n",
    "    print(axe)\n",
    "\n",
    "#code pour l'environnement complet\n",
    "def codepstricks(X,Y,listeX,listeY,listeDer):\n",
    "    psset = \"\\\\psset{xunit=1cm,yunit=1cm,algebraic=true,tickwidth=1pt}\"\n",
    "    print(psset)\n",
    "    defgrillepstricks(X,Y)\n",
    "    begpspicture(X[0:2],Y[0:2])\n",
    "    axespstricks(X[0:3],Y[0:3])\n",
    "    nb_points = len(listeX)\n",
    "    for i in range(nb_points-1):\n",
    "        fonction = \"    \\\\psplot[linewidth=1.25pt,linecolor=red,plotpoints=200]{\"+str(listeX[i])+\"}{\"+str(listeX[i+1])+\"}{\"\n",
    "        print(fonction,end='')\n",
    "        splinepstricks(listeX[i],listeY[i],listeDer[i],listeX[i+1],listeY[i+1],listeDer[i+1])\n",
    "    fin = \"\\\\end{pspicture}\"\n",
    "    print(fin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On travaille dans le repère délimité par les points (-5,-3) et (8,4).\n",
    "Les graduations sont 1 en principal et 1 en secondaire pour les x et les y.\n",
    "La courbe doit passer par :\n",
    "* le point (-4,-1) avec une demie-tangente horizontale ;\n",
    "* le point (-2,-2) avec une tangente horizontale ;\n",
    "* le point (2,2) avec une tangente horizontale ;\n",
    "* le point (4,1) avec une tangente horizontale ;\n",
    "* le point (7,3) avec une tangente de pente 1.5.\n",
    "\n",
    "Voilà le résultat après compilation d'un fichier tex."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](./img/splines.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\psset{xunit=1cm,yunit=1cm,algebraic=true,tickwidth=1pt}\n",
      "\\defgrille{-5}{8}{1}{1}{-3}{4}{1}{1}\n",
      "\\begin{pspicture}(-5,-3)(8,4)\n",
      "    \\grilles{linewidth=0.3pt,linecolor=orange!50}\n",
      "    \\grillep{linewidth=0.6pt,linecolor=orange!50}\n",
      "    \\psaxes[linewidth=1pt,Dx=1,Dy=1]{->}(0,0)(-5,-3)(8,4)\n",
      "    \\psplot[linewidth=1.25pt,linecolor=red,plotpoints=200]{-4}{-2}{0.25*x^3+2.25*x^2+6.0*x+3.0}\n",
      "    \\psplot[linewidth=1.25pt,linecolor=red,plotpoints=200]{-2}{2}{-0.125*x^3+0.0*x^2+1.5*x+0.0}\n",
      "    \\psplot[linewidth=1.25pt,linecolor=red,plotpoints=200]{2}{4}{0.25*x^3+-2.25*x^2+6.0*x+-3.0}\n",
      "    \\psplot[linewidth=1.25pt,linecolor=red,plotpoints=200]{4}{7}{0.0185*x^3+-0.0556*x^2+-0.4444*x+2.4815}\n",
      "\\end{pspicture}\n"
     ]
    }
   ],
   "source": [
    "codepstricks([-5,8,1,1],[-3,4,1,1],[-4,-2,2,4,7],[-1,-2,2,1,3],[0,0,0,0,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Remarque**<br>\n",
    "Le code est facilement modifiable (couleurs, rajouts, etc) !<br>\n",
    "Les lignes relatives à la grille peuvent être enlevées et/ou modifiées.<br>\n",
    "Chaque portion de courbe peut également être modifiée !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# avec matplotlib\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def splineplotlib(xa,ya,ypa,xb,yb,ypb):\n",
    "    A = np.array([[xa**3,xa**2,xa,1],[3*xa**2,2*xa,1,0],[xb**3,xb**2,xb,1],[3*xb**2,2*xb,1,0]])\n",
    "    B = np.array([ya,ypa,yb,ypb])\n",
    "    sol = np.linalg.solve(A,B)\n",
    "    return sol\n",
    "\n",
    "def courbespline(X,Y,listeX,listeY,listeDer):\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(1, 1, 1)\n",
    "    \n",
    "    # les axes\n",
    "    plt.axis([X[0], X[1], Y[0], Y[1]])\n",
    "    ax.spines['left'].set_position('zero')\n",
    "    ax.spines['bottom'].set_position('zero')\n",
    "    ax.spines['right'].set_color('none')\n",
    "    ax.spines['top'].set_color('none')\n",
    "    ax.xaxis.set_ticks_position('bottom')\n",
    "    ax.yaxis.set_ticks_position('left')\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_xticks(np.arange(X[0], X[1], X[2]))\n",
    "    ax.set_yticks(np.arange(Y[0], Y[1], Y[2]))\n",
    "    \n",
    "    #code\n",
    "    nb_points = len(listeX)\n",
    "    for i in range(nb_points-1):\n",
    "        x = np.linspace(listeX[i],listeX[i+1],100)\n",
    "        coeff = splineplotlib(listeX[i],listeY[i],listeDer[i],listeX[i+1],listeY[i+1],listeDer[i+1])\n",
    "        plt.plot(x,coeff[0]*x**3+coeff[1]*x**2+coeff[2]*x+coeff[3])\n",
    "    \n",
    "    #affichage\n",
    "    plt.grid()\n",
    "    return plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "courbespline([-5,8,1,1],[-3,4,1,1],[-4,-2,2,4,7],[-1,-2,2,1,3],[0,0,0,0,1.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec TiKZ, on peut avoir besoin des commandes suivantes\n",
    "\n",
    "```latex\n",
    "\\newcommand\\tunits[2]{%\n",
    "    \\def\\xunit{#1}\\def\\yunit{#2}\n",
    "}\n",
    "\n",
    "\\newcommand\\tdefgrille[8]{%\n",
    "    \\def\\xmin{#1}\\def\\xmax{#2}\\def\\ymin{#5}\\def\\ymax{#6}\n",
    "    \\def\\xgrille{#3}\\def\\xgrilles{#4}\\def\\ygrille{#7}\\def\\ygrilles{#8}\n",
    "\n",
    "}\n",
    "\n",
    "\\newcommand\\tgrilles[1][ultra thin,lightgray]{%\n",
    "    \\draw[xstep=\\xgrilles,ystep=\\ygrilles,#1] (\\xmin,\\ymin) grid (\\xmax,\\ymax)\n",
    "}\n",
    "\\newcommand\\tgrillep[1][thin,gray]{%\n",
    "    \\draw[xstep=\\xgrille,ystep=\\ygrille,#1] (\\xmin,\\ymin) grid (\\xmax,\\ymax)\n",
    "}\n",
    "\n",
    "% ========= DEF DES CLES AXES =========\n",
    "\\define@key{tikzaxex}{Ox}{\\def\\axex@Ox{#1}}\n",
    "\\define@key{tikzaxex}{width}{\\def\\axex@width{#1}}\n",
    "\\define@key{tikzaxex}{size}{\\def\\axex@size{#1}}\n",
    "\n",
    "\\define@key{tikzaxey}{Oy}{\\def\\axey@Oy{#1}}\n",
    "\\define@key{tikzaxey}{width}{\\def\\axey@width{#1}}\n",
    "\\define@key{tikzaxey}{size}{\\def\\axey@size{#1}}\n",
    "\n",
    "\\define@key{tikzaxes}{width}{\\def\\axes@width{#1}}\n",
    "\\define@key{tikzaxes}{labelx}{\\def\\axes@labelx{#1}}\n",
    "\\define@key{tikzaxes}{labely}{\\def\\axes@labely{#1}}\n",
    "\\define@key{tikzaxes}{poslabelx}{\\def\\axes@poslabelx{#1}}\n",
    "\\define@key{tikzaxes}{poslabely}{\\def\\axes@poslabely{#1}}\n",
    "\\define@key{tikzaxes}{echellefleche}{\\def\\axes@echellefleche{#1}}\n",
    "\\define@key{tikzaxes}{typefleche}{\\def\\axes@typefleche{#1}}\n",
    "\n",
    "% ========= CLES PAR DEFAUT =========\n",
    "\\setkeys{tikzaxex}{Ox=0,width=1.25pt,size=\\normalsize}\n",
    "\\setkeys{tikzaxey}{Oy=0,width=1.25pt,size=\\normalsize}\n",
    "\\setkeys{tikzaxes}{width=1.25pt,labelx=,labely=,poslabelx=right,poslabely=above,echellefleche=1,typefleche=>}\n",
    "\n",
    "% ========= COMMANDES AXES ==========\n",
    "\\newcommand\\axextikz[2][]{%\n",
    "    \\setkeys{tikzaxex}{#1}% on paramètres les nouvelles clés\n",
    "    \\foreach \\x in {#2}\n",
    "        \\draw[line width=\\axex@width] (\\x-\\axex@Ox,4pt) -- (\\x-\\axex@Ox,-4pt) node[below] {\\axex@size \\np{\\x}}\n",
    "}\n",
    "\n",
    "\\newcommand{\\axeytikz}[2][]{%\n",
    "    \\setkeys{tikzaxey}{#1}% on paramètres les nouvelles clés\n",
    "    \\foreach \\y in {#2}\n",
    "        \\draw[line width=\\axey@width] (4pt,\\y-\\axey@Oy) -- (-4pt,\\y-\\axey@Oy) node[left] {\\axey@size \\np{\\y}}\n",
    "}\n",
    "\n",
    "\\newcommand\\axestikz{\\@ifstar{\\axestikz@star}{\\axestikz@nostar}}\n",
    "\n",
    "\\newcommand\\axestikz@nostar[1][]{%\n",
    "    \\setkeys{tikzaxes}{#1}% on paramètres les nouvelles clés\n",
    "    \\draw[line width=\\axes@width,-{\\axes@typefleche[scale=\\axes@echellefleche]}] (\\xmin,0) -- (\\xmax,0) node[\\axes@poslabelx] {\\axes@labelx} ;\n",
    "    \\draw[line width=\\axes@width,-{\\axes@typefleche[scale=\\axes@echellefleche]}] (0,\\ymin) -- (0,\\ymax) node[\\axes@poslabely] {\\axes@labely}\n",
    "}\n",
    "\n",
    "\\newcommand\\axestikz@star[1][]{%\n",
    "    \\setkeys{tikzaxes}{#1}% on paramètres les nouvelles clés\n",
    "    \\draw[line width=\\axes@width,-{\\axes@typefleche[scale=\\axes@echellefleche]}] (\\xmin,0) -- (\\xmax,0) ;\n",
    "    \\draw[line width=\\axes@width,-{\\axes@typefleche[scale=\\axes@echellefleche]}] (0,\\ymin) -- (0,\\ymax)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#codes splines TiKZ\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "#code pour les splines en version gnuplot\n",
    "def splinegnuplot(xa,ya,ypa,xb,yb,ypb):\n",
    "    A = np.array([[xa**3,xa**2,xa,1],[3*xa**2,2*xa,1,0],[xb**3,xb**2,xb,1],[3*xb**2,2*xb,1,0]])\n",
    "    B = np.array([ya,ypa,yb,ypb])\n",
    "    sol = np.linalg.solve(A,B)\n",
    "    print(f\"{round(sol[0],4)}*x**3+{round(sol[1],4)}*x**2+{round(sol[2],4)}*x+{round(sol[3],4)}\"+\"} ;\")\n",
    "\n",
    "#code pour les splines en version pgf\n",
    "def splinepgf(xa,ya,ypa,xb,yb,ypb):\n",
    "    A = np.array([[xa**3,xa**2,xa,1],[3*xa**2,2*xa,1,0],[xb**3,xb**2,xb,1],[3*xb**2,2*xb,1,0]])\n",
    "    B = np.array([ya,ypa,yb,ypb])\n",
    "    sol = np.linalg.solve(A,B)\n",
    "    print(f\"{round(sol[0],4)}*\\\\x*\\\\x*\\\\x+{round(sol[1],4)}*\\\\x*\\\\x+{round(sol[2],4)}*\\\\x+{round(sol[3],4)}\"+\"}) ;\")\n",
    "    \n",
    "#code pour l'env tikz\n",
    "def defgrilletikz(X,Y,units):\n",
    "    xa, xb = X[0], X[1]\n",
    "    ya, yb = Y[0], Y[1]\n",
    "    pasx, passx = X[2], X[3]\n",
    "    pasy, passy = Y[2], Y[3]\n",
    "    tunits = \"\\\\tunits{\" + str(units[0]) + \"}{\" + str(units[1]) + \"}\"\n",
    "    print(tunits)\n",
    "    chaine = \"\\\\tdefgrille{\"+str(xa)+\"}{\"+str(xb)+\"}{\"+str(pasx)+\"}{\"+str(passx)+\"}{\"+str(ya)+\"}{\"+str(yb)+\"}{\"+str(pasy)+\"}{\"+str(passy)+\"}\"\n",
    "    print(chaine)\n",
    "    print(r\"\\begin{tikzpicture}[x=\\xunit cm,y=\\yunit cm]\")\n",
    "\n",
    "#code pour grilles/axes\n",
    "def begtikz(X,Y):\n",
    "    print(f\"    %grilles & axes\")\n",
    "    grilles = r\"    \\tgrilles[line width=0.3pt,lightgray!50] ;\"\n",
    "    grillep = r\"    \\tgrillep[line width=0.6pt,lightgray!50] ;\"\n",
    "    print(grilles)\n",
    "    print(grillep)\n",
    "\n",
    "#code pour les axes\n",
    "def axestikz(X,Y):\n",
    "    print(r\"    \\axestikz* ;\")\n",
    "    axex = \"    \\\\axextikz[]{\" + str(X[0]) + \",\" + str(X[0]+X[2]) + \",...,\" + str(X[1]-X[2]) + \"} ;\"\n",
    "    axey = \"    \\\\axeytikz[]{\" + str(Y[0]) + \",\" + str(Y[0]+Y[2]) + \",...,\" + str(Y[1]-Y[2]) + \"} ;\"\n",
    "    print(axex)\n",
    "    print(axey)\n",
    "\n",
    "#code pour l'environnement complet\n",
    "def codetikz(X,Y,listeX,listeY,listeDer,units):\n",
    "    defgrilletikz(X,Y,units)\n",
    "    begtikz(X[0:2],Y[0:2])\n",
    "    axestikz(X[0:3],Y[0:3])\n",
    "    print(r\"    \\clip (\\xmin,\\ymin) rectangle (\\xmax,\\ymax) ; %on restreint les fonctions à la fenêtre\")\n",
    "    nb_points = len(listeX)\n",
    "    print(r\"    %les splines en gnuplot\")\n",
    "    for i in range(nb_points-1):\n",
    "        fonction = \"    \\\\draw[line width=1.25pt,red,samples=200,domain=\" +str(listeX[i])+\":\"+str(listeX[i+1])+\"] plot function{\"\n",
    "        print(fonction,end='')\n",
    "        splinegnuplot(listeX[i],listeY[i],listeDer[i],listeX[i+1],listeY[i+1],listeDer[i+1])\n",
    "    print(r\"    %les splines en pgf\")\n",
    "    for i in range(nb_points-1):\n",
    "        fonction = \"    \\\\draw[line width=1.25pt,red,samples=200,domain=\" +str(listeX[i])+\":\"+str(listeX[i+1])+\"] plot(\\\\x,{\"\n",
    "        print(fonction,end='')\n",
    "        splinepgf(listeX[i],listeY[i],listeDer[i],listeX[i+1],listeY[i+1],listeDer[i+1])\n",
    "    fin = \"\\\\end{tikzpicture}\"\n",
    "    print(fin)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\tunits{1}{1}\n",
      "\\tdefgrille{-5}{8}{1}{1}{-3}{4}{1}{1}\n",
      "\\begin{tikzpicture}[x=\\xunit cm,y=\\yunit cm]\n",
      "    %grilles & axes\n",
      "    \\tgrilles[line width=0.3pt,lightgray!50] ;\n",
      "    \\tgrillep[line width=0.6pt,lightgray!50] ;\n",
      "    \\axestikz* ;\n",
      "    \\axextikz[]{-5,-4,...,7} ;\n",
      "    \\axeytikz[]{-3,-2,...,3} ;\n",
      "    clip (\\xmin,\\ymin rectangle (\\xmax,\\ymax) ; %on restreint les fonctions à la fenêtre\n",
      "    %les splines en gnuplot\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=-4:-2] plot function{0.25*x**3+2.25*x**2+6.0*x+3.0} ;\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=-2:2] plot function{-0.125*x**3+0.0*x**2+1.5*x+0.0} ;\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=2:4] plot function{0.25*x**3+-2.25*x**2+6.0*x+-3.0} ;\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=4:7] plot function{0.0185*x**3+-0.0556*x**2+-0.4444*x+2.4815} ;\n",
      "    %les splines en pgf\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=-4:-2] plot(\\x,{0.25*\\x*\\x*\\x+2.25*\\x*\\x+6.0*\\x+3.0}) ;\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=-2:2] plot(\\x,{-0.125*\\x*\\x*\\x+0.0*\\x*\\x+1.5*\\x+0.0}) ;\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=2:4] plot(\\x,{0.25*\\x*\\x*\\x+-2.25*\\x*\\x+6.0*\\x+-3.0}) ;\n",
      "    \\draw[line width=1.25pt,red,samples=200,domain=4:7] plot(\\x,{0.0185*\\x*\\x*\\x+-0.0556*\\x*\\x+-0.4444*\\x+2.4815}) ;\n",
      "\\end{tikzpicture}\n"
     ]
    }
   ],
   "source": [
    "codetikz([-10,12,2,2],[-4,],[-4,-2,2,4,7],[-1,-2,2,1,3],[0,0,0,0,1.5],[1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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