CoordinateSystem_Cylindrical2Cartesian.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bingsen-wang/Math/blob/main/CoordinateSystem_Cylindrical2Cartesian.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jAMKoELNpsK-"
      },
      "source": [
        "<center><h1><b>Cylindrical vs Cartesian Coordinate System</h1></b>\n",
        "\n",
        "Dr. Bingsen Wang\n",
        "\n",
        "4//2025\n",
        "</center>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hv0YxDrWU4h8"
      },
      "source": [
        "#Python Code"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 75,
      "metadata": {
        "id": "XeGsHYTt8IXU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "2ed8c468-70ca-4c4e-8313-ae55ce739043"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0\n",
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            "150\n",
            "200\n",
            "250\n",
            "300\n",
            "350\n",
            "400\n",
            "450\n",
            "0\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x900 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from matplotlib import pyplot,animation,cm,patches,path\n",
        "import numpy as np\n",
        "pyplot.rcParams.update({\"font.family\":\"sans-serif\", \"mathtext.fontset\":\"cm\"})\n",
        "def d32(xyz):\n",
        "  theta=np.pi/4\n",
        "  x=xyz[1]-xyz[0]*np.sin(theta)\n",
        "  y=xyz[2]-xyz[0]*np.cos(theta)\n",
        "  return np.array([x,y])\n",
        "Nf=500\n",
        "r=.4\n",
        "phi=np.linspace(0,np.pi*2,Nf)\n",
        "x=r*np.cos(phi-np.pi/10)*.5\n",
        "y=r*np.sin(phi)\n",
        "phi1=np.linspace(0,np.pi,Nf)\n",
        "x1=r*np.cos(phi1-np.pi/10)*.5\n",
        "y1=r*np.sin(phi1)\n",
        "z1=x*0\n",
        "z2=.5+x*0\n",
        "arc1=[d32([x[k],y[k],0]) for k in range(len(phi))] #points\n",
        "arc1x=[d32([x[k],0,0]) for k in range(len(phi))] #points\n",
        "arc1y=[d32([0,y[k],0]) for k in range(len(phi))] #points\n",
        "arc1phi=[d32([x1[k],y1[k],0]) for k in range(len(phi))] #points\n",
        "arc1line=d32([x,y,z1]) #line\n",
        "arc2=[d32([x[k],y[k],.5]) for k in range(len(phi))] #points\n",
        "\n",
        "cl = list(cm.tab10.colors) #colors of lines\n",
        "fig = pyplot.figure(figsize=([9,9]))\n",
        "xlim=[-.5,.6];ylim=[-.3,.8]\n",
        "ax = fig.add_axes([0,0,1,1],xlim=xlim,ylim=ylim)\n",
        "ax.axis('off')\n",
        "pmax=[d32((.3,0,0)),d32((0,.5,0)),d32((0,0,.7))]\n",
        "pmin=[d32((-.3,0,0)),d32((0,-.45,0)),d32((0,0,0))]\n",
        "[ax.annotate('',pmax[k],pmin[k],arrowprops=dict(arrowstyle='->',lw=1.5,color='k')) for k in range(3)] #x,y,z-axis\n",
        "# [ax.text(pmax[k][0],pmax[k][1],[r'$x$',r'$y$',r'$z$'][k],size=25,va=['top','top','center'][k],ha=['center','right','left'][k]) for k in range(3)]\n",
        "ax.text(0,.5,'$z=z$',size=25,va='center')\n",
        "lines = [ax.plot([],[],c=cl[k],lw=[3,5,3][k])[0] for k in range(3)]\n",
        "lines += [ax.plot([],[],c=cl[1],lw=2)[0]]\n",
        "lines += [ax.plot([],[],'--',c=cl[0],lw=1.5)[0] for k in range(3)]\n",
        "lines += [ax.plot([],[],c='.7',lw=2)[0]]\n",
        "txts=[ax.text(0,0,[r'$\\rho$',r'$\\varphi$','$z$'][k],c=cl[k],size=25,va='center',ha='left') for k in range(3)]\n",
        "# txts=[ax.text(0,0,[r'$\\rho=\\sqrt{x^2+y^2}$',r'$\\varphi=\\arctan\\left(\\frac{y}{x}\\right)$','$z=z$'][k],c=cl[k],size=25,va='center',ha='left') for k in range(3)]\n",
        "txts+=[ax.text(0,0,r'$P\\ (\\rho,\\varphi,z)$',size=35,va='center')]\n",
        "txts+=[ax.text(0,0,[r'$x=\\rho\\cos\\varphi$',r'$y=\\rho\\sin\\varphi$'][k],size=25,ha=['left','center'][k],va=['center','top'][k]) for k in range(2)]\n",
        "pointP=ax.scatter(0,0,s=120,marker='o',c='k',zorder=4)\n",
        "def animate(i):\n",
        "  # i=50\n",
        "  if i%50==0: print(i)\n",
        "  pointP.set_offsets(arc2[i])\n",
        "  lines[0].set_data([0,arc1[i][0]],[0,arc1[i][1]])\n",
        "  lines[1].set_data(arc1line[0][:i+1],arc1line[1][:i+1])\n",
        "  lines[2].set_data([arc1[i][0],arc2[i][0]],[arc1[i][1],arc2[i][1]])\n",
        "  lines[3].set_data(.2*arc1line[0][:i+1],.2*arc1line[1][:i+1])\n",
        "  lines[4].set_data([arc2[i][0],0],[arc2[i][1],.5])\n",
        "  lines[5].set_data([arc1[i][0],arc1x[i][0]],[arc1[i][1],arc1x[i][1]])\n",
        "  lines[6].set_data([arc1[i][0],arc1y[i][0]],[arc1[i][1],arc1y[i][1]])\n",
        "  lines[7].set_data([arc2[i][0],0],[arc2[i][1],0])\n",
        "  txts[0].set_position((arc1[i][0]/2,arc1[i][1]/2))\n",
        "  txts[1].set_position((arc1phi[i][0]*.3,arc1phi[i][1]*.3))\n",
        "  txts[2].set_position(((arc1[i][0]+arc2[i][0])/2,(arc1[i][1]+arc2[i][1])/2))\n",
        "  txts[3].set_position((arc2[i][0],arc2[i][1]))\n",
        "  txts[4].set_position((arc1x[i][0],arc1x[i][1]))\n",
        "  txts[5].set_position((arc1y[i][0],arc1y[i][1]))\n",
        "  # txts[1].set_position((arc1[i][0],arc1[i][1]))\n",
        "  return\n",
        "ax.text(np.average(ax.get_xlim()),ax.get_ylim()[0]*.99+ax.get_ylim()[1]*.01,r'@eeanimation',size=12,c='.2',alpha=.3,ha='center',va='bottom')\n",
        "anim = animation.FuncAnimation(fig, animate, frames=len(phi), interval=20)\n",
        "anim.save(\"cyl2cart.mp4\",writer=animation.FFMpegWriter(fps=50),dpi=200)"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "g-lRWq8pQZ5x"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}