{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from biot_savart_v4_3 import parse_coil, plot_coil, slice_coil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# COIL = '6'\n",
    "COIL = \"12\"\n",
    "\n",
    "# load up the simple spiral coil\n",
    "coil1 = parse_coil(f\"coils/coil_{COIL}_spiral.csv\")\n",
    "plot_coil(f\"coils/coil_{COIL}_spiral.csv\")\n",
    "coil1 = slice_coil(coil1, 0.01)\n",
    "coil1 = coil1.T\n",
    "print(coil1.shape)\n",
    "\n",
    "coil2 = parse_coil(f\"coils/coil_{COIL}_custom.csv\")\n",
    "plot_coil(f\"coils/coil_{COIL}_custom.csv\")\n",
    "coil2 = slice_coil(coil2, 0.01)\n",
    "coil2 = coil2.T\n",
    "print(coil2.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# show a simple dipole magnet\n",
    "# magnetic field at a point x,y,z of a dipole magnet with moment m in the z direction\n",
    "def dipole(x, y, z, m=0.185):\n",
    "    mu0 = 1e-7 / 4 * np.pi\n",
    "    r = np.sqrt(x**2 + y**2 + z**2)\n",
    "    return (\n",
    "        np.array(\n",
    "            [3 * x * z / r**5, 3 * y * z / r**5, (3 * z**2 / r**5 - 1 / r**3)]\n",
    "        )\n",
    "        * m\n",
    "        * mu0\n",
    "    )\n",
    "\n",
    "\n",
    "def plot_field_slice(x, y, bx, by, mag, name=\"magnetic_field.png\", draw_magnet=True):\n",
    "    # plot the magnetic field\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.streamplot(\n",
    "        x,\n",
    "        y,\n",
    "        bx,\n",
    "        by,\n",
    "        linewidth=1,\n",
    "        cmap=plt.cm.inferno,\n",
    "        density=2,\n",
    "        arrowstyle=\"->\",\n",
    "        arrowsize=1.5,\n",
    "    )\n",
    "\n",
    "    ax.set_xlabel(\"$x$\")\n",
    "    ax.set_ylabel(\"$y$\")\n",
    "    ax.set_xlim(-0.1, 0.1)\n",
    "    ax.set_ylim(-0.1, 0.1)\n",
    "    ax.set_aspect(\"equal\")\n",
    "\n",
    "    # plot the magniture of the field as an image\n",
    "    im = ax.imshow(\n",
    "        mag, extent=[-0.1, 0.1, -0.1, 0.1], origin=\"lower\", cmap=plt.cm.inferno\n",
    "    )\n",
    "    if draw_magnet:\n",
    "        # draw the magnet\n",
    "        ax.add_patch(\n",
    "            plt.Rectangle((-0.005, -0.0015), 0.01, 0.003, fc=\"w\", ec=\"k\", lw=1)\n",
    "        )\n",
    "\n",
    "    # make the figure bigger\n",
    "    fig.set_size_inches(10, 10)\n",
    "\n",
    "    fig.show()\n",
    "    # save the figure\n",
    "    fig.savefig(name)\n",
    "\n",
    "\n",
    "# # calculate the magnetic field at y = 0, over z = -1, 1 and x = -1, 1\n",
    "x = np.linspace(-0.1, 0.1, 100)\n",
    "z = np.linspace(-0.1, 0.1, 100)\n",
    "X, Z = np.meshgrid(x, z)\n",
    "Bx, By, Bz = dipole(X, 0, Z)\n",
    "\n",
    "print(Bx.shape, By.shape, Bz.shape)\n",
    "\n",
    "plot_field_slice(\n",
    "    X,\n",
    "    Z,\n",
    "    Bx,\n",
    "    Bz,\n",
    "    np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
    "    \"dipole_field_side.png\",\n",
    "    False,\n",
    ")\n",
    "\n",
    "# # calculate the magnetic field at z = 1, over y = -1, 1 and x = -1, 1\n",
    "x = np.linspace(-0.1, 0.1, 100)\n",
    "y = np.linspace(-0.1, 0.1, 100)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Bx, By, Bz = dipole(X, Y, 0.01)\n",
    "\n",
    "plot_field_slice(\n",
    "    X,\n",
    "    Y,\n",
    "    Bx,\n",
    "    By,\n",
    "    np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
    "    \"dipole_field_bottom.png\",\n",
    "    False,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Simulation of a dipole magnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def B(x, y, z, m=0.185, l=0.003, d=0.006):\n",
    "    d = d * 0.75\n",
    "    l = l * 0.75\n",
    "    # simulate multiple points in the cylinder and add them together to create a disk of field\n",
    "    bx = 0\n",
    "    by = 0\n",
    "    bz = 0\n",
    "    for degrees in range(0, 360, 10):\n",
    "        angle = np.deg2rad(degrees)\n",
    "        x_, y_, z_ = dipole(\n",
    "            x + d / 2 * np.cos(angle),\n",
    "            y + d / 2 * np.sin(angle),\n",
    "            z - l / 2,\n",
    "            m / (360 / 10),\n",
    "        )\n",
    "        bx += x_\n",
    "        by += y_\n",
    "        bz += z_\n",
    "        x_, y_, z_ = dipole(\n",
    "            x + d / 2 * np.cos(angle),\n",
    "            y + d / 2 * np.sin(angle),\n",
    "            z + l / 2,\n",
    "            m / (360 / 10),\n",
    "        )\n",
    "        bx += x_\n",
    "        by += y_\n",
    "        bz += z_\n",
    "    return np.array([bx, by, bz])\n",
    "\n",
    "\n",
    "# # calculate the magnetic field at y = 0, over z = -1, 1 and x = -1, 1\n",
    "x = np.linspace(-0.1, 0.1, 100)\n",
    "z = np.linspace(-0.1, 0.1, 100)\n",
    "X, Z = np.meshgrid(x, z)\n",
    "Bx, By, Bz = B(X, 0, Z)\n",
    "\n",
    "print(Bx.shape, By.shape, Bz.shape)\n",
    "\n",
    "plot_field_slice(\n",
    "    X,\n",
    "    Z,\n",
    "    Bx,\n",
    "    Bz,\n",
    "    np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
    "    \"magnetic_field_side.png\",\n",
    ")\n",
    "\n",
    "# # calculate the magnetic field at z = 1, over y = -1, 1 and x = -1, 1\n",
    "x = np.linspace(-0.1, 0.1, 100)\n",
    "y = np.linspace(-0.1, 0.1, 100)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Bx, By, Bz = B(X, Y, 0.01)\n",
    "\n",
    "plot_field_slice(\n",
    "    X,\n",
    "    Y,\n",
    "    Bx,\n",
    "    By,\n",
    "    np.log(np.sqrt(Bx**2 + By**2 + Bz**2)),\n",
    "    \"magnetic_field_bottom.png\",\n",
    ")\n",
    "\n",
    "# calculate the magnetic field in a 3d volume\n",
    "x = np.linspace(-0.1, 0.1, 100)\n",
    "y = np.linspace(-0.1, 0.1, 100)\n",
    "z = np.linspace(-0.1, 0.1, 100)\n",
    "X, Y, Z = np.meshgrid(x, y, z)\n",
    "Bx, By, Bz = B(X, Y, Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# do a 3d quivwer plot of the magnetic field\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection=\"3d\")\n",
    "# down sample the results\n",
    "ax.quiver(\n",
    "    X[::10, ::10, ::10],\n",
    "    Y[::10, ::10, ::10],\n",
    "    Z[::10, ::10, ::10],\n",
    "    Bx[::10, ::10, ::10],\n",
    "    By[::10, ::10, ::10],\n",
    "    Bz[::10, ::10, ::10],\n",
    "    length=0.01,\n",
    "    normalize=True,\n",
    ")\n",
    "ax.set_xlabel(\"$x$\")\n",
    "ax.set_ylabel(\"$y$\")\n",
    "ax.set_zlabel(\"$z$\")\n",
    "ax.set_xlim(-0.1, 0.1)\n",
    "ax.set_ylim(-0.1, 0.1)\n",
    "ax.set_zlim(-0.1, 0.1)\n",
    "ax.set_aspect(\"equal\")\n",
    "# make the plot larger\n",
    "fig.set_size_inches(10, 10)\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the force on a wire of length l carrying current I at a point x,y,z with a direction vector d\n",
    "def F(p, d, I, l):\n",
    "    return I * l * np.cross(d, B(p[0], p[1], p[2]))\n",
    "\n",
    "\n",
    "def calculate_forces_on_wire_points(points):\n",
    "    Fx = []\n",
    "    Fy = []\n",
    "    Fz = []\n",
    "    # calculate the force on each point\n",
    "    for i in range(len(points) - 1):\n",
    "        # calculate the direction vector\n",
    "        dx = points[i][0] - points[(i + 1)][0]\n",
    "        dy = points[i][1] - points[(i + 1)][1]\n",
    "        dz = points[i][2] - points[(i + 1)][2]\n",
    "        d = np.array([dx, dy, dz])\n",
    "        # get the length of d\n",
    "        l = np.sqrt(dx**2 + dy**2 + dz**2)\n",
    "        if l > 0:\n",
    "            # normalise d\n",
    "            d = d / l\n",
    "            # calculate the force\n",
    "            fx, fy, fz = F(points[i], d, points[i][3], l)\n",
    "            Fx.append(fx)\n",
    "            Fy.append(fy)\n",
    "            Fz.append(fz)\n",
    "        else:\n",
    "            Fx.append(0)\n",
    "            Fy.append(0)\n",
    "            Fz.append(0)\n",
    "    return Fx, Fy, Fz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import multiprocess as mp\n",
    "\n",
    "\n",
    "def calculate_forces_on_coil(coil, x, y, z):\n",
    "    points = coil.copy()\n",
    "    for i in range(len(points)):\n",
    "        points[i][0] = points[i][0] / 100 + x\n",
    "        points[i][1] = points[i][1] / 100 + y\n",
    "        points[i][2] = points[i][2] / 100 + z\n",
    "    # feel the force\n",
    "    Fx_, Fy_, Fz_ = calculate_forces_on_wire_points(points)\n",
    "    return sum(Fx_), sum(Fy_), sum(Fz_)\n",
    "\n",
    "\n",
    "# instead of sweeping horizontally, we'll sweep the coils around a circle\n",
    "def sweep_coil_circle(coil, coil_center_radius, theta):\n",
    "    X = coil_center_radius * np.cos(np.deg2rad(theta))\n",
    "    Y = coil_center_radius * np.sin(np.deg2rad(theta)) - coil_center_radius\n",
    "    Z = -0.0025\n",
    "\n",
    "    # loop through the locations and calculate the forces, sum up the force in the X direction for each location\n",
    "    Fx = []\n",
    "    Fy = []\n",
    "    Fz = []\n",
    "\n",
    "    # run this in parallel\n",
    "    with mp.Pool(mp.cpu_count()) as pool:\n",
    "        params = [(coil, X[p], Y[p], Z) for p in range(len(theta))]\n",
    "        results = [\n",
    "            pool.apply_async(calculate_forces_on_coil, params) for params in params\n",
    "        ]\n",
    "\n",
    "        for result in results:\n",
    "            fx, fy, fz = result.get()\n",
    "            Fx.append(fx)\n",
    "            Fy.append(fy)\n",
    "            Fz.append(fz)\n",
    "    return Fx, Fy, Fz\n",
    "\n",
    "\n",
    "# sweep the coils from -45 to 45 degrees in 1 degree steps\n",
    "theta = np.linspace(25, 175, 100)\n",
    "\n",
    "# do a quick sanity check\n",
    "# coil center in meters\n",
    "coil_center_radius = 20.5 / 1000\n",
    "X = coil_center_radius * np.cos(np.deg2rad(theta))\n",
    "Y = coil_center_radius * np.sin(np.deg2rad(theta)) - coil_center_radius\n",
    "\n",
    "# plot X and Y along with the coil\n",
    "plt.plot(X, Y, color=\"red\")\n",
    "points = coil2.copy()\n",
    "plt.plot(\n",
    "    # points in meters (coil is in cm)\n",
    "    [x / 100 for x, y, z, _ in points],\n",
    "    [y / 100 for x, y, z, _ in points],\n",
    "    label=\"coil2\",\n",
    "    color=\"blue\",\n",
    ")\n",
    "points = coil1.copy()\n",
    "plt.plot(\n",
    "    # points in meters (coil is in cm)\n",
    "    [x / 100 for x, y, z, _ in points],\n",
    "    [y / 100 for x, y, z, _ in points],\n",
    "    label=\"coil1\",\n",
    "    color=\"red\",\n",
    ")\n",
    "# plot the 6 mm diagmeter magnet as a circle\n",
    "plt.plot(\n",
    "    0.006 * np.cos(np.linspace(0, 2 * np.pi, 100)),\n",
    "    0.006 * np.sin(np.linspace(0, 2 * np.pi, 100)),\n",
    "    color=\"black\",\n",
    ")\n",
    "\n",
    "# make the aspect ratio equal\n",
    "plt.gca().set_aspect(\"equal\")\n",
    "\n",
    "Fx_1_curve, Fy_1_curve, Fz_1_curve = sweep_coil_circle(coil1, 20.5 / 1000, theta)\n",
    "Fx_2_curve, Fy_2_curve, Fz_2_curve = sweep_coil_circle(coil2, 20.5 / 1000, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(theta, np.array(Fx_1_curve), label=\"coil1\", color=\"red\")\n",
    "plt.plot(theta, -np.array(Fx_2_curve), label=\"coil2\", color=\"blue\")\n",
    "# plot a dotted line along y = 0\n",
    "plt.gcf().set_size_inches(16, 9)\n",
    "plt.plot([theta[0], theta[-1]], [0, 0], \"--\")\n",
    "print(np.max(np.abs(Fx_1_curve)))\n",
    "# save the plot\n",
    "plt.savefig(f\"torque_{COIL}_coil_sweep_circle_1mm_spiral.png\")"
   ]
  }
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