{
 "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, plot_coil2\n",
    "from tqdm.notebook import trange, tqdm\n",
    "from helpers import get_arc_point, draw_arc, rotate, scale, rotate_point, translate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Track width and spacing\n",
    "TRACK_WIDTH = 0.127\n",
    "TRACK_SPACING = 0.127\n",
    "\n",
    "# via defaults\n",
    "VIA_DIAM = 0.8\n",
    "VIA_DRILL = 0.4\n",
    "\n",
    "# this is for a 1.27mm pitch pin\n",
    "PIN_DIAM = 1.0\n",
    "PIN_DRILL = 0.65\n",
    "\n",
    "# this is for the PCB connector - see https://www.farnell.com/datasheets/2003059.pdf\n",
    "PAD_WIDTH = 3\n",
    "PAD_HEIGHT = 2\n",
    "PAD_PITCH = 2.5\n",
    "\n",
    "STATOR_HOLE_RADIUS = 5.5\n",
    "HOLE_SPACING = 0.25\n",
    "\n",
    "# PCB Edge size\n",
    "STATOR_RADIUS = 30\n",
    "\n",
    "# where to puth the mounting pins\n",
    "SCREW_HOLE_DRILL_DIAM = 2.3  # 2.3mm drill for a 2mm screw\n",
    "SCREW_HOLE_RADIUS = STATOR_RADIUS\n",
    "\n",
    "# Coil params\n",
    "TURNS = 16\n",
    "COIL_CENTER_RADIUS = 19.95\n",
    "COIL_VIA_RADIUS = 20.95\n",
    "\n",
    "\n",
    "def get_points(spacing, inner_radius, outer_radius, start_angle, end_angle):\n",
    "    # first calculate the angle step size from the spacing and the inner_radius\n",
    "    spacing_angle = np.rad2deg(np.arctan2(spacing, inner_radius))\n",
    "    print(spacing_angle)\n",
    "    # now calculate the points be iterating from start_angle to end_angle with the spacing_angle\n",
    "    points = []\n",
    "    for angle in np.arange(start_angle, end_angle, spacing_angle * 2):\n",
    "        p1 = get_arc_point(angle, inner_radius)\n",
    "        points.append([p1[0], p1[1], 0, 0.5])\n",
    "        p2 = get_arc_point(angle + spacing_angle, outer_radius)\n",
    "        points.append([p2[0], p2[1], 0, 0.5])\n",
    "        points.append([p2[0], p2[1], -0.8, 0.5])\n",
    "        points.append([p1[0], p1[1], -0.8, 0.5])\n",
    "    return points\n",
    "\n",
    "\n",
    "coil1 = get_points(\n",
    "    TRACK_SPACING + TRACK_WIDTH,\n",
    "    (COIL_CENTER_RADIUS - 10),\n",
    "    COIL_CENTER_RADIUS + 10,\n",
    "    -15,\n",
    "    15,\n",
    ")\n",
    "# move all the points in by COIL_CENTER_RADIUS\n",
    "for p in coil1:\n",
    "    p[0] -= COIL_CENTER_RADIUS\n",
    "# rotate the points by 90 degrees\n",
    "for p in coil1:\n",
    "    p[0], p[1] = rotate_point(p[0], p[1], 90)\n",
    "coil1 = np.array(coil1).T\n",
    "plot_coil2(coil1)\n",
    "coil1 = slice_coil(coil1, 0.1)\n",
    "coil1 = coil1.T\n",
    "print(coil1.shape)\n",
    "print(len(coil1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Simulation of a dipole magnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# magnetic field at a point x,y,z of a dipole magnet with moment m in the z direction\n",
    "def B(x, y, z, m=0.185):\n",
    "    mu0 = 4 * np.pi * 1e-7\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\"):\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",
    "\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 = B(X, 0, Z)\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, Y, Bx, By, np.sqrt(Bx**2 + By**2 + Bz**2), \"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": [
    "# 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)):\n",
    "        # calculate the direction vector\n",
    "        dx = points[i][0] - points[(i + 1) % len(points)][0]\n",
    "        dy = points[i][1] - points[(i + 1) % len(points)][1]\n",
    "        dz = points[i][2] - points[(i + 1) % len(points)][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\n",
    "\n",
    "\n",
    "# locate the loop of wire directly below the magnet\n",
    "x = 0.01\n",
    "y = 0\n",
    "z = -0.002\n",
    "r1 = 0.001\n",
    "r2 = 0.01\n",
    "\n",
    "\n",
    "points = coil1.copy()\n",
    "# scale the points from mm to m\n",
    "# shift the coil to the correct position\n",
    "for i in range(len(points)):\n",
    "    points[i][0] = points[i][0] / 1000 + x\n",
    "    points[i][1] = points[i][1] / 1000 + y\n",
    "    points[i][2] = points[i][2] / 1000 + z\n",
    "\n",
    "\n",
    "# plot the points in 2D x,y\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot([p[0] for p in points], [p[1] for p in points])\n",
    "ax.set_xlabel(\"$x$\")\n",
    "ax.set_ylabel(\"$y$\")\n",
    "ax.set_xlim(-0.01 + x, 0.01 + x)\n",
    "ax.set_ylim(-0.01 + y, 0.01 + y)\n",
    "ax.set_aspect(\"equal\")\n",
    "fig.show()\n",
    "\n",
    "Fx, Fy, Fz = calculate_forces_on_wire_points(points)\n",
    "\n",
    "\n",
    "# plot the wire along with arrows showing the force\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection=\"3d\")\n",
    "ax.plot([p[0] for p in points], [p[1] for p in points], [p[2] for p in points])\n",
    "\n",
    "print(sum(Fx) / 9.8)\n",
    "\n",
    "# subsample the points and force vectors to make the plot clearer\n",
    "points = points[::50]\n",
    "Fx = Fx[::50]\n",
    "Fy = Fy[::50]\n",
    "Fz = Fz[::50]\n",
    "\n",
    "ax.quiver(\n",
    "    [p[0] for p in points],\n",
    "    [p[1] for p in points],\n",
    "    [p[2] for p in points],\n",
    "    np.sqrt(Fx),\n",
    "    0,\n",
    "    0,\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(x - 0.02, x + 0.02)\n",
    "ax.set_ylim(y - 0.02, y + 0.02)\n",
    "ax.set_zlim(z - 0.02, z + 0.02)\n",
    "ax.set_aspect(\"equal\")\n",
    "\n",
    "# change the figure size\n",
    "fig.set_size_inches(10, 10)\n",
    "\n",
    "fig.show()\n",
    "# coil2 = -0.01311082557350831\n",
    "# coil1 =  0.0088435517657609"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_coil(coil, X):\n",
    "    Y = np.zeros(len(X))\n",
    "    Z = -0.01 * np.ones(len(X))\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",
    "    for p in trange(len(X)):\n",
    "        points = coil.copy()\n",
    "        # scale the points from mm to m\n",
    "        # shift the coil to the correct position\n",
    "        for i in range(len(points)):\n",
    "            points[i][0] = points[i][0] / 1000 + X[p]\n",
    "            points[i][1] = points[i][1] / 1000 + Y[p]\n",
    "            points[i][2] = points[i][2] / 1000 + Z[p]\n",
    "        Fx_, Fy_, Fz_ = calculate_forces_on_wire_points(points)\n",
    "        Fx.append(sum(Fx_))\n",
    "        Fy.append(sum(Fy_))\n",
    "        Fz.append(sum(Fz_))\n",
    "    return Fx, Fy, Fz\n",
    "\n",
    "\n",
    "# sweep the coild from -3cm to 3cm in 0.01m steps\n",
    "X = np.linspace(-0.03, 0.03, 100)\n",
    "Fx_1_straight, Fy_1_straight, Fz_1_straight = sweep_coil(coil1, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot the force as a function of x\n",
    "plt.plot(X, -np.array(Fx_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
    "# plot a dotted line along y = 0\n",
    "plt.plot([X[0], X[-1]], [0, 0], \"--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot the force as a function of x\n",
    "plt.plot(X, -np.array(Fz_1_straight) / 9.8, label=\"coil1\", color=\"red\")\n",
    "# plot a dotted line along y = 0\n",
    "plt.plot([X[0], X[-1]], [0, 0], \"--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# instead of sweeping horizontally, we'll sweep the coils around a circle\n",
    "def sweep_coil_cirlc(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))\n",
    "    Z = -0.01 * np.ones(100)\n",
    "\n",
    "    # loop through the locations and calculate the forces, sum up the force in the X direction for each location\n",
    "    Torque = []\n",
    "    Fx = []\n",
    "    Fy = []\n",
    "    Fz = []\n",
    "    for p in trange(len(theta)):\n",
    "        angle = np.deg2rad(theta[p]) - np.pi / 2\n",
    "        x = X[p]\n",
    "        y = Y[p]\n",
    "        z = Z[p]\n",
    "\n",
    "        points = coil.copy()\n",
    "        for i in range(len(points)):\n",
    "            px = points[i][0] / 1000\n",
    "            py = points[i][1] / 1000\n",
    "            pz = points[i][2] / 1000\n",
    "            # rotate the points so the coil is correctly oriented\n",
    "            points[i][0] = px * np.cos(angle) - py * np.sin(angle) + x\n",
    "            points[i][1] = (\n",
    "                px * np.sin(angle) + py * np.cos(angle) + y - coil_center_radius\n",
    "            )\n",
    "            points[i][2] = pz + z\n",
    "        # feel the force\n",
    "        Fx_, Fy_, Fz_ = calculate_forces_on_wire_points(points)\n",
    "        Fx.append(sum(Fx_))\n",
    "        Fy.append(sum(Fy_))\n",
    "        Fz.append(sum(Fz_))\n",
    "        # calculate the torque - which should be 90 degress to the angle\n",
    "        torque_angle = np.deg2rad(theta[p] - 90)\n",
    "        Torque.append(sum(Fx_) * np.cos(torque_angle) + sum(Fy_) * np.sin(torque_angle))\n",
    "\n",
    "    return Fx, Fy, Fz, Torque\n",
    "\n",
    "\n",
    "# sweep the coils from -45 to 45 degrees in 1 degree steps\n",
    "theta = np.linspace(0, 180, 100)\n",
    "Fx_1_curve, Fy_1_curve, Fz_1_curve, Torque_1 = sweep_coil_cirlc(\n",
    "    coil1, 19.5 / 1000, theta\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(theta, -np.array(Torque_1) / 9.8, label=\"coil1\", color=\"red\")\n",
    "# plot a dotted line along y = 0\n",
    "plt.plot([theta[0], theta[-1]], [0, 0], \"--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot arrows for the Fx and Fy components\n",
    "X = 19.5 * np.cos(np.deg2rad(theta)) / 1000\n",
    "Y = 19.5 * np.sin(np.deg2rad(theta)) / 1000\n",
    "plt.quiver(X[::5], Y[::5], Fx_1_curve[::5], Fy_1_curve[::5], color=\"red\")\n",
    "# make the axis equal so the arrows are not stretched\n",
    "plt.axis(\"equal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(theta, -np.array(Fz_1_curve) / 9.8, label=\"coil1\", color=\"red\")\n",
    "plt.plot(theta, np.array(Fz_2_curve) / 9.8, label=\"coil2\", color=\"blue\")\n",
    "# plot a dotted line along y = 0\n",
    "plt.plot([theta[0], theta[-1]], [0, 0], \"--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# instead of sweeping horizontally, we'll sweep the coils around a circle\n",
    "def sweep_coil_cirlc(coil, coil_center_radius):\n",
    "    # sweep the coils from -45 to 45 degrees in 1 degree steps\n",
    "    theta = np.linspace(0, 180, 20)\n",
    "    X = coil_center_radius * np.cos(np.deg2rad(theta))\n",
    "    Y = coil_center_radius * np.sin(np.deg2rad(theta))\n",
    "    Z = 1 * np.ones(100)\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",
    "    for p in trange(len(theta)):\n",
    "        angle = np.deg2rad(theta[p]) - np.pi / 2\n",
    "        x = X[p]\n",
    "        y = Y[p]\n",
    "        z = Z[p]\n",
    "\n",
    "        points = coil.copy()\n",
    "        for i in range(len(points)):\n",
    "            px = points[i][0] / 1000\n",
    "            py = points[i][1] / 1000\n",
    "            pz = points[i][2] / 1000\n",
    "            # rotate the points so the coil is correctly oriented\n",
    "            points[i][0] = px * np.cos(angle) - py * np.sin(angle) + x\n",
    "            points[i][1] = (\n",
    "                px * np.sin(angle) + py * np.cos(angle) + y - coil_center_radius\n",
    "            )\n",
    "            points[i][2] = pz + z\n",
    "        plt.plot([p[0] for p in points], [p[1] for p in points], linewidth=0.5)\n",
    "        # add the torque arrow to the plot\n",
    "        torque_angle = np.deg2rad(theta[p] - 90)\n",
    "        torque_x1 = x\n",
    "        torque_y1 = y\n",
    "        torque_x2 = x + 0.01 * np.cos(torque_angle)\n",
    "        torque_y2 = y + 0.01 * np.sin(torque_angle)\n",
    "        plt.arrow(\n",
    "            torque_x1,\n",
    "            torque_y1,\n",
    "            torque_x2 - torque_x1,\n",
    "            torque_y2 - torque_y1,\n",
    "            head_width=0.001,\n",
    "            head_length=0.002,\n",
    "            fc=\"k\",\n",
    "            ec=\"k\",\n",
    "        )\n",
    "\n",
    "\n",
    "sweep_coil_cirlc(coil2, 19.5 / 1000)"
   ]
  }
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