pcb-stator-coil-generator/coil_version2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# import matplotlib as plt\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "from skspatial.objects import LineSegment, Line\n",
    "from enum import Enum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "VIA_DIAM = 0.8\n",
    "VIA_DRILL = 0.4\n",
    "STATOR_HOLE_RADIUS = 4\n",
    "TRACK_WIDTH = 0.2\n",
    "TRACK_SPACING = 0.2\n",
    "TURNS = 11\n",
    "STATOR_RADIUS = 20\n",
    "Layer = Enum(\"Layer\", \"FRONT BACK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "template = [(-1.5, -0.1), (1.5, -2), (2.0, -1), (2.0, 1), (1.5, 2), (-1.5, 0.1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot the template shape wrapping around to the first point\n",
    "plt.plot(\n",
    "    [x for x, y in template] + [template[0][0]],\n",
    "    [y for x, y in template] + [template[0][1]],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# this speeds things up dramatically as we only have to compute the line intersections once\n",
    "# there are probably much faster ways of doing this - we're just doing a brute force search\n",
    "# for the intersections - consult algorithms from games for inspiration...\n",
    "def get_template_point_cache(template):\n",
    "    # sweep a line from the origin through 360 degress times the number of turns in 1 degree increments\n",
    "    # and find the intersection points with the template shape\n",
    "    cache = {}\n",
    "    for angle in np.arange(0, 360 + 1, 1):\n",
    "        line = LineSegment(\n",
    "            np.array([0, 0]),\n",
    "            np.array(\n",
    "                [1000 * np.cos(np.deg2rad(angle)), 1000 * np.sin(np.deg2rad(angle))]\n",
    "            ),\n",
    "        )\n",
    "        for i in range(len(template)):\n",
    "            segment = LineSegment(\n",
    "                np.array(template[i]), np.array(template[(i + 1) % len(template)])\n",
    "            )\n",
    "            try:\n",
    "                intersection = line.intersect_line_segment(segment)\n",
    "                if intersection is not None:\n",
    "                    cache[angle] = (intersection, segment)\n",
    "            except ValueError:\n",
    "                try:\n",
    "                    # nudge the angle slightly\n",
    "                    new_angle = angle + 0.1\n",
    "                    line = LineSegment(\n",
    "                        np.array([0, 0]),\n",
    "                        np.array(\n",
    "                            [\n",
    "                                1000 * np.cos(np.deg2rad(new_angle)),\n",
    "                                1000 * np.sin(np.deg2rad(new_angle)),\n",
    "                            ]\n",
    "                        ),\n",
    "                    )\n",
    "                    intersection = line.intersect_line_segment(segment)\n",
    "                    if intersection is not None:\n",
    "                        cache[angle] = (intersection, segment)\n",
    "                except ValueError:\n",
    "                    pass\n",
    "    return cache\n",
    "\n",
    "\n",
    "def get_point(angle, template, layer, spacing, cache):\n",
    "    if layer == Layer.BACK:\n",
    "        angle = angle + 180\n",
    "    intersection, segment = cache[angle % 360]\n",
    "    return intersection, segment\n",
    "\n",
    "\n",
    "# get the points in a coil shape\n",
    "# Use reverse for bottom layer (basically flips the y coordinate so that the coil goes in the opposite direction)\n",
    "# Also rotates the endpoints by 90 degress so that the exit point on the bottom layer is to the left hand side\n",
    "def get_points(template, turns, spacing, layer=Layer.FRONT, cache=None):\n",
    "    if cache is None:\n",
    "        cache = get_template_point_cache(template)\n",
    "    coil_points = []\n",
    "    last_segment = None\n",
    "    for angle in np.arange(0, 360 * turns + 1, 1):\n",
    "        offset = spacing * angle / 360\n",
    "        intersection, segment = get_point(angle, template, layer, spacing, cache)\n",
    "        vector = np.array(segment.point_a) - np.array(segment.point_b)\n",
    "        normal = vector / np.linalg.norm(vector)\n",
    "        # rotate the vector 90 degrees\n",
    "        normal = np.array([-normal[1], normal[0]])\n",
    "        # move the intersection point along the normal vector by the spacing\n",
    "        coil_point = intersection + normal * offset\n",
    "        if layer == Layer.BACK:\n",
    "            coil_points.append((coil_point[0], -coil_point[1], segment))\n",
    "        else:\n",
    "            coil_points.append((coil_point[0], coil_point[1], segment))\n",
    "    # run through the generated coil points and where the line segments change add a point that is the intersection of the previous and next lines\n",
    "    # this prevents any corner cutting\n",
    "    points = []\n",
    "    last_segment = coil_points[0][2]\n",
    "    for i in range(len(coil_points)):\n",
    "        x, y, segment = coil_points[i]\n",
    "        same_segment = (\n",
    "            (last_segment.point_a == segment.point_a).all()\n",
    "            and (last_segment.point_b == segment.point_b).all()\n",
    "        ).all()\n",
    "        if (not same_segment) and i > 2 and i < len(coil_points) - 2:\n",
    "            # create a line from the previous two points\n",
    "            line = Line(\n",
    "                np.array(coil_points[i - 2][0:2]),\n",
    "                np.array(coil_points[i - 2][0:2]) - np.array(coil_points[i - 1][0:2]),\n",
    "            )\n",
    "            # create a line from the next two points\n",
    "            line2 = Line(\n",
    "                np.array(coil_points[i][0:2]),\n",
    "                np.array(coil_points[i][0:2]) - np.array(coil_points[i + 1][0:2]),\n",
    "            )\n",
    "            # find the intersection of the two lines\n",
    "            intersection = line.intersect_line(line2)\n",
    "            # add the intersection point to the list of points\n",
    "            points.append(intersection)\n",
    "        last_segment = segment\n",
    "        points.append((x, y))\n",
    "    return points\n",
    "\n",
    "\n",
    "def optimize_points(points):\n",
    "    # follow the line and remove points that are in the same direction as the previous poin\n",
    "    # keep doing this until the direction changes significantly\n",
    "    # this is a very simple optimization that removes a lot of points\n",
    "    # it's not perfect but it's a good start\n",
    "    optimized_points = []\n",
    "    for i in range(len(points)):\n",
    "        if i == 0:\n",
    "            optimized_points.append(points[i])\n",
    "        else:\n",
    "            vector1 = np.array(points[i]) - np.array(points[i - 1])\n",
    "            vector2 = np.array(points[(i + 1) % len(points)]) - np.array(points[i])\n",
    "            length1 = np.linalg.norm(vector1)\n",
    "            length2 = np.linalg.norm(vector2)\n",
    "            if length1 > 0 and length2 > 0:\n",
    "                dot = np.dot(vector1, vector2) / (length1 * length2)\n",
    "                # clamp dot between -1 and 1\n",
    "                dot = max(-1, min(1, dot))\n",
    "                angle = np.arccos(dot)\n",
    "                if angle > np.deg2rad(5):\n",
    "                    optimized_points.append(points[i])\n",
    "    print(\"Optimised from {} to {} points\".format(len(points), len(optimized_points)))\n",
    "    return optimized_points\n",
    "\n",
    "\n",
    "def chaikin(points, iterations):\n",
    "    if iterations == 0:\n",
    "        return points\n",
    "    l = len(points)\n",
    "    smoothed = []\n",
    "    for i in range(l - 1):\n",
    "        x1, y1 = points[i]\n",
    "        x2, y2 = points[i + 1]\n",
    "        smoothed.append([0.9 * x1 + 0.1 * x2, 0.9 * y1 + 0.1 * y2])\n",
    "        smoothed.append([0.1 * x1 + 0.9 * x2, 0.1 * y1 + 0.9 * y2])\n",
    "    smoothed.append(points[l - 1])\n",
    "    return chaikin(smoothed, iterations - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "points = get_points(template, 10, TRACK_SPACING + TRACK_WIDTH, Layer.BACK, None)\n",
    "optimized_points = optimize_points(points)\n",
    "df = pd.DataFrame(points, columns=[\"x\", \"y\"])\n",
    "ax = df.plot.line(x=\"x\", y=\"y\", label=\"Coil A\", color=\"blue\")\n",
    "ax.axis(\"equal\")\n",
    "\n",
    "df_optim = pd.DataFrame(optimized_points, columns=[\"x\", \"y\"])\n",
    "df_optim.plot.line(x=\"x\", y=\"y\", label=\"Coil A\", color=\"green\", ax=ax)\n",
    "print(len(df_optim), len(df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "cache = get_template_point_cache(template)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vias = []\n",
    "\n",
    "points_f = get_points(template, TURNS, TRACK_SPACING + TRACK_WIDTH, Layer.FRONT, cache)\n",
    "points_b = get_points(template, TURNS, TRACK_SPACING + TRACK_WIDTH, Layer.BACK, cache)\n",
    "\n",
    "points_f = [(0, 0)] + chaikin(optimize_points(points_f), 3)\n",
    "points_b = [(0, 0)] + chaikin(optimize_points(points_b), 3)\n",
    "print(\"Track points\", len(points_f), len(points_b))\n",
    "\n",
    "# calculat the total length of the track to compute the resistance\n",
    "total_length_front = 0\n",
    "for i in range(len(points_f) - 1):\n",
    "    total_length_front += np.linalg.norm(\n",
    "        np.array(points_f[i + 1]) - np.array(points_f[i])\n",
    "    )\n",
    "print(\"Total length front\", total_length_front)\n",
    "\n",
    "total_length_back = 0\n",
    "for i in range(len(points_b) - 1):\n",
    "    total_length_back += np.linalg.norm(\n",
    "        np.array(points_b[i + 1]) - np.array(points_b[i])\n",
    "    )\n",
    "print(\"Total length back\", total_length_back)\n",
    "\n",
    "\n",
    "COIL_CENTER_RADIUS = STATOR_RADIUS / 2 + 1.5\n",
    "\n",
    "angle_A = 0\n",
    "angle_B = 120\n",
    "angle_C = 240\n",
    "\n",
    "# get the point on an arc at the given angle\n",
    "def get_arc_point(angle, radius):\n",
    "    return (\n",
    "        radius * np.cos(np.deg2rad(angle)),\n",
    "        radius * np.sin(np.deg2rad(angle)),\n",
    "    )\n",
    "\n",
    "\n",
    "# draw an arc\n",
    "def draw_arc(start_angle, end_angle, radius, step=10):\n",
    "    points = []\n",
    "    for angle in np.arange(start_angle, end_angle + step, step):\n",
    "        x = radius * np.cos(np.deg2rad(angle))\n",
    "        y = radius * np.sin(np.deg2rad(angle))\n",
    "        points.append((x, y))\n",
    "    return points\n",
    "\n",
    "\n",
    "# roate the points by the required angle\n",
    "def rotate(points, angle):\n",
    "    return [\n",
    "        [\n",
    "            x * np.cos(np.deg2rad(angle)) - y * np.sin(np.deg2rad(angle)),\n",
    "            x * np.sin(np.deg2rad(angle)) + y * np.cos(np.deg2rad(angle)),\n",
    "        ]\n",
    "        for x, y in points\n",
    "    ]\n",
    "\n",
    "\n",
    "# move the points out to the distance at the requited angle\n",
    "def translate(points, distance, angle):\n",
    "    return [\n",
    "        [\n",
    "            x + distance * np.cos(np.deg2rad(angle)),\n",
    "            y + distance * np.sin(np.deg2rad(angle)),\n",
    "        ]\n",
    "        for x, y in points\n",
    "    ]\n",
    "\n",
    "\n",
    "def create_via(point):\n",
    "    return {\"x\": point[0], \"y\": point[1]}\n",
    "\n",
    "\n",
    "# flip the y coordinate\n",
    "def flip(points):\n",
    "    return [[x, -y] for x, y in points]\n",
    "\n",
    "\n",
    "# the main coils\n",
    "coil_A_f = translate(rotate(points_f, angle_A), COIL_CENTER_RADIUS, angle_A)\n",
    "coil_A_b = translate(rotate(points_b, angle_A), COIL_CENTER_RADIUS, angle_A)\n",
    "\n",
    "coil_B_f = translate(rotate(points_f, angle_B), COIL_CENTER_RADIUS, angle_B)\n",
    "coil_B_b = translate(rotate(points_b, angle_B), COIL_CENTER_RADIUS, angle_B)\n",
    "\n",
    "coil_C_f = translate(rotate(points_f, angle_C), COIL_CENTER_RADIUS, angle_C)\n",
    "coil_C_b = translate(rotate(points_b, angle_C), COIL_CENTER_RADIUS, angle_C)\n",
    "\n",
    "# the opposite coils - for more power!\n",
    "angle_A_opp = angle_A + 180\n",
    "angle_B_opp = angle_B + 180\n",
    "angle_C_opp = angle_C + 180\n",
    "\n",
    "print(angle_A_opp, angle_B_opp, angle_C_opp)\n",
    "\n",
    "coil_A_opp_f = translate(\n",
    "    rotate(flip(points_f), angle_A_opp), COIL_CENTER_RADIUS, angle_A_opp\n",
    ")\n",
    "coil_A_opp_b = translate(\n",
    "    rotate(flip(points_b), angle_A_opp), COIL_CENTER_RADIUS, angle_A_opp\n",
    ")\n",
    "\n",
    "coil_B_opp_f = translate(\n",
    "    rotate(flip(points_f), angle_B_opp), COIL_CENTER_RADIUS, angle_B_opp\n",
    ")\n",
    "coil_B_opp_b = translate(\n",
    "    rotate(flip(points_b), angle_B_opp), COIL_CENTER_RADIUS, angle_B_opp\n",
    ")\n",
    "\n",
    "coil_C_opp_f = translate(\n",
    "    rotate(flip(points_f), angle_C_opp), COIL_CENTER_RADIUS, angle_C_opp\n",
    ")\n",
    "coil_C_opp_b = translate(\n",
    "    rotate(flip(points_b), angle_C_opp), COIL_CENTER_RADIUS, angle_C_opp\n",
    ")\n",
    "\n",
    "# connect the front and back coils together\n",
    "vias.append(create_via(get_arc_point(angle_A, COIL_CENTER_RADIUS)))\n",
    "vias.append(create_via(get_arc_point(angle_B, COIL_CENTER_RADIUS)))\n",
    "vias.append(create_via(get_arc_point(angle_C, COIL_CENTER_RADIUS)))\n",
    "vias.append(create_via(get_arc_point(angle_A_opp, COIL_CENTER_RADIUS)))\n",
    "vias.append(create_via(get_arc_point(angle_B_opp, COIL_CENTER_RADIUS)))\n",
    "vias.append(create_via(get_arc_point(angle_C_opp, COIL_CENTER_RADIUS)))\n",
    "\n",
    "# connect the front copper opposite coils together\n",
    "common_connection_radius = STATOR_RADIUS - (TRACK_WIDTH + TRACK_SPACING)\n",
    "common_coil_connections_b = draw_arc(angle_A_opp, angle_C_opp, common_connection_radius)\n",
    "coil_A_opp_f.append(get_arc_point(angle_A_opp, common_connection_radius))\n",
    "coil_B_opp_f.append(get_arc_point(angle_B_opp, common_connection_radius))\n",
    "coil_C_opp_f.append(get_arc_point(angle_C_opp, common_connection_radius))\n",
    "\n",
    "vias.append(create_via(get_arc_point(angle_A_opp, common_connection_radius)))\n",
    "vias.append(create_via(get_arc_point(angle_B_opp, common_connection_radius)))\n",
    "vias.append(create_via(get_arc_point(angle_C_opp, common_connection_radius)))\n",
    "\n",
    "# route coil A and coil C round to coil B so we have a good place to connect to them\n",
    "coil_input_radius = STATOR_RADIUS - (TRACK_WIDTH + TRACK_SPACING * 2 + VIA_DIAM / 2)\n",
    "coil_A_input_connection_b = draw_arc(angle_A, 80, coil_input_radius)\n",
    "coil_B_input_connection_f = draw_arc(90, angle_B, coil_input_radius)\n",
    "coil_C_input_connection_b = draw_arc(100, angle_C, coil_input_radius)\n",
    "\n",
    "coil_A_f.append(coil_A_input_connection_b[0])\n",
    "coil_B_f.append(get_arc_point(angle_B, coil_input_radius))\n",
    "coil_C_f.append(coil_C_input_connection_b[-1])\n",
    "\n",
    "vias.append(create_via(coil_A_input_connection_b[0]))\n",
    "vias.append(create_via(coil_C_input_connection_b[-1]))\n",
    "\n",
    "\n",
    "# wires for connecting to opposite coils\n",
    "connection_radius1 = STATOR_HOLE_RADIUS + (TRACK_SPACING)\n",
    "connection_radius2 = connection_radius1 + (TRACK_SPACING + VIA_DIAM / 2)\n",
    "\n",
    "# draw a 45 degree line from each coil at connection radius 1\n",
    "# then connect up to connection radius 2\n",
    "# draw a 45 degree line to the opposite coil\n",
    "\n",
    "# coil A\n",
    "coil_A_b.append(get_arc_point(angle_A, connection_radius1))\n",
    "coil_A_opp_b.append(get_arc_point(angle_A_opp, connection_radius2))\n",
    "a_connection_b = draw_arc(angle_A, angle_A + 90, connection_radius1)\n",
    "a_connection_f = draw_arc(angle_A + 90, angle_A + 180, connection_radius2)\n",
    "a_connection_b.append(a_connection_f[0])\n",
    "\n",
    "# coil B\n",
    "coil_B_b.append(get_arc_point(angle_B, connection_radius1))\n",
    "coil_B_opp_b.append(get_arc_point(angle_B_opp, connection_radius2))\n",
    "b_connection_b = draw_arc(angle_B, angle_B + 90, connection_radius1)\n",
    "b_connection_f = draw_arc(angle_B + 90, angle_B + 180, connection_radius2)\n",
    "b_connection_b.append(b_connection_f[0])\n",
    "\n",
    "# coil C\n",
    "coil_C_b.append(get_arc_point(angle_C, connection_radius1))\n",
    "coil_C_opp_b.append(get_arc_point(angle_C_opp, connection_radius2))\n",
    "c_connection_b = draw_arc(angle_C, angle_C + 90, connection_radius1)\n",
    "c_connection_f = draw_arc(angle_C + 90, angle_C + 180, connection_radius2)\n",
    "c_connection_b.append(c_connection_f[0])\n",
    "\n",
    "vias.append(create_via(a_connection_f[0]))\n",
    "vias.append(create_via(b_connection_f[0]))\n",
    "vias.append(create_via(c_connection_f[0]))\n",
    "\n",
    "vias.append(create_via(a_connection_f[-1]))\n",
    "vias.append(create_via(b_connection_f[-1]))\n",
    "vias.append(create_via(c_connection_f[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_track(points):\n",
    "    return [{\"x\": x, \"y\": y} for x, y in points]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dump out the results to json\n",
    "json_result = {\n",
    "    \"parameters\": {\n",
    "        \"trackWidth\": TRACK_WIDTH,\n",
    "        \"statorHoleRadius\": STATOR_HOLE_RADIUS,\n",
    "        \"viaDiameter\": VIA_DIAM,\n",
    "        \"viaDrillDiameter\": VIA_DRILL,\n",
    "    },\n",
    "    \"vias\": vias,\n",
    "    \"silk\": [\n",
    "        {\n",
    "            \"x\": COIL_CENTER_RADIUS * np.cos(np.deg2rad(angle_A)),\n",
    "            \"y\": COIL_CENTER_RADIUS * np.sin(np.deg2rad(angle_A)),\n",
    "            \"text\": \"A\",\n",
    "        },\n",
    "        {\n",
    "            \"x\": COIL_CENTER_RADIUS * np.cos(np.deg2rad(angle_B)),\n",
    "            \"y\": COIL_CENTER_RADIUS * np.sin(np.deg2rad(angle_B)),\n",
    "            \"text\": \"B\",\n",
    "        },\n",
    "        {\n",
    "            \"x\": COIL_CENTER_RADIUS * np.cos(np.deg2rad(angle_C)),\n",
    "            \"y\": COIL_CENTER_RADIUS * np.sin(np.deg2rad(angle_C)),\n",
    "            \"text\": \"C\",\n",
    "        },\n",
    "    ],\n",
    "    \"tracks\": {\n",
    "        \"f\": [\n",
    "            create_track(points)\n",
    "            for points in [\n",
    "                coil_A_f,\n",
    "                coil_A_opp_f,\n",
    "                coil_B_f,\n",
    "                coil_B_opp_f,\n",
    "                coil_C_f,\n",
    "                coil_C_opp_f,\n",
    "                a_connection_f,\n",
    "                b_connection_f,\n",
    "                c_connection_f,\n",
    "                coil_B_input_connection_f,\n",
    "            ]\n",
    "        ],\n",
    "        \"b\": [\n",
    "            create_track(points)\n",
    "            for points in [\n",
    "                coil_A_b,\n",
    "                coil_A_opp_b,\n",
    "                coil_B_b,\n",
    "                coil_B_opp_b,\n",
    "                coil_C_b,\n",
    "                coil_C_opp_b,\n",
    "                common_coil_connections_b,\n",
    "                a_connection_b,\n",
    "                b_connection_b,\n",
    "                c_connection_b,\n",
    "                coil_A_input_connection_b,\n",
    "                coil_C_input_connection_b,\n",
    "            ]\n",
    "        ],\n",
    "    },\n",
    "}\n",
    "\n",
    "import json\n",
    "\n",
    "json.dump(json_result, open(\"coil.json\", \"w\"))\n",
    "\n",
    "\n",
    "df = pd.DataFrame(coil_A_f, columns=[\"x\", \"y\"])\n",
    "ax = df.plot.line(x=\"x\", y=\"y\", label=\"Coil A\", color=\"blue\")\n",
    "ax.axis(\"equal\")\n",
    "df = pd.DataFrame(coil_A_b, columns=[\"x\", \"y\"])\n",
    "ax = df.plot.line(x=\"x\", y=\"y\", label=\"Coil B\", color=\"green\")\n",
    "ax.axis(\"equal\")\n",
    "\n",
    "# print the number of segments in each front track\n",
    "for track in json_result[\"tracks\"][\"f\"]:\n",
    "    print(len(track))\n",
    "\n",
    "# print the number of segments in each back track\n",
    "for track in json_result[\"tracks\"][\"b\"]:\n",
    "    print(len(track))\n",
    "\n",
    "# print the total number of segments in both front and back tracks\n",
    "print(sum([len(track) for track in json_result[\"tracks\"][\"f\"]]))\n",
    "print(sum([len(track) for track in json_result[\"tracks\"][\"b\"]]))\n",
    "\n",
    "\n",
    "# plot the back tracks\n",
    "ax = None\n",
    "for track in json_result[\"tracks\"][\"b\"]:\n",
    "    df = pd.DataFrame(track, columns=[\"x\", \"y\"])\n",
    "    ax = df.plot.line(x=\"x\", y=\"y\", color=\"blue\", ax=ax)\n",
    "    ax.axis(\"equal\")\n",
    "\n",
    "# plot the front tracks\n",
    "for track in json_result[\"tracks\"][\"f\"]:\n",
    "    df = pd.DataFrame(track, columns=[\"x\", \"y\"])\n",
    "    ax = df.plot.line(x=\"x\", y=\"y\", color=\"red\", ax=ax)\n",
    "    ax.axis(\"equal\")\n",
    "\n",
    "# hide the legend\n",
    "ax.legend().set_visible(False)\n",
    "# make the plot bigger\n",
    "ax.figure.set_size_inches(10, 10)\n",
    "\n",
    "# plot the vias\n",
    "for via in json_result[\"vias\"]:\n",
    "    ax.add_patch(\n",
    "        plt.Circle(\n",
    "            (via[\"x\"], via[\"y\"]),\n",
    "            radius=VIA_DIAM / 2,\n",
    "            fill=True,\n",
    "            color=\"black\",\n",
    "        )\n",
    "    )"
   ]
  }
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