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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing and inspheres and circumspheres\n",
    "\n",
    "Under different conditions, various types of spheres containing or contained within a shape can be useful.\n",
    "For example, for spheres contained in a shape we may be interested in the largest sphere contained by a shape, or the largest *concentric* sphere contained within the shape.\n",
    "For a polyhedron, we may instead want to find the sphere that touches all the faces, if it exists."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import fresnel\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import coxeter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_polyhedron_with_sphere(shape, insphere=True):\n",
    "    \"\"\"Image a polyhedron along with a sphere contained within it.\"\"\"\n",
    "    device = fresnel.Device()\n",
    "    scene = fresnel.Scene(device)\n",
    "\n",
    "    transparent_material = fresnel.material.Material(\n",
    "        color=fresnel.color.linear([1, 1, 1]),\n",
    "        spec_trans=0.95,\n",
    "        roughness=0.2,\n",
    "        primitive_color_mix=0.0,\n",
    "    )\n",
    "    colored_material = fresnel.material.Material(\n",
    "        color=fresnel.color.linear([0.9, 0.714, 0.169]),\n",
    "        roughness=0.8,\n",
    "    )\n",
    "\n",
    "    # First make the shape and set up its properties.\n",
    "    primitive = fresnel.geometry.ConvexPolyhedron(\n",
    "        scene,\n",
    "        fresnel.util.convex_polyhedron_from_vertices(shape.vertices),\n",
    "        N=1,\n",
    "        outline_width=0.01,\n",
    "        material=transparent_material if insphere else colored_material,\n",
    "    )\n",
    "    primitive.color_by_face = 0.0\n",
    "\n",
    "    # Now draw the insphere within the shape.\n",
    "    sphere = fresnel.geometry.Sphere(\n",
    "        scene,\n",
    "        N=1,\n",
    "        material=colored_material if insphere else transparent_material,\n",
    "    )\n",
    "\n",
    "    # Make the sphere a little bit smaller than it really is,\n",
    "    # otherwise you get artifacts near the intersection of the\n",
    "    # polyhedron and the insphere.\n",
    "    sphere.radius[:] = [\n",
    "        shape.insphere.radius * 0.99 if insphere else shape.circumsphere.radius * 1.01\n",
    "    ]\n",
    "\n",
    "    scene.camera = fresnel.camera.Orthographic.fit(scene, view=\"front\")\n",
    "    tracer = fresnel.tracer.Path(device=device, w=300, h=300)\n",
    "    return tracer.sample(scene, samples=24, light_samples=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [Platonic solids](https://en.wikipedia.org/wiki/Platonic_solid) are a canonical set of shapes we can use for our analysis.\n",
    "Conveniently, they can easily be generated using coxeter.\n",
    "A good example is the dodecahedron."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dodecahedron = coxeter.families.PlatonicFamily.get_shape(\"Dodecahedron\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can query different types of spheres from this shape now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The sphere tangent to all the faces of the polyhedron.\n",
    "print(dodecahedron.insphere)\n",
    "\n",
    "# The largest concentric sphere contained in the shape.\n",
    "print(dodecahedron.maximal_centered_bounded_sphere)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize what these shapes look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_polyhedron_with_sphere(dodecahedron)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we instead want to look at spheres _containing_ a shape, we can get those as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The sphere tangent to all the faces of the polyhedron.\n",
    "print(dodecahedron.circumsphere)\n",
    "\n",
    "# The largest concentric sphere contained in the shape.\n",
    "print(dodecahedron.minimal_centered_bounding_sphere)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_polyhedron_with_sphere(dodecahedron, False)"
   ]
  }
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