doc/All.ipynb

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   "source": [
    "## Imports"
   ]
  },
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   "source": [
    "import numpy as np\n",
    "import math\n",
    "import igl\n",
    "import meshplot as mp\n",
    "import wildmeshing as wm\n",
    "import polyfempy as pf"
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## Read the Mesh"
   ]
  },
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   "source": [
    "V, F = igl.read_triangle_mesh(\"mesh.obj\")\n",
    "mp.plot(V, F, shading={\"wireframe\": True})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Tetrahedralization with Wildmeshing"
   ]
  },
  {
   "cell_type": "code",
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   "outputs": [],
   "source": [
    "wm.tetrahedralize(\"mesh.obj\", \"out.mesh\", mute_log=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Loading the Mesh in Polyfem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "solver = pf.Solver()\n",
    "solver.load_mesh_from_path(\"out.mesh\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Advanced Sidesets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "minn = np.min(V, axis=0)\n",
    "maxx = np.max(V, axis=0)\n",
    "\n",
    "center = (minn+maxx)/2"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Function to select sidesets:\n",
    "\n",
    "- Sideset 2: $z$-component close to the bottom boundary `minn[2]` and larger than $y$ of center\n",
    "- Sideset 3: $z$-component close to the bottom boundary `minn[2]` and smaller than $y$ of center"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "def sideset(p):\n",
    "    if abs(p[2] - minn[2]) < 0.5:\n",
    "        if p[1] > center[1]:\n",
    "            return 2\n",
    "        else:\n",
    "            return 3\n",
    "    return 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Loading a Visualizing Sidesets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "solver.set_boundary_side_set_from_bary(sideset)\n",
    "ps, ts, s = solver.get_boundary_sidesets()\n",
    "\n",
    "mp.plot(ps, ts, s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Setup Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "settings = pf.Settings()\n",
    "problem = pf.Problem()\n",
    "\n",
    "settings.set_pde(pf.PDEs.LinearElasticity)\n",
    "\n",
    "settings.set_material_params(\"E\", 200)\n",
    "settings.set_material_params(\"nu\", 0.35)\n",
    "\n",
    "\n",
    "problem.set_displacement(2, [0, 0, 0])\n",
    "problem.set_force(3, [0, 0.5, 0])\n",
    "\n",
    "settings.set_problem(problem)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "## Solve!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "solver.settings(settings)\n",
    "solver.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Visualization of Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p, t, d = solver.get_sampled_solution()\n",
    "m = np.linalg.norm(d, axis=1)\n",
    "\n",
    "mp.plot(p+d, t, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Isolines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
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   "outputs": [],
   "source": [
    "p_uni, indices, inverse = np.unique(p, return_index=True, return_inverse=True, axis=0)\n",
    "\n",
    "t_uni = np.array([inverse[t[:, 0]], inverse[t[:, 1]], inverse[t[:, 2]], inverse[t[:, 3]]]).transpose()\n",
    "d_uni = d[indices, :]\n",
    "m_uni = m[indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   },
   "outputs": [],
   "source": [
    "surf = igl.boundary_facets(t_uni)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "iso_p, iso_l = igl.isolines(p_uni+d_uni, surf, m_uni, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Plot!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "p = mp.plot(p_uni+d_uni, surf, m_uni, return_plot=True)\n",
    "p.add_edges(iso_p, iso_l, shading={\"line_color\": \"white\"})"
   ]
  }
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