{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Triangle Mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import plotly.io as pio\n",
    "\n",
    "from lapy import Solver, TetMesh, TriaMesh, io, plot\n",
    "\n",
    "pio.renderers.default = \"sphinx_gallery\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial will show you some of our visualization functionality. For that we load a larger mesh of the cube and compute the first three eigenvalues and eigenvectors. We also show how to save the eigenfunctions to disk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tria = TriaMesh.read_vtk(\"../data/cubeTria.vtk\")\n",
    "fem = Solver(tria)\n",
    "evals, evecs = fem.eigs(k=3)\n",
    "evDict = dict()\n",
    "evDict[\"Refine\"] = 0\n",
    "evDict[\"Degree\"] = 1\n",
    "evDict[\"Dimension\"] = 2\n",
    "evDict[\"Elements\"] = len(tria.t)\n",
    "evDict[\"DoF\"] = len(tria.v)\n",
    "evDict[\"NumEW\"] = 3\n",
    "evDict[\"Eigenvalues\"] = evals\n",
    "evDict[\"Eigenvectors\"] = evecs\n",
    "io.write_ev(\"../data/cubeTria.ev\", evDict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the result by visualizing the first non-constant eigenfunction on top of the cube mesh. You can see that the extrema localize in two diametrically opposed corners."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.plot_tria_mesh(\n",
    "    tria,\n",
    "    vfunc=evecs[:, 1],\n",
    "    xrange=None,\n",
    "    yrange=None,\n",
    "    zrange=None,\n",
    "    showcaxis=False,\n",
    "    caxis=None,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also adjust the axes and add a color scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.plot_tria_mesh(\n",
    "    tria,\n",
    "    vfunc=evecs[:, 1],\n",
    "    xrange=[-2, 2],\n",
    "    yrange=[-2, 2],\n",
    "    zrange=[-2, 2],\n",
    "    showcaxis=True,\n",
    "    caxis=[-0.3, 0.5],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tetrahedral Mesh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we load a tetrahedral mesh and again compute the first 3 eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tetra = TetMesh.read_vtk(\"../data/cubeTetra.vtk\")\n",
    "fem = Solver(tetra)\n",
    "evals, evecs = fem.eigs(k=3)\n",
    "evDict = dict()\n",
    "evDict[\"Refine\"] = 0\n",
    "evDict[\"Degree\"] = 1\n",
    "evDict[\"Dimension\"] = 2\n",
    "evDict[\"Elements\"] = len(tetra.t)\n",
    "evDict[\"DoF\"] = len(tetra.v)\n",
    "evDict[\"NumEW\"] = 3\n",
    "evDict[\"Eigenvalues\"] = evals\n",
    "evDict[\"Eigenvectors\"] = evecs\n",
    "io.write_ev(\"../data/cubeTetra.ev\", evDict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The eigenvector defines a function on all vertices, also inside the cube. Here we can see it as a color overlay on the boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.plot_tet_mesh(\n",
    "    tetra,\n",
    "    vfunc=evecs[:, 1],\n",
    "    xrange=None,\n",
    "    yrange=None,\n",
    "    zrange=None,\n",
    "    showcaxis=False,\n",
    "    caxis=None,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot function allows cutting the solid object open (here we keep every vertex where the function is larger than 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot.plot_tet_mesh(\n",
    "    tetra,\n",
    "    cutting=(\"f>0\"),\n",
    "    vfunc=evecs[:, 1],\n",
    "    xrange=[-2, 2],\n",
    "    yrange=[-2, 2],\n",
    "    zrange=[-2, 2],\n",
    "    showcaxis=True,\n",
    "    caxis=[-0.3, 0.5],\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}