{
 "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(tria, vfunc=evecs[:,1], xrange=None, yrange=None, zrange=None, showcaxis=False, caxis=None)"
   ]
  },
  {
   "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(tria, vfunc=evecs[:,1], xrange=[-2, 2], yrange=[-2, 2], zrange=[-2, 2], showcaxis=True, caxis=[-0.3, 0.5])"
   ]
  },
  {
   "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(tetra, vfunc=evecs[:,1], xrange=None, yrange=None, zrange=None, showcaxis=False, caxis=None)"
   ]
  },
  {
   "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(tetra, cutting=('f>0'), vfunc=evecs[:,1], xrange=[-2, 2], yrange=[-2, 2], zrange=[-2, 2], showcaxis=True, caxis=[-0.3, 0.5])"
   ]
  }
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