Domain_Tutorial_pythreejs.ipynb

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      ":0: FutureWarning: IPython widgets are experimental and may change in the future.\n"
     ]
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   "source": [
    "from pythreejs import *\n",
    "%matplotlib inline\n",
    "from IPython.html.widgets import interact, interactive, fixed\n",
    "from IPython.html import widgets\n",
    "import pylab\n",
    "pylab.rcParams['figure.figsize'] = (5.0*4.0/4.0, 4.0)\n",
    "import numpy as np\n",
    "from IPython.display import set_matplotlib_formats,display\n",
    "set_matplotlib_formats('svg')\n",
    "def plot_rectangular_domain(domain):\n",
    "    from matplotlib import pyplot, collections\n",
    "    cmap = pylab.get_cmap(\"hsv\")\n",
    "    lines = [[domain.x,(domain.x[0],domain.x[1]+domain.L[1])], \n",
    "             [(domain.x[0],domain.x[1]+domain.L[1]),(domain.x[0]+domain.L[0],domain.x[1]+domain.L[1])],\n",
    "             [(domain.x[0]+domain.L[0],domain.x[1]+domain.L[1]),(domain.x[0]+domain.L[0],domain.x[1])],\n",
    "             [(domain.x[0]+domain.L[0],domain.x[1]),domain.x]]\n",
    "    lc = collections.LineCollection(lines,linewidths=3)\n",
    "    fig, ax = pyplot.subplots()\n",
    "    ax.add_collection(lc)\n",
    "    ax.margins(0.1)\n",
    "    ax.set_aspect('equal')\n",
    "    pylab.savefig(\"rectangle.pdf\")\n",
    "def plot_pslg_domain(domain):\n",
    "    from matplotlib import pyplot, collections\n",
    "    lines = []\n",
    "    cmap = pylab.get_cmap(\"hsv\")\n",
    "    c = []\n",
    "    sF_max = float(max(domain.segmentFlags))\n",
    "    for s,sF in zip(domain.segments,domain.segmentFlags):\n",
    "        lines.append([domain.vertices[s[0]],domain.vertices[s[1]]])\n",
    "        c.append(cmap(float(sF/sF_max)))\n",
    "    lc = collections.LineCollection(lines,colors=c,linewidths=3)\n",
    "    fig, ax = pyplot.subplots()\n",
    "    ax.add_collection(lc)\n",
    "    ax.margins(0.1)\n",
    "    ax.set_aspect('equal')\n",
    "    pylab.savefig(\"pslg.pdf\")\n",
    "def plot_plc_domain(domain,elev=0,azim=0):\n",
    "    import mpl_toolkits.mplot3d as a3\n",
    "    import matplotlib.colors as colors\n",
    "    import pylab as pl\n",
    "    from matplotlib import pyplot as plt\n",
    "    ax = a3.Axes3D(pl.figure(),elev=elev,azim=azim)\n",
    "    cmap = pylab.get_cmap(\"hsv\")\n",
    "    fN_max = float(max(domain.facetFlags))\n",
    "    verts=[]\n",
    "    c=[]\n",
    "    for f,fN in zip(domain.facets,domain.facetFlags):\n",
    "        verts.append([domain.vertices[vN] for vN in f[0]])\n",
    "        c.append(cmap(fN/fN_max))\n",
    "    ply = a3.art3d.Poly3DCollection(verts)\n",
    "    ply.set_facecolors(c)\n",
    "    ax.add_collection3d(ply)\n",
    "    ax.margins(0.1,0.1,0.1)\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_xlim(domain.x[0],domain.L[0])\n",
    "    ax.set_ylim(domain.x[1],domain.L[1])\n",
    "    ax.set_zlim(domain.x[2],domain.L[2])\n",
    "    pylab.savefig(\"plc.pdf\")"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Domain Tutorial\n",
    "\n",
    "The domain of the PDE is represented as an object. There are many useful types of domain defined in `proteus.Domain`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from proteus import Domain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\Omega = (0,1) \\times (0,1)$. $\\Omega$ can be defined as a `RectangularDomain`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    "    box.L=(Lx,Ly)\n",
    "    plot_rectangular_domain(box)\n",
    "    return box\n",
    "boxWidget = interactive(f,Lx=1.0,Ly=1.0,box=fixed(box))\n",
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    "Real world problems typically require something more complex. A `PlanarStraightLineGraph` can be used to describe many two-dimensional domains. Note how we also can tag boundaries with an integer that partitions the boundary (used later for boundary condtions)."
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    "polygon = Domain.PlanarStraightLineGraphDomain(\n",
    "vertices=[[0.0,0.0],[0.0,1.0],[1.1,2.0],[2.3,1.0],[1.0,0.1]],\n",
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    "name=\"SomePolygon\",\n",
    "units='cm')\n",
    "plot_pslg_domain(polygon)"
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   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "source": [
    "import copy\n",
    "def g(xscale,yscale,polygon,polygonOriginal):\n",
    "    new_vertices=[]\n",
    "    for vi,v in enumerate(polygonOriginal.vertices):\n",
    "        new_vertices.append([v[0]*xscale,v[1]*yscale])\n",
    "    polygon = Domain.PlanarStraightLineGraphDomain(vertices=new_vertices,\n",
    "                                                   segments    = polygonOriginal.segments,\n",
    "                                                   segmentFlags= polygonOriginal.segmentFlags,\n",
    "                                                   name=\"SomePolygon\",\n",
    "                                                   units='cm')\n",
    "    plot_pslg_domain(polygon)\n",
    "    return polygon\n",
    "pslg_domain_editor = interactive(g,xscale=1.0,yscale=1.0,polygon=fixed(polygon),\n",
    "                            polygonOriginal=fixed(copy.deepcopy(polygon)))\n",
    "display(pslg_domain_editor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `PiecewiseLinearComplex` is a general three-dimensional domain type. Here we create one by extruding the previous 2D domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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   "source": [
    "vertices3D = []\n",
    "facets3D = []\n",
    "facetFlags3D=[]\n",
    "#extrude\n",
    "nVertices2D=len(polygon.vertices)\n",
    "maxFlag = max(polygon.segmentFlags)\n",
    "for v in polygon.vertices: \n",
    "    vertices3D.append([v[0],v[1],0.0])\n",
    "    facets3D.append([range(nVertices2D)])\n",
    "    facetFlags3D.append(maxFlag+1)\n",
    "for v in polygon.vertices:\n",
    "    vertices3D.append([v[0],v[1],1.0])\n",
    "    facets3D.append([range(nVertices2D,nVertices2D*2)])\n",
    "    facetFlags3D.append(maxFlag+2)\n",
    "nSegments2D  = len(polygon.segments)\n",
    "for s,sN in zip(polygon.segments,polygon.segmentFlags):\n",
    "    facets3D.append([[s[0],s[1],(s[1]+nSegments2D)%(2*nSegments2D),s[0]+nSegments2D]])\n",
    "    facetFlags3D.append(sN)\n",
    "polyhedron = Domain.PiecewiseLinearComplexDomain(\n",
    "vertices=vertices3D,\n",
    "facets=facets3D,\n",
    "facetFlags=facetFlags3D)\n",
    "plot_plc_domain(polyhedron,elev=15,azim=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
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   "source": [
    "import copy\n",
    "def edit_plc_domain(xscale=1.0,yscale=1.0,zscale=1.0,\n",
    "                    elev=15,azim=15,\n",
    "                    plc=polyhedron,plcOriginal=copy.deepcopy(polyhedron)):\n",
    "    new_vertices=[]\n",
    "    for vi,v in enumerate(plcOriginal.vertices):\n",
    "        new_vertices.append([v[0]*xscale,v[1]*yscale,v[2]*zscale])\n",
    "    plc = Domain.PiecewiseLinearComplexDomain(vertices=new_vertices,\n",
    "                                              facets=plc.facets,\n",
    "                                              facetFlags=plc.facetFlags)\n",
    "    plot_plc_domain(plc,elev,azim)\n",
    "    return plc\n",
    "plc_domain_editor = interactive(edit_plc_domain,\n",
    "                              xscale=(0.1,10.0),\n",
    "                              yscale=(0.1,10.0),\n",
    "                              zscale=(0.1,10.0),\n",
    "                              elev=(-90,90,10),azim=(-180,180,10),\n",
    "                              plc=fixed(polyhedron),\n",
    "                              plcOriginal=fixed(copy.deepcopy(polyhedron)))\n",
    "display(plc_domain_editor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_plc_domain(plc_domain_editor.result,15,15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "faces3=[]\n",
    "facesn=[]\n",
    "vertices=[]\n",
    "va = np.array(polyhedron.vertices)\n",
    "cg = va.mean(0)\n",
    "for v in polyhedron.vertices:\n",
    "    vertices+=(np.array(v)-cg).tolist()\n",
    "for facet in polyhedron.facets:\n",
    "    for face in facet:\n",
    "        facesn.append(face)\n",
    "        for i in range(len(face)-2):\n",
    "            faces3.append([face[0],face[i+1],face[i+2]])\n",
    "p  = FaceGeometry(face3=[],face4=[],facen=facesn,vertices=vertices)\n",
    "mat = BasicMaterial(side='DoubleSide',color='red')\n",
    "m = Mesh(geometry=p, material=mat)\n",
    "scene = Scene(children=[m, AmbientLight(color=0x777777)])\n",
    "scene.background=0x777777\n",
    "c = PerspectiveCamera(position=[0,polyhedron.x[1]+1.5*polyhedron.L[1],polyhedron.x[2]+1.5*polyhedron.L[2]], up=[0,0,1], \n",
    "                      children=[DirectionalLight(color=0x777777, position=[3,5,1], intensity=0.6)])\n",
    "renderer = Renderer(camera=c, scene = scene, controls=[OrbitControls(controlling=c)],background=\"grey\")\n",
    "display(renderer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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