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   "source": [
    "# Field visualisation using `pyvista`\n",
    "\n",
    "**Note:** If you experience any problems in plotting with `pyvista`, please make sure you run the Jupyter notebook in Google Chrome.\n",
    "\n",
    "There are several ways how a field can be visualised, using:\n",
    "\n",
    "- `matplotlib`\n",
    "-`pyvista`\n",
    "- `holoviews`\n",
    "- vtk-based libraries, e.g. `pyvista`\n",
    "\n",
    "\n",
    "`pyvista` provides three-dimensional interactive plots of fields inside Jupyter notebook.\n",
    "\n",
    "Let us say we have a sample, which is an ellipsoid\n",
    "\n",
    "$$\\frac{x^2}{a^2} + \\frac{y^2}{b^2} + \\frac{z^2}{c^2} <= 1$$\n",
    "\n",
    "with $a=5\\,\\text{nm}$, $b=3\\,\\text{nm}$, and $c=2\\,\\text{nm}$. The space is discretised into cells with dimensions $(0.5\\,\\text{nm}, 0.5\\,\\text{nm}, 0.5\\,\\text{nm})$. The value of the field at $(x, y, z)$ point is $(-cy, cx, cz)$, with $c=10^{9}$. The norm of the field inside the cylinder is $10^{6}$.\n",
    "\n",
    "Let us first build that field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import discretisedfield as df\n",
    "\n",
    "a, b, c = 5e-9, 3e-9, 2e-9\n",
    "cell = (0.5e-9, 0.5e-9, 0.5e-9)\n",
    "\n",
    "mesh = df.Mesh(p1=(-a, -b, -c), p2=(a, b, c), cell=cell)\n",
    "\n",
    "\n",
    "def norm_fun(pos):\n",
    "    x, y, z = pos\n",
    "    if (x / a) ** 2 + (y / b) ** 2 + (z / c) ** 2 <= 1:\n",
    "        return 1e6\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "\n",
    "def value_fun(pos):\n",
    "    x, y, z = pos\n",
    "    c = 1e9\n",
    "    return (-c * y, c * x, c * z)\n",
    "\n",
    "\n",
    "field = df.Field(mesh, nvdim=3, value=value_fun, norm=norm_fun, valid=\"norm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most basic plot we can show is the plot of all the cells where the value is valid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
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   "outputs": [
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fce5850e980_0&reconnect=auto' style='widt…"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.valid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot is interactive, so it can be manipulated using a mouse. To change the color of voxels, we can pass the new color via `color` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
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   "outputs": [
    {
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdcdbcb850_1&reconnect=auto' style='widt…"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.valid(color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we can plot a scalar field. For plotting a scalar field, we are using `discretisedfield.Field.pyvista.scalar()` method. This produces an interactive slice of the field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
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   "outputs": [
    {
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdcf1224a0_2&reconnect=auto' style='widt…"
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     "metadata": {},
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   ],
   "source": [
    "field.pyvista.scalar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, this plots the last `vdims`. However, we can plot any `vdims` by using the `scalars` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
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   ],
   "source": [
    "field.pyvista.scalar(scalars=\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, we can also create a scalar field using `discreitsedfield` syntax and plot that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
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   "outputs": [
    {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.scalar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To further modify the plot, keyword arguments for `pyvista.plotter.add_mesh` function are accepted. Please refer to its [documentation](https://docs.pyvista.org/version/stable/api/plotting/_autosummary/pyvista.Plotter.add_mesh.html)\n",
    "\n",
    "Next, we can plot the vector field itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
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   "outputs": [
    {
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fce5846dfc0_5&reconnect=auto' style='widt…"
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     },
     "metadata": {},
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    }
   ],
   "source": [
    "field.pyvista.vector()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By cascading, we can plot its slice at $x=0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdcdbcbc70_6&reconnect=auto' style='widt…"
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    }
   ],
   "source": [
    "field.orientation.sel(x=(0, 0)).pyvista.vector()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To improve the understanding of the plot, we can colour the vectors plotted. For that, we need to tell it according to which the vectors will be coloured."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
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   "outputs": [
    {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.vector(scalars=\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also colour by any field by using the `color_field` argument "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdcda92380_8&reconnect=auto' style='widt…"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.vector(color_field=field.x**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting a scalar can also be done using `volume`. The density and color within the volume represent the scalar value at each point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
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   "outputs": [
    {
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     "metadata": {},
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    }
   ],
   "source": [
    "field.pyvista.volume()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Isosurfaces of a scalar field can also be plotted using `contour`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
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       "version_minor": 0
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdcda91e10_10&reconnect=auto' style='wid…"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.contour()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`contour_scalars` can be used to select the dimension for which the isosurfaces are plotted. If `isosurfaces` controls the number of isosurfaces plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
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       "model_id": "80f3a43a0108415ea2a9f72b4e48c188",
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdcda93520_11&reconnect=auto' style='wid…"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.contour(isosurfaces=4, contour_scalars=\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If `isosurfaces` is an iterable, then an isosurface will be plotted at each specific value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
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       "model_id": "a55b0b1b5a6b4f5e9d0ece71fb2dbc96",
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       "version_minor": 0
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      "text/plain": [
       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdc679ee30_12&reconnect=auto' style='wid…"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.contour(isosurfaces=[-6e5, 0.0, 2e5], contour_scalars=\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Streamlines can also be plotted. However, it is common for the default values not to produce desired plots as the optimal values of the arguments can very unique to the specific field being plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "30aed2bab872451aaa018a9cc5843769",
       "version_major": 2,
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdb7f85330_13&reconnect=auto' style='wid…"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "field.pyvista.streamlines()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multiple visualisation on the same plot\n",
    "\n",
    "Sometimes, it is necessary to show, for example, multiple planes of the sample on the same plot. This can be done by exposing the `pyvista.Plotter` and passing it to different plotting methods. For instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": [
     "nbval-ignore-output"
    ]
   },
   "outputs": [
    {
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      "application/vnd.jupyter.widget-view+json": {
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       "version_major": 2,
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       "Widget(value=\"<iframe src='http://localhost:45445/index.html?ui=P_0x7fcdb7f87dc0_14&reconnect=auto' style='wid…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pyvista\n",
    "\n",
    "plotter = pyvista.Plotter()\n",
    "field.pyvista.vector(plotter=plotter, scalars=\"y\", cmap=\"hsv\")\n",
    "field.pyvista.contour(plotter=plotter, isosurfaces=4, contour_scalars=\"x\")\n",
    "plotter.show()"
   ]
  }
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