01-Geometry.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from tyssue import Sheet\n",
    "from tyssue import PlanarGeometry\n",
    "from tyssue.generation import generate_ring\n",
    "from tyssue import config\n",
    "from tyssue.draw import sheet_view\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Geometry classes\n",
    "\n",
    "A `Geometry` class is a stateless class holding functions to compute geometrical aspects of an epithelium,\n",
    "such as the edge lengths or the cells volume. As they are classes, inheritance can be used to define more and more specialized geometries.\n",
    "\n",
    "For the user, a geometry class is expected to have an `update_all` method that takes an `Epithelium` instance as sole argument.\n",
    "\n",
    "Calling this method will compute the relevant geometry on the epithelium.\n",
    "\n",
    "\n",
    "## 2D Geometries \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sheet_2d = Sheet.planar_sheet_2d('planar', nx=6, ny=6, \n",
    "                                 distx=1, disty=1)\n",
    "sheet_2d.sanitize(trim_borders=True, order_edges=True)\n",
    "fig, ax = sheet_view(sheet_2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Displacing vertices\n",
    "\n",
    "Most of the geometry is purely defined by the vertex positions. It is possible to change those by modifying directly the vertex dataframe\n",
    "\n",
    "\n",
    "For exemple, we can center the vertices around 0 like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sheet center of mass :\n",
      "x    2.75\n",
      "y    2.50\n",
      "dtype: float64\n",
      "New center of mass :\n",
      "x    0.0\n",
      "y    0.0\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "com = sheet_2d.vert_df[sheet_2d.coords].mean(axis=0)\n",
    "print(\"Sheet center of mass :\")\n",
    "print(com)\n",
    "\n",
    "# Translate vertices by - \n",
    "\n",
    "sheet_2d.vert_df[sheet_2d.coords] -= com\n",
    "\n",
    "print(\"New center of mass :\")\n",
    "print(sheet_2d.vert_df[sheet_2d.coords].mean(axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The view does not change though:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = sheet_view(sheet_2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to propagate the change in vertex positions, we need to **update the geometry**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "PlanarGeometry.update_all(sheet_2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the sheet is centered:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = sheet_view(sheet_2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Closed 2D geometry\n",
    "\n",
    "We can also use the `generate_ring` function to create a 2D ring of 4-sided cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ring = generate_ring(Nf=24, R_in=12, R_out=14)\n",
    "PlanarGeometry.update_all(ring)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = sheet_view(ring)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is an `AnnularGeometry` class that does all `PlanarGeometry` does plus computing the \"lumen\" volume, here the area inside the ring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tyssue.geometry.planar_geometry import AnnularGeometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "894.4786198743117\n"
     ]
    }
   ],
   "source": [
    "AnnularGeometry.update_all(ring)\n",
    "print(ring.settings[\"lumen_volume\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sheet geometry in 2.5D\n",
    "\n",
    "\n",
    "The `SheetGeometry` class computes the geometry of a 2D surface mesh embeded in 3D. The positions of the vertices and edges are thus defined in 3D."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tyssue import SheetGeometry\n",
    "\n",
    "sheet_3d = Sheet.planar_sheet_3d(\n",
    "    'sheet', nx=6, ny=6, distx=1, disty=1\n",
    ")\n",
    "sheet_3d.sanitize(trim_borders=True)\n",
    "SheetGeometry.update_all(sheet_3d)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>is_active</th>\n",
       "      <th>x</th>\n",
       "      <th>z</th>\n",
       "      <th>rho</th>\n",
       "      <th>height</th>\n",
       "      <th>basal_shift</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vert</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.625</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.375</td>\n",
       "      <td>1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.625</td>\n",
       "      <td>1</td>\n",
       "      <td>2.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.375</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.625</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y  is_active    x  z  rho  height  basal_shift\n",
       "vert                                                    \n",
       "0     2.625          1  0.5  0    0    -4.0          4.0\n",
       "1     3.375          1  1.5  0    0    -4.0          4.0\n",
       "2     2.625          1  2.5  0    0    -4.0          4.0\n",
       "3     3.375          1  0.5  0    0    -4.0          4.0\n",
       "4     3.625          1  1.0  0    0    -4.0          4.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_3d.vert_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>is_alive</th>\n",
       "      <th>perimeter</th>\n",
       "      <th>area</th>\n",
       "      <th>x</th>\n",
       "      <th>num_sides</th>\n",
       "      <th>id</th>\n",
       "      <th>z</th>\n",
       "      <th>height</th>\n",
       "      <th>rho</th>\n",
       "      <th>vol</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>face</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.250000</td>\n",
       "      <td>1</td>\n",
       "      <td>3.118034</td>\n",
       "      <td>0.5000</td>\n",
       "      <td>1.125000</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>0</td>\n",
       "      <td>-2.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.125000</td>\n",
       "      <td>1</td>\n",
       "      <td>3.618034</td>\n",
       "      <td>0.8750</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>0</td>\n",
       "      <td>-3.50</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.125000</td>\n",
       "      <td>1</td>\n",
       "      <td>3.618034</td>\n",
       "      <td>0.8750</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>0</td>\n",
       "      <td>-3.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.125000</td>\n",
       "      <td>1</td>\n",
       "      <td>3.618034</td>\n",
       "      <td>0.8750</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>0</td>\n",
       "      <td>-3.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.208333</td>\n",
       "      <td>1</td>\n",
       "      <td>2.427051</td>\n",
       "      <td>0.1875</td>\n",
       "      <td>4.666667</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             y  is_alive  perimeter    area         x  num_sides  id  z  \\\n",
       "face                                                                      \n",
       "0     1.250000         1   3.118034  0.5000  1.125000          4   0  0   \n",
       "1     1.125000         1   3.618034  0.8750  2.000000          5   0  0   \n",
       "2     1.125000         1   3.618034  0.8750  3.000000          5   0  0   \n",
       "3     1.125000         1   3.618034  0.8750  4.000000          5   0  0   \n",
       "4     1.208333         1   2.427051  0.1875  4.666667          3   0  0   \n",
       "\n",
       "      height  rho   vol  \n",
       "face                     \n",
       "0       -4.0    0 -2.00  \n",
       "1       -4.0    0 -3.50  \n",
       "2       -4.0    0 -3.50  \n",
       "3       -4.0    0 -3.50  \n",
       "4       -4.0    0 -0.75  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_3d.face_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the `height` columns to compute a pseudo-volume for each face, computed as the face area times it's height."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relative coordinates in `edge_df`\n",
    "\n",
    "The edge dataframe stores a copy of the face and source and target vertices positions, and other relative values.\n",
    "\n",
    "![](illus/double_edges.svg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>trgt</th>\n",
       "      <th>nz</th>\n",
       "      <th>length</th>\n",
       "      <th>face</th>\n",
       "      <th>srce</th>\n",
       "      <th>dx</th>\n",
       "      <th>dy</th>\n",
       "      <th>sx</th>\n",
       "      <th>sy</th>\n",
       "      <th>tx</th>\n",
       "      <th>...</th>\n",
       "      <th>is_active</th>\n",
       "      <th>ux</th>\n",
       "      <th>uy</th>\n",
       "      <th>uz</th>\n",
       "      <th>is_valid</th>\n",
       "      <th>rx</th>\n",
       "      <th>ry</th>\n",
       "      <th>rz</th>\n",
       "      <th>sub_area</th>\n",
       "      <th>sub_vol</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>edge</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "    <tr>\n",
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       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.5</td>\n",
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       "      <td>0.5</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>True</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.375</td>\n",
       "      <td>0</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>-0.750</td>\n",
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       "      <td>0</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>-0.750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5</td>\n",
       "      <td>0.3750</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.375</td>\n",
       "      <td>3.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>True</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.375</td>\n",
       "      <td>0</td>\n",
       "      <td>0.18750</td>\n",
       "      <td>-0.750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10</td>\n",
       "      <td>0.3125</td>\n",
       "      <td>0.559017</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.625</td>\n",
       "      <td>3.5</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>0.0</td>\n",
       "      <td>True</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>-0.375</td>\n",
       "      <td>0</td>\n",
       "      <td>0.15625</td>\n",
       "      <td>-0.625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.2500</td>\n",
       "      <td>0.559017</td>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>0.25</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.375</td>\n",
       "      <td>3.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
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       "      <td>0.25</td>\n",
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       "      <td>True</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.250</td>\n",
       "      <td>0</td>\n",
       "      <td>0.12500</td>\n",
       "      <td>-0.500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 29 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      trgt      nz    length  face  srce   dx    dy   sx     sy   tx  ...  \\\n",
       "edge                                                                  ...   \n",
       "0        0  0.3750  0.750000    10     3  0.0 -0.75  0.5  3.375  0.5  ...   \n",
       "1        6  0.3750  0.750000     7     5  0.0  0.75  3.0  1.625  3.0  ...   \n",
       "2        5  0.3750  0.750000     8     6  0.0 -0.75  3.0  2.375  3.0  ...   \n",
       "3       10  0.3125  0.559017     8     5  0.5 -0.25  3.0  1.625  3.5  ...   \n",
       "4        5  0.2500  0.559017     2    10 -0.5  0.25  3.5  1.375  3.0  ...   \n",
       "\n",
       "      is_active   ux    uy   uz  is_valid   rx     ry  rz  sub_area  sub_vol  \n",
       "edge                                                                          \n",
       "0             1  0.0 -0.75  0.0      True -0.5  0.375   0   0.18750   -0.750  \n",
       "1             1  0.0  0.75  0.0      True  0.5 -0.375   0   0.18750   -0.750  \n",
       "2             1  0.0 -0.75  0.0      True -0.5  0.375   0   0.18750   -0.750  \n",
       "3             1  0.5 -0.25  0.0      True -0.5 -0.375   0   0.15625   -0.625  \n",
       "4             1 -0.5  0.25  0.0      True  0.5  0.250   0   0.12500   -0.500  \n",
       "\n",
       "[5 rows x 29 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_3d.edge_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Closed sheet in 2.5D\n",
    "\n",
    "\n",
    "For closed surfaces, a `ClosedSheetGeometry` is available. Calling `update_all` computes the enclosed volume of the sheet, and stores it the `settings` attribute as `\"lumen_vol\"`\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tyssue.geometry.sheet_geometry import ClosedSheetGeometry\n",
    "from tyssue.generation import ellipsoid_sheet\n",
    "\n",
    "ellipso = ellipsoid_sheet(a=12, b=12, c=21, n_zs=12)\n",
    "ClosedSheetGeometry.update_all(ellipso)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lumen volume:  11440\n"
     ]
    }
   ],
   "source": [
    "lumen_vol = ellipso.settings['lumen_vol']\n",
    "\n",
    "print(f\"Lumen volume: {lumen_vol: .0f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax0, ax1) = plt.subplots(1, 2)\n",
    "\n",
    "fig, ax0 = sheet_view(\n",
    "    ellipso, \n",
    "    coords=[\"z\", \"y\"],\n",
    "    ax=ax0\n",
    ")\n",
    "fig, ax1 = sheet_view(\n",
    "    ellipso, \n",
    "    coords=[\"x\", \"y\"],\n",
    "    ax=ax1\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`sheet_view` can be called in 3D mode with ipyvolume:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "177e5cda32894370817b07c7d4ee17b7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Figure(camera=PerspectiveCamera(fov=45.0, position=(0.0, 0.0, 2.0), projectionMatrix=(1.0, 0.0, 0.0, 0.0, 0.0,…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import ipyvolume as ipv\n",
    "ipv.clear()\n",
    "fig, mesh = sheet_view(ellipso, mode=\"3D\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![3D view of the ellipsoid](illus/small_ellipsoid3D.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monolayer \n",
    "\n",
    "To represent monolayers, we add a `cell` element and dataframe to the datasets.\n",
    "\n",
    "One easy way to create a monolayer is to extrude it from a sheet, that means duplicating the 2D mesh to represent the basal surface and linking both meshes together to form lateral faces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "from tyssue import Monolayer, MonolayerGeometry, ClosedMonolayerGeometry\n",
    "from tyssue.generation import extrude\n",
    "\n",
    "extruded = extrude(sheet_3d.datasets, method='translation')\n",
    "specs = config.geometry.bulk_spec()\n",
    "monolayer = Monolayer('mono', extruded, specs)\n",
    "MonolayerGeometry.update_all(monolayer)\n",
    "MonolayerGeometry.center(monolayer)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "      <th>is_alive</th>\n",
       "      <th>area</th>\n",
       "      <th>vol</th>\n",
       "      <th>num_faces</th>\n",
       "      <th>id</th>\n",
       "      <th>num_ridges</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cell</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.125000</td>\n",
       "      <td>1.250000</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>1</td>\n",
       "      <td>4.118034</td>\n",
       "      <td>0.5000</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.125000</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>1</td>\n",
       "      <td>5.368034</td>\n",
       "      <td>0.8750</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.125000</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>1</td>\n",
       "      <td>5.368034</td>\n",
       "      <td>0.8750</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>1.125000</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>1</td>\n",
       "      <td>5.368034</td>\n",
       "      <td>0.8750</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.666667</td>\n",
       "      <td>1.208333</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>1</td>\n",
       "      <td>2.802051</td>\n",
       "      <td>0.1875</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             x         y    z  is_alive      area     vol  num_faces  id  \\\n",
       "cell                                                                       \n",
       "0     1.125000  1.250000 -0.5         1  4.118034  0.5000          6   0   \n",
       "1     2.000000  1.125000 -0.5         1  5.368034  0.8750          7   0   \n",
       "2     3.000000  1.125000 -0.5         1  5.368034  0.8750          7   0   \n",
       "3     4.000000  1.125000 -0.5         1  5.368034  0.8750          7   0   \n",
       "4     4.666667  1.208333 -0.5         1  2.802051  0.1875          5   0   \n",
       "\n",
       "      num_ridges  \n",
       "cell              \n",
       "0             24  \n",
       "1             30  \n",
       "2             30  \n",
       "3             30  \n",
       "4             18  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monolayer.cell_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In `cell_df`, the `num_faces` is self-explanatory, and the `num_ridges` the number of half_edges on the face.\n",
    "\n",
    "Similarly to edges, in 3D each face is a \"half face\", i.e. the interface between two cells consists of two faces, one per cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a407018b1f2b424d9deefec90b68ae80",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Figure(camera=PerspectiveCamera(fov=45.0, position=(0.0, 0.0, 2.0), projectionMatrix=(1.0, 0.0, 0.0, 0.0, 0.0,…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ipv.clear()\n",
    "fig, mesh = sheet_view(monolayer, mode=\"3D\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](illus/simple_monolayer.png)\n",
    "\n",
    "Faces and edges in a monolayer belong to a segment: apical, basal or lateral."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['apical', 'basal', 'lateral'], dtype=object)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monolayer.face_df[\"segment\"].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can filter the data based on these segments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "apical_faces = monolayer.face_df[\n",
    "    monolayer.face_df[\"segment\"] == \"apical\"\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to extract the basal or apical sheets from a monolayer with `monolayer.get_sub_sheet`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "basal = monolayer.get_sub_sheet(\"basal\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = sheet_view(basal, coords=['x', 'y'], edge={\"head_width\": 0.1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Notice the basal sheet is oriented downward)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Closed Monolayer\n",
    "\n",
    "Similarly to sheet, monolayers can be closed with a defined lumen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e6034c04af0241b4824f387b32dfa208",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Figure(camera=PerspectiveCamera(fov=45.0, position=(0.0, 0.0, 2.0), projectionMatrix=(1.0, 0.0, 0.0, 0.0, 0.0,…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "datasets = extrude(ellipso.datasets, method='homotecy', scale=0.9)\n",
    "\n",
    "mono_ellipso = Monolayer('mono_ell', datasets)\n",
    "mono_ellipso.vert_df['z'] += 5\n",
    "\n",
    "ClosedMonolayerGeometry.update_all(mono_ellipso)\n",
    "\n",
    "ipv.clear()\n",
    "\n",
    "fig, mesh = sheet_view(mono_ellipso, mode=\"3D\")\n",
    "fig\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'lumen_vol': 8344.553887776496}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mono_ellipso.settings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bulk tissue \n",
    "\n",
    "\n",
    "Eventually, we can define arbitrary assemblies of cells. \n",
    "\n",
    "A way to generate such a tissue is through 3D Voronoi tessalation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5670994bd11844a0afdfed51a0e03b35",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Figure(camera=PerspectiveCamera(fov=45.0, position=(0.0, 0.0, 2.0), projectionMatrix=(1.0, 0.0, 0.0, 0.0, 0.0,…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from tyssue import Epithelium, BulkGeometry\n",
    "from tyssue.generation import from_3d_voronoi, hexa_grid3d\n",
    "from tyssue.draw import highlight_cells\n",
    "from scipy.spatial import Voronoi\n",
    "\n",
    "cells = hexa_grid3d(4, 4, 6)\n",
    "datasets = from_3d_voronoi(Voronoi(cells))\n",
    "bulk = Epithelium('bulk', datasets)\n",
    "bulk.reset_topo()\n",
    "bulk.reset_index(order=True)\n",
    "bulk.sanitize()\n",
    "\n",
    "BulkGeometry.update_all(bulk)\n",
    "\n",
    "# We'll see next how to configure visualisation\n",
    "\n",
    "bulk.face_df['visible'] = False\n",
    "\n",
    "highlight_cells(bulk, [12, 4])\n",
    "ipv.clear()\n",
    "fig2, mesh = sheet_view(bulk, mode=\"3D\",\n",
    "                        face={\"visible\":True})\n",
    "fig2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Advanced example: better initial cells\n",
    "\n",
    "Due to artifacts in the Voronoï tessalation at the boundaries of the above epithelium, the cells are ugly, with vertices protruding away from the tissue.\n",
    "\n",
    "Here we show how to bring the vertices too far from the cell at a closer distance to the cells.\n",
    "\n",
    "This will be the occasion to apply \"upcasting\" and \"downcasting\".\n",
    "\n",
    "\n",
    "\n",
    "Our algorithm is simple: for each vertex belonging to only one cell[^1], bring the vertex at a distance equal to the median cell-vertex distance towards the cell. Here is a 2D illustration:\n",
    "\n",
    "\n",
    "![](illus/vertexcorrection.svg)\n",
    "\n",
    "[^1]: This is not strictly necessary, we could do this for all the vertices, but it makes for an interesting example of filtering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Step 1. get the vertices that belong to a single cell\n",
    "\n",
    "\n",
    "`edge_df` stores the topology of the tissue. We can use [Apply / Groupby](https://pandas.pydata.org/pandas-docs/stable/user_guide/groupby.html) strategies to get vertices with only one cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "vert\n",
       "0    3\n",
       "1    1\n",
       "2    1\n",
       "3    2\n",
       "4    1\n",
       "Name: num_cells, dtype: int64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bulk.vert_df['num_cells'] = bulk.edge_df.groupby(\"srce\").apply(lambda df: df['cell'].unique().size)\n",
    "bulk.vert_df['num_cells'].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 2. Create a binary mask over  vertices with only one neighbor cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "lonely_vs = bulk.vert_df['num_cells'] < 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 3. For each source vertex, compute the vector from cell center to the vertex, its length, and the median distance\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "rel_pos = bulk.edge_df[['sx', 'sy', 'sz']].to_numpy() - bulk.edge_df[['cx', 'cy', 'cz']].to_numpy()\n",
    "    \n",
    "rel_dist = np.linalg.norm(rel_pos, axis=1)\n",
    "med_dist = np.median(rel_dist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The displacement we need to apply is parallel to the cell-to-vertex vector, and can be expressed as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "displacement = rel_pos * (med_dist / rel_dist - 1)[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use [`np.newaxis`](https://numpy.org/doc/stable/reference/constants.html#numpy.newaxis) to multiply 2D arrays of shape (Ne, 3) with 1D arrays of shape (Ne,). \n",
    "\n",
    "This is still defined for each edge source.\n",
    "\n",
    "We can come back to vertices by taking the mean over all outgoing edges:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a df so we can groupby\n",
    "displacement = pd.DataFrame(displacement, index=bulk.edge_df.index)\n",
    "displacement['srce'] = bulk.edge_df['srce']\n",
    "vert_displacement = displacement.groupby(\"srce\").mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we filter this with `lonely_vs`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "vert_displacement[~lonely_vs] = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apply the displacement and update the geometry:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "779b0cbab0ed464f8eb94b7050eab411",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Figure(camera=PerspectiveCamera(fov=45.0, position=(0.0, 0.0, 2.0), projectionMatrix=(1.0, 0.0, 0.0, 0.0, 0.0,…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bulk.vert_df[['x', 'y', 'z']] += vert_displacement.to_numpy()\n",
    "\n",
    "BulkGeometry.update_all(bulk)\n",
    "ipv.clear()\n",
    "fig2, mesh = sheet_view(bulk, mode=\"3D\",\n",
    "                        face={\"visible\":True})\n",
    "fig2"
   ]
  }
 ],
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