ray_tracer.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "167142dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch as t\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5aeed3a3-b336-4196-8118-eb3c540ff7d2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 1.0000, -0.3000, -0.3000],\n",
      "        [ 1.0000, -0.2793, -0.3000],\n",
      "        [ 1.0000, -0.2586, -0.3000],\n",
      "        ...,\n",
      "        [ 1.0000,  0.2586,  0.3000],\n",
      "        [ 1.0000,  0.2793,  0.3000],\n",
      "        [ 1.0000,  0.3000,  0.3000]])\n"
     ]
    }
   ],
   "source": [
    "H = W = 30\n",
    "B=H*W\n",
    "\n",
    "ray_origins = t.tensor([-5.0, 0, 0]).reshape([1, 3]).expand([B, 3])\n",
    "\n",
    "x_dirs = t.linspace(-0.3, 0.3, W).unsqueeze(0).expand([H, W]).reshape([-1])\n",
    "y_dirs = t.linspace(-0.3, 0.3, H).unsqueeze(1).expand([H, W]).reshape([-1])\n",
    "\n",
    "# todo: we should normalize these\n",
    "ray_directions = t.stack([t.ones(B), x_dirs, y_dirs], dim=1)\n",
    "print(ray_directions)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1649612f-508d-47fc-9302-714b187016e4",
   "metadata": {},
   "source": [
    "## Step 1: render a single triangle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "79c44bb1-8a98-4cc3-9f7c-f5a3fa51cc56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([900, 3, 3])\n"
     ]
    }
   ],
   "source": [
    "vertices = t.tensor([[[3.0, 0, 0], [3, 0, 1], [3, 1, 1]]]).expand([B, 3, 3])\n",
    "\n",
    "vertex_0 = vertices[:, 0]\n",
    "vertex_1 = vertices[:, 1]\n",
    "vertex_2 = vertices[:, 2]\n",
    "\n",
    "edge_1 = vertex_1 - vertex_0\n",
    "\n",
    "edge_2 = vertex_2 - vertex_0\n",
    "\n",
    "h = ray_directions.cross(edge_2, dim=1)\n",
    "\n",
    "a = t.einsum(\"bx,bx->b\", edge_1, h)\n",
    "\n",
    "EPSILON = 1e-7\n",
    "\n",
    "mask = (a > -EPSILON) & (a < EPSILON)\n",
    "\n",
    "f = 1.0 / a\n",
    "s = ray_origins - vertex_0\n",
    "u = f * t.einsum(\"bx,bx->b\", s, h)\n",
    "\n",
    "mask2 = (u < 0) | (u > 1)\n",
    "\n",
    "q = s.cross(edge_1, dim=1)\n",
    "v = f * t.einsum(\"bx,bx->b\", ray_directions, q)\n",
    "mask3 = (v < 0) | (u + v > 1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c933f6e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f9ecb7745e0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow((mask | mask2 | mask3).reshape([H, W]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fdc7e09-8e18-4f92-96ac-05004ced00f8",
   "metadata": {},
   "source": [
    "## Step 2: render multiple triangles\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fcf1bc70-6930-48b0-b8b2-51147b4069d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from stl import mesh\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "282ec149-43da-4242-9f3d-6b2dbd270a65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(412, 3, 3)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mesh.Mesh.from_file(\"pikachu_1gen_flowalistik.STL\").vectors.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "430ad675-3b2a-44f3-9021-618ca6b0458e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.thingiverse.com/thing:376601\n",
    "model = mesh.Mesh.from_file(\"pikachu_1gen_flowalistik.STL\")\n",
    "model.translate(np.array([0, 0, -30]))\n",
    "# model = mesh.Mesh.from_file('utahteapot.stl')\n",
    "# teapot.translate(np.array([20, 0, -4]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "02d836f0-f28f-41ee-80bc-8d606aff223b",
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = t.tensor(model.vectors.copy())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9ccff5e8-80b6-4674-8db3-282fed46300d",
   "metadata": {},
   "outputs": [],
   "source": [
    "vertex_0 = vertices[:, 0].unsqueeze(0)\n",
    "vertex_1 = vertices[:, 1].unsqueeze(0)\n",
    "vertex_2 = vertices[:, 2].unsqueeze(0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "387a03ed-f807-4d29-b0e0-e29acc94deb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "H = W = 300\n",
    "B = H * W\n",
    "\n",
    "ray_origins = t.tensor([-150.0, -50, 50]).reshape([1, 3]).expand([B, 3])\n",
    "\n",
    "x_dirs = t.linspace(0.15, 0.65, W).unsqueeze(0).expand([H, W]).reshape([-1])\n",
    "\n",
    "y_dirs = t.linspace(-0.6, -0.1, H).unsqueeze(1).expand([H, W]).reshape([-1])\n",
    "\n",
    "ray_directions = t.stack([t.ones(B), x_dirs, y_dirs], dim=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2b1a9d7d-a909-4202-b4b5-af5d55faac29",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_vertices = vertices.shape[0]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "5b7523a7-9413-4fe1-beec-c178ac1cd4bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 9.19 s, sys: 1.07 s, total: 10.3 s\n",
      "Wall time: 2.59 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "edge_1 = vertex_1 - vertex_0\n",
    "edge_2 = vertex_2 - vertex_0\n",
    "\n",
    "h = ray_directions.unsqueeze(1).expand([B, num_vertices, 3]).cross(edge_2.expand([B, num_vertices, 3]), dim=2)\n",
    "\n",
    "a = t.einsum('bvx,bvx->bv', edge_1, h)\n",
    "\n",
    "EPSILON = 1e-7\n",
    "\n",
    "mask = (a > -EPSILON) & (a < EPSILON)\n",
    "\n",
    "f = 1. / a\n",
    "s = ray_origins.unsqueeze(1) - vertex_0\n",
    "u = f * t.einsum('bvx,bvx->bv', s, h)\n",
    "\n",
    "mask2 = (u < 0) | (u > 1)\n",
    "\n",
    "q = s.cross(edge_1.expand([B, num_vertices, 3]), dim=2)\n",
    "v = f * t.einsum('bx,bvx->bv', ray_directions, q)\n",
    "mask3 = (v < 0) | (u + v > 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "db3146ec-5599-422a-9780-b4b7011a60af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([90000, 412])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask2.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "09b05445-db92-4663-9149-01570ddc3f49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f9eaecd24c0>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pixel_mask = (mask2 | mask3).all(dim=1)\n",
    "plt.imshow(pixel_mask.reshape([H, W]), origin=\"lower\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "33e49987-ee6d-4497-a402-5fc538e0984d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# this variable is called `t` in the wikipedia C++ code\n",
    "t_ = f * t.einsum(\"zvd,pvd->pv\", edge_2, q)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4f74d66d-b521-48e4-8702-443343f9e96d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([90000, 412])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "dadb67cc-bd55-4414-a8bb-ee7084055454",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f9eaed56d00>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this shows how many triangles every ray hits\n",
    "plt.imshow((~mask2 & ~mask3).sum(dim=1).reshape([H, W]), origin=\"lower\")\n",
    "plt.colorbar()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "22039660-c432-4b0b-9a08-dd2c7ee1beb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "intersection_points = t.einsum(\n",
    "    \"pv,pd->pvd\", t_, ray_directions\n",
    ") + ray_origins.unsqueeze(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ecd5b6a7-1e26-4ffb-b793-4daeca149365",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([90000, 412, 3])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intersection_points.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "28f21f83-758c-41fc-84c7-6697ea325d11",
   "metadata": {},
   "outputs": [],
   "source": [
    "pixel_vertex_mask = mask2 | mask3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "29fb11ad-0879-4dab-8446-054d07776820",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([90000, 412])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pixel_vertex_mask.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "567f3bb5-5ddf-4b0d-ad1e-cde645b037b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5bd8750f-3821-4f7e-b6d2-b6dbb7661bef",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_[pixel_vertex_mask] = float(\"inf\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "44be6607-00be-4cf5-a204-4d8dbc7c7f9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "selected_triangle_ids = t_.argmin(dim=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9cdb7bda-d3f2-4052-87ab-56c07a454fc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f9eac928f40>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(selected_triangle_ids.reshape([H, W]), origin=\"lower\", cmap=\"Reds\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "37506748-b7e7-4e17-b9a7-9eabfa90cdff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f9eac9132b0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(t_.min(dim=1).values.reshape([H, W]), origin=\"lower\", cmap=\"Reds\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "da584eee-d1e8-4e85-b097-8ccf07219e38",
   "metadata": {},
   "outputs": [],
   "source": [
    "selected_t = t.gather(t_, dim=1, index=selected_triangle_ids.unsqueeze(1)).squeeze(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "62b7cf32-3409-4227-b91a-eaba10a6090b",
   "metadata": {},
   "outputs": [],
   "source": [
    "triangle_ids_2d = selected_triangle_ids.reshape([H, W])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "a3bb799f-38a9-4847-977c-2489384a2c86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f9eac86ff70>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQEAAAD4CAYAAADsBlOYAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAb4UlEQVR4nO2dbcxlVXXHf0uqEIEEKHQyzkwKGvyATapkQkk0hmqrMmkyGhOCH2RsSaem0GpjE7F+kLQhocaXaGqQIRChsSKJGiYNVZFojElBB4LIS5CpYpjJMCOVKGi0BVc/3HPL4cze++y9z973nHvP+iWT5z7nZZ91z5z132uvvfZ5RFUxDGO+vGRsAwzDGBcTAcOYOSYChjFzTAQMY+aYCBjGzPmdsQ0AOElETzU9MoyqPMVvn1LVs7rbJyECp/IS3snLxzbDMDaa63n2J67t1v0axswxETCMmWMiYBgzx0TAMGaOiYBhzBwTAcOYOSYChjFzTAQMY+aYCBjGzJlExaAR5rO/PHTctveevH0ES4xNxCKBidMWAHN8owYmAmtCWwBMDIySmAisEe2owDVEMIwcTATWjGUU8N6Tt5sQGEUwEZgwSydfOrwNA4wamAisAb4e30TBKIGJwETpOr45vFELE4E1x/ICxlBMBCZMOwloGLUwEZgosQJgswTGUKxseIIsZwLMuY1VYCIwMZaO354ejD3Phg1GDjYcmDgWDRi1MRGYKFYZaKwKE4EJ4asQNCEwamIiYBgzx0RgQrz35O3e5J5FA0YtTAQMY+aYCEyEmLUCFg0YNbA6gTXDt6y4RI2ArVacJ72RgIjsEJFvisjDIvKQiLyv2X61iBwWkfubf7ta53xIRA6KyKMi8taaX2CTGKuX/+wvD71oZqI9K2ECsPnERALPAR9Q1ftE5FTgXhG5s9n3SVX9WPtgETkPuBR4DfAK4Bsi8mpVfb6k4ZtEqvPXcEwbasyX3khAVY+o6n3N52eAR4BtgVN2A7eq6m9U9cfAQeCCEsZuMm3HjnHGoQ7b7f3bP00M5kVSYlBEzgZeB9zTbLpSRB4QkZtE5PRm2zbgidZphwiLhpHBkJ7btS6hu2bBmA/RIiAipwBfAt6vqr8ArgNeBbwWOAJ8POXCIrJXRA6IyIFfoymnbhRDnC51WOAa94f2mzDMgygREJGXshCAz6vqlwFU9aiqPq+qvwVu4IWQ/zCwo3X69mbbi1DVfaq6U1V3noQM+Q5rT+pQoE0JB7U/cDJvYmYHBLgReERVP9HavrV12DuAB5vP+4FLReREETkHOBf4bjmTN5eabxLqEwtz/vkSEwm8Hng38KbOdOBHReQHIvIA8MfA3wGo6kPAbcDDwFeBK2xmII6c8LsvbF8mAGOc3FV7YEOBzad3ilBVvwPOeP2OwDnXANcMsGs2xFQGDn3FWOz5Fg3ME6sYnAjdPzEWyhOklBSbYxt9mAiMSLe3dzl/TNWebxiwbLfvGt3jjHlhC4gmQGj5cOz5vujAMPowERiZGEeNTc61K/5S2g0da0Ky+ZgITIgSLxSxbL6RionAyKT28qF2Usb3JhbGEhOBkeg67NKJ+5yztPNauG+YCIxId9VejCC4hgauWYaU6xvzxkRgZLqvGV9+bu9P/TPly7Ys5DdiMBEYEdffGeiuH3Ct8W9HCr48QLutriDkVAeaoGwuViw0MqHwvVvcE3oPQN81Yq5nzBMTgRHw/aUhF765/9zlv7ZGwOhiIrBiUgSgTYm3Cw95V4EJx+ZiOYEV0h2XDzk/t42UP3WecryxvlgksCJSM/wuQrmB5e+h6CJlIZI5/3wwEajMVJJwuS8WMTYfE4EVkPqSEBdDxCS2CnHoakZjPTERqIRr/J+axW+f0y0mSl1Q1Pd24XWmbxrVCGMiUIEcZ22ftzzXxZBcgutam+As3ToIsKnQFGx2oBIpU3q+vwXYPSbkzCls0mrDkH1WOh2HRQIV8K0DAPcsQZ9AuNppn788znWtTX6VWGyh1fLY7jZjgYlABULv/IP0BzHl+NAqw01ygL4IwBeJ2TDheEwEChNaB5DTVkpFYUw0kHr9qeL7Tn022+vVj8dyApWIeUtwiNiHOcaOTcP3vYdOhc4VE4EJkzNs2PSqv1zhK1FyvanYcKAgvnAcVluzXyr8n+qy41CyNXY61IYFL2AiUIH2w5VSxDJUAIYuSuomz6YmAEOc1nWeCcECE4EKuB6uWDEY+kCmRhzdc0osdFolMXmA2GnEudIrAiKyA7gF2AIosE9VPyUiZwBfBM4GHgcuUdWnmz9l/ilgF/Ar4D2qel8d86eLr5dJDWVjiCkN7u5ftyrC0FBrSd/+lLbnREwk8BzwAVW9T0ROBe4VkTuB9wB3qeq1InIVcBXwQeBi4Nzm3x8B1zU/N57UF3+EklVDawly25qiM/TVXYD/+8eunJyzEPSKgKoeAY40n58RkUeAbcBu4KLmsJuBb7EQgd3ALaqqwN0icpqIbG3amR2u8bVvUVCojTau8N214CjFxr79YzpIagTQt9137NjfcyyScgIicjbwOuAeYEvLsZ9kMVyAhUA80TrtULPtRSIgInuBvQCnIKl2rw0xjt734MWEuSVyCVNLBEJYgHw25zrzHAUAEuoEROQU4EvA+1X1F+19Ta+vKRdW1X2qulNVd560ASIQU8BSysl84/n2v1im3Pv1DQNqiNYUhbA2UZGAiLyUhQB8XlW/3Gw+ugzzRWQrcKzZfhjY0Tp9e7NtdnSXFIey8KnkhK+5EcQYobIregoNrbrH5DLHYUFvJNBk+28EHlHVT7R27Qf2NJ/3ALe3tl8mCy4Efj7HfEDNHiW37WUpc2p4PRah3Ed3/3JfCeed2n2oTcxw4PXAu4E3icj9zb9dwLXAn4rIY8CfNL8D3AH8CDgI3AD8dXmz14O+RS65i4rmgK+4x7dvFdffVGJmB74D3kH7mx3HK3DFQLvWCleo331g22Fm7rLWUj1du52YxNuUhgGhoVVpO+cyLLAFRIXpe3BSE3ex7dZmldcO5QFKLtWOsWMOkZeJQEFiV7ilPrAlIwBfOXP797EefF9EFaqBqC2OFgkYvcQU8rT3pTpYaYfsKy2eCr77OoZTTvH+lMREoAClputC7W86oenL7uKr0Dk12PRhga0iLECqQ8ccH5PsKpVU7IpYaFajhiB1E5Vtm1z21bTFxybXD1gkMIC+OeuhlHrg1q0X6+YsapRJ57CJAgAWCWSRsuZ+SGFPSab6APt6175cy1jfZxOjAVlM64/LWXKCvpOXj21GFH1O3VcgtDym7+EvGQUMaatmGO4L/VPsGYMp2JDD9Tx7r6ru7G634UACXUfuTvctH2bXIpf28X2LjUo+YFN9WEMCUHuR0FA2LVFoIpCIa57fldRqEzN86FYTlmDIdGStKrw2rnoFV5KwbdNURG2ThMByAon4HsRQ5n15XntbqJ6gBLUe0BJZ8piy5VB0YJTFIoFEYnoAXzY79EDXKntNPX6VztbX0/dFWGORW/o9VSwSyKBvNqBvbr8bdk9x4UuNefGUef9QafOqcUVxUxqaDMUigQRcPWVfr9C3r4YADKF2NBAzHTilxGA3sdvetimYCAykm/GPXZCzakebUvsu8ZvimobQMGRTogCwOoHihB6c9qq42uW3U2vPV10Zu3JwVfRdd52HAVYnsCL6FruM3bulUCqKCQmA65quz7VZDuv6pmnXVQBCmAhUZPlg+caVJQWhVhKvFH1TqN1rrsrZuv8/fcduIjY7kEGJkl9fkrG9P8WeVZEbBfTNBnQjpZoi4BLl2OM3EROBAqQ8JKE1BC6niH3wSj+goVmC2GuFRM2XbKs95s516E0VADARyCa2N+nLhPsq52IjjdpO03bMlCigLw/gSwbWnDLNKcte50RgLCYCGdSYS49xAl8Jci1q1QzETqMOYYz8wrpiicFMYgtHUh7w2GOXPdry+G4CsiZDwui+mYbS05E5Pb+rnU3H6gQGErMYpr0vNrwsFYaWWKeQ6qgp3zHXJl9b1uv78dUJ2HBgIN3CllLOW6qtmEq8kslHX+/p+y4lhW6qhVJTx0SgAN2EnuuhzHmgaj2E3XZLRAu+dnzbfVOHOdeqmUycAyYChXE91CUeqpo9U2i+fkhbQ7b7qB32z3FY0SsCInIT8GfAMVX9g2bb1cBfAj9tDvsHVb2j2fch4HLgeeBvVfVrFeyeLKGQd4gjr2Lu3HWtWDEIFVCVEMVVOuecBADiIoHPAf8C3NLZ/klV/Vh7g4icB1wKvAZ4BfANEXm1qj5fwNa1oG+8HesUqbUHsfa42g45b0xuImcYkFKiOzTLH8uc8gBtekVAVb8tImdHtrcbuFVVfwP8WEQOAhcA/5lv4vrR1yOmFAa5jkl1yCEFMinTmy47hoz3V+mQc8sDtBmSE7hSRC4DDgAfUNWngW3A3a1jDjXbjkNE9gJ7AU7x/uXz9cKV7OqrGPQxJIQeY2485nvGtD2mAMwxCoB8EbgO+CdAm58fB/4ipQFV3Qfsg0WdQKYdkyOUZOtbRNPXrisjXrqeYMgsRkwtRF859FiOOFcBgEwRUNWjy88icgPw782vh4EdrUO3N9tmQagcthtepz7wPictUU/ga7stOjHXCFU8DskP1GSueYA2WWXDIrK19es7gAebz/uBS0XkRBE5BzgX+O4wE9eDlLFz21n6zmuXA4d616Fj2lLRRKidthBOQQCMBTFThF8ALgLOFJFDwEeAi0TktSyGA48DfwWgqg+JyG3Aw8BzwBVzmhlIoW8abrk/dbhQIrpw7Ytd0+DKh3SHQ1NwfBOhF4iZHXiXY/ONgeOvAa4ZYtS6kRICd8mZkw+1lVq3X9oJXGXU7X1TYmr2jIVVDA7E5Uw+J+hro9uOa7/vmJh9Pntz2wqdtwz5fcI0pjhYHuDFmAgUIFQl2EdqtNA9x3edkOPVFID2+SEhiB0OGfUxEShMdxwM8U6XU5jjixJ8PXBMpBFrc4ihdQ21IoU5FwX5sPcJFMT3gIV66+7+0qFqioOHHC8nh7CqlX4WNcRh7xOoQF95beq8eWlyHKXEdKOrrdKJyJzhhOUC3JgIFKDrbLEPW80Hckj57/Jndwyf22b7ntRwxJjhhA0D/Ng7BjPpjv3bRUChh7ybLOsy5IFdtt3tdWNmDNp2l3RSlwCswiHb9QhWExDGRGAAMQU1vpmD0o6Q6vg5Ng0VqPbPVWDOH4eJQAah+v/QWDU0TeZro88O14Mec432+a7jS+cGurbUFIP296rxfTYNE4FMXNnzIQKQ+oC6opCcHm9VvWSNoYYL6/3TMRHIoK9XcQlA6PeYNlz7QsOQ2DbarMpBl9eqPSQy4rDZgYF0S4S74Wesw6ZcZ2jCy1dNmFLUlBt1dJODJWYLzPmHYZFAJt2eLDQFFlO158M37u978GvUJ5TuuUs4rQnAcEwEChGT5EstpQ0lIEPX9O1PdZgaIXvJqUITgDLYcGAAuSF1Si9donzX11a7zZT2hjhddxjgmqGIacMnjCFMLNyYCBQi9CD7HLdvrYEvoZjzME+pZNb1/YYKqJGPicBA+nr10Hi+S9+cfm5vPVXH6doYU23ZPc8YjolAQXyFO77knuv37r6cB7/tTDHi0WdDKXKTleb8dbHEYAW6YS64Q+CYar6+4/rsiFk3kNt2DqlVkiYA9bFIYCCubLdr7B8zLIipKIx16ho5gCE1Ai5c3z90T0pd0wTlxZgIFCI21M19yFMKhFLWHqySlGKk2OON4ZgIFMA3512jNDdGDFJ6u9iMfI0eOWSD756aMJTHRKAQrgrC5fZa12sTm2twHZ97/RRxyJkCzPkeJhLpmAhUYEghTC454/WxHCZUYg1pdvXVXpgo9GMiUBDfDMAQIdjUIppa9sYWZBkvYFOEhXFl530VgKWvmUJqb+sbn8dcu31Puvelds9tkUA/JgKV8D3gpYUgp70hNuR+h64glrarr82Y688VE4FKdMuGl5SMCtZtzjumDqIE3bqMGuK7SfSKgIjcJCLHROTB1rYzROROEXms+Xl6s11E5NMiclBEHhCR82saPzVSQuahD2ZuGL2qSr/uMa6Zk5y2+ggVZa2TYK6SmEjgc8DbOtuuAu5S1XOBu5rfAS4Gzm3+7QWuK2PmetFe5hpyuqFCMDQ0XxWxi6yGXiO0xNgEwE+vCKjqt4GfdTbvBm5uPt8MvL21/RZdcDdwmohsLWTrWpO6bLivrVBonWpDTUJrJ9rbU5106fTdsN91nAlAmNycwBZVPdJ8fhLY0nzeBjzROu5Qs+04RGSviBwQkQO/Zvy/h1iDEhn4LkOz6WM4RMrKyRj6HL97nBFmcGJQF3/RNNmLVXWfqu5U1Z0nIUPNmBRDxt2hGYWpjm1LVB+mXqtkWfTcyRWBo8swv/l5rNl+GNjROm57s21W9C2LjTnXl0yMXYWYYlcsJZc2p+QDYsL+0LWMMLkisB/Y03zeA9ze2n5ZM0twIfDz1rBhluQ+iH0Z9XUJddvl0659Ptpj/ljHj23beDG9ZcMi8gXgIuBMETkEfAS4FrhNRC4HfgJc0hx+B7ALOAj8CvjzCjZPlphxfarzhnrf1DC65mKmvvZd98Z1ToloY8j5c6RXBFT1XZ5db3Ycq8AVQ43aRGKWAHfphs85MwIlGboOIkRJ5zUBSMMqBivTDelLTOflRhNj4UpuLre3t5nzjoOtIixITLgLeHv3UPJrqIOM7WAuIcgd77swIcnHRKASKTMBy+P7HuBVLxZKIad8OFRSXcsG43hMBAqTOm6PqakPXaPG8X1t5fa6sQ6fOvU59nBn3TERqEBoGOBK8G3qi0O6tL9r990C3eP6cOUWjDwsMViY2lNxqzinNjnRT5cpfq91xUSgMDFVe6lO0K2Yi3WcVUcOKdcrUb1o7woog4nABIhZBDOlcXHJQp6ctnxDKiMPE4GC1HoYNyH0DS0pTl1GbZTFRKAwMUKQUjA0JHFWUzxiS6R99f/dWonYYZGvrsCigXxMBCox9wcyJnvvWzfQ156PTYiYxsBEoDAlMt9Dz10FoTn/lOm75f4SeREjD6sTKIhrwU9OWB5bPdi3am/V9Dl/qAjI931S75+9RyAdE4GC+B4+35LZWg/rGI4Q6q1jhwah5KFRDxsOFCSmLj6ljXWj27OnvhHIt5gq1YZ1vodjYJFAQXw92NDZAN+1Qi/lqI3vJSHLfUPqGnKXX7dtM+IxEaiAq0dbfm4nwnLFIuX6qyAnjA8NG0LCZg5eHhOByvgeaJcYlCilXTVDqgBd98JFzMxB91hLEMZjIrBCQj1lqcVB6/LglxK+UNRgQhCHicAIdJfUris5U6A25z89TARGoqQATL3HS0kYpra5bNf12YjDRGBEfBFBTs86RUr2+ilJ1KmL4tQwEZgA3Yc2x3lW8eDnrPYbYlPO7MmURXGqmAiMjCubnTJ9lkvIWWKq/lz25Ib9PmevUW5tHI+JwJrgW5wTyi2kOroPnwB1bcp1/BrDBSMeWfzRoHE5S07Qd/Lysc0YnRRnqlVoNGQR0JBjh2ARQBzX8+y9qrqzu90igQmx7NVDK+q6x7u25xDTM6ceEzquFCYAwxkkAiLyOPAM8DzwnKruFJEzgC8CZwOPA5eo6tPDzJwP3fA+xqlylyx3209Zt+BrI6UdYxoMGg40IrBTVZ9qbfso8DNVvVZErgJOV9UPhtqx4cDxpDpnrAjkOH2pCse+NmMxkcljlcOB3Sz+lDnAzcC3gKAIGG5SEm8pq/ZynSh2CDC0PWO1DBUBBb4uIgpcr6r7gC2qeqTZ/ySwxXWiiOwF9gKcggw0Y7PxzQzEMNT5Y16XZs683gwdDmxT1cMi8nvAncDfAPtV9bTWMU+r6umhdmw4kE/oRSalQnZz8s2gynBAVQ83P4+JyFeAC4CjIrJVVY+IyFbg2JBrGGHaUUKNMl0TgM0nWwRE5GTgJar6TPP5LcA/AvuBPcC1zc/bSxg6J/qSfDFFQEOc2Kbd5sWQSGAL8BURWbbzb6r6VRH5HnCbiFwO/AS4ZLiZBvQn4Fyr6XJmGYx5kS0Cqvoj4A8d2/8bePMQo4wXCNXst1cgxryVJzbCsChgXljF4MRwFd64evMYAejie/fhkGIjY/0xEZg4vtV63ZV2qU7sEwRjfpgITJC+pbrt30ut17coYL6YCEwI11uGfI6aIwCuZciGYX+BaGLUXiJszm90sUhgYnSn9rrRQV+OoL2tfZw5vuHDIoGJUaLyz6b6jBQsEpgQ3d7dN+6PSRyaABixmAhMnG5x0JL2W4ja2wwjFROBidI3xreQ3yiFicCaYc5vlMZEYE0wpzdqYbMDhjFzTAQMY+aYCBjGzDERMIyZYyJgGDPHRMAwZo6JgGHMHBMBw5g5JgKGMXNMBAxj5pgIGMbMMREwjJljImAYM8dEwDBmjomAYcycaiIgIm8TkUdF5KCIXFXrOoZhDKOKCIjICcBngIuB84B3ich5Na5lGMYwakUCFwAHVfVHqvo/wK3A7krXMgxjALVEYBvwROv3Q822/0dE9orIARE58Gu0khmGYfQx2jsGVXUfsA9ARH56Pc/+EnhqLHscnInZ08fUbDJ7wvy+a2MtETgM7Gj9vr3Z5kRVzxKRA6q6s5I9yZg9/UzNJrMnj1rDge8B54rIOSLyMuBSYH+laxmGMYAqkYCqPiciVwJfA04AblLVh2pcyzCMYVTLCajqHcAdCafsq2VLJmZPP1OzyezJQFQtM28Yc8bKhg1j5pgIGMbMGV0EprDGQEQeF5EfiMj9InKg2XaGiNwpIo81P0+vbMNNInJMRB5sbXPaIAs+3dyzB0Tk/BXZc7WIHG7u0/0isqu170ONPY+KyFsr2LNDRL4pIg+LyEMi8r5m+5j3yGfTaPcpC1Ud7R+LmYP/Al4JvAz4PnDeCHY8DpzZ2fZR4Krm81XAP1e24Y3A+cCDfTYAu4D/AAS4ELhnRfZcDfy949jzmv+7E4Fzmv/TEwrbsxU4v/l8KvDD5rpj3iOfTaPdp5x/Y0cCU15jsBu4ufl8M/D2mhdT1W8DP4u0YTdwiy64GzhNRLauwB4fu4FbVfU3qvpj4CCL/9uS9hxR1fuaz88Aj7AoRR/zHvls8lH9PuUwtgj0rjFYEQp8XUTuFZG9zbYtqnqk+fwksGUEu3w2jHnfrmzC65taQ6SV2iMiZwOvA+5hIveoYxNM4D7FMrYITIU3qOr5LJY+XyEib2zv1EUsN+pc6hRsAK4DXgW8FjgCfHzVBojIKcCXgPer6i/a+8a6Rw6bRr9PKYwtAklrDGqhqoebn8eAr7AI0Y4uw8fm57FV2xWwYZT7pqpHVfV5Vf0tcAMvhLIrsUdEXsrC2T6vql9uNo96j1w2jX2fUhlbBEZfYyAiJ4vIqcvPwFuABxs79jSH7QFuX6VdDT4b9gOXNRnwC4Gft0LianTG1O9gcZ+W9lwqIieKyDnAucB3C19bgBuBR1T1E61do90jn01j3qcsxs5Mssji/pBFpvTDI1z/lSwytt8HHlraAPwucBfwGPAN4IzKdnyBRej4vyzGipf7bGCR8f5Mc89+AOxckT3/2lzvARYP9NbW8R9u7HkUuLiCPW9gEeo/ANzf/Ns18j3y2TTafcr5Z2XDhjFzxh4OGIYxMiYChjFzTAQMY+aYCBjGzDERMIyZYyJgGDPHRMAwZs7/AeJP/gJV9YPaAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(\n",
    "    (triangle_ids_2d[1:, 1:] == triangle_ids_2d[:-1, 1:])\n",
    "    & (triangle_ids_2d[1:, 1:] == triangle_ids_2d[1:, :-1]),\n",
    "    origin=\"lower\",\n",
    "    cmap=\"Reds\",\n",
    "    interpolation=\"nearest\",\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "1f9a62f5-d242-40bc-9b05-945c499d1e63",
   "metadata": {},
   "outputs": [],
   "source": [
    "selected_vertices = t.gather(\n",
    "    vertices, 0, selected_triangle_ids.reshape([-1, 1, 1]).expand([-1, 3, 3])\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8eeb7f93-558c-4af5-9a2b-50888cd8a3a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([90000, 3, 3])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selected_vertices.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ff910497-ebd2-4601-8bb7-c91c75948c1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(412, 3)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.normals.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d49ec9fc-e2eb-4c33-97fe-8174e76eda3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "normals = t.tensor(model.normals.copy())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "85c1b002-a418-44fc-989c-ba9317d58859",
   "metadata": {},
   "outputs": [],
   "source": [
    "relevant_normals = t.gather(\n",
    "    normals, 0, selected_triangle_ids.reshape([-1, 1]).expand([-1, 3])\n",
    ")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "622114c1-fb42-449f-afac-f8e9ab6cd6a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "594a6282-457e-4d2a-9e75-c50f715cc2b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def foo(x=1.0, y=0.0, z=0.0):\n",
    "    total = (x ** 2 + y ** 2 + z ** 2) ** 0.5\n",
    "    vec = t.tensor([x, y, z]) / total\n",
    "    plt.imshow(\n",
    "        (\n",
    "            (\n",
    "                t.max(\n",
    "                    (relevant_normals * vec).sum(dim=1) / relevant_normals.norm(dim=1),\n",
    "                    t.tensor(0.0),\n",
    "                )\n",
    "                * ~pixel_mask\n",
    "            )\n",
    "        ).reshape([H, W]),\n",
    "        origin=\"lower\",\n",
    "        cmap=\"Reds\",\n",
    "    )\n",
    "    plt.colorbar()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3de97944-59d8-4494-84e1-4c057f8b8ece",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([90000, 3])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relevant_normals.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "0aa1af55-13a9-47de-9062-8a82577edfa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0605a86cafb34aea8ea13bdbf4858997",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='x', max=3.0, min=-1.0), FloatSlider(value=0.0, descr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.foo(x=1.0, y=0.0, z=0.0)>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(foo)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "071289c1-4222-4ae2-a7f0-51876a2de372",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 + 2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f5dedf92-f6c1-4bcd-b873-59bf86e7df8a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "781aa517-7557-4b81-b03c-94064c348995",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f9eac423ac0>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(\n",
    "    (\n",
    "        (\n",
    "            (\n",
    "                t.max(relevant_normals[:, 0]) / relevant_normals.norm(dim=1)\n",
    "                + 200\n",
    "                + t_.min(dim=1).values * 20\n",
    "            )\n",
    "        )\n",
    "        * (~mask2 & ~mask3).any(dim=1)\n",
    "    ).reshape([H, W]),\n",
    "    origin=\"lower\",\n",
    "    cmap=\"Reds\",\n",
    ")\n",
    "plt.colorbar()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa1a7dfc-edf2-48e4-a5c5-7561b8b38de1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}