{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "-P3OUvJirQdR"
   },
   "outputs": [],
   "source": [
    "# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "44lB2sH-rQdW"
   },
   "source": [
    "# Camera position optimization using differentiable rendering\n",
    "\n",
    "In this tutorial we will learn the [x, y, z] position of a camera given a reference image using differentiable rendering. \n",
    "\n",
    "We will first initialize a renderer with a starting position for the camera. We will then use this to generate an image, compute a loss with the reference image, and finally backpropagate through the entire pipeline to update the position of the camera. \n",
    "\n",
    "This tutorial shows how to:\n",
    "- load a mesh from an `.obj` file\n",
    "- initialize a `Camera`, `Shader` and `Renderer`,\n",
    "- render a mesh\n",
    "- set up an optimization loop with a loss function and optimizer\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AZGmIlmWrQdX"
   },
   "source": [
    "##  0. Install and import modules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qkX7DiM6rmeM"
   },
   "source": [
    "If `torch`, `torchvision` and `pytorch3d` are not installed, run the following cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 717
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "sEVdNGFwripM",
    "outputId": "27047061-a29b-4562-c164-c1288e24c266"
   },
   "outputs": [],
   "source": [
    "!pip install torch torchvision\n",
    "!pip install 'git+https://github.com/facebookresearch/pytorch3d.git'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "w9mH5iVprQdZ"
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import torch\n",
    "import numpy as np\n",
    "from tqdm import tqdm_notebook\n",
    "import imageio\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import matplotlib.pyplot as plt\n",
    "from skimage import img_as_ubyte\n",
    "\n",
    "# io utils\n",
    "from pytorch3d.io import load_obj\n",
    "\n",
    "# datastructures\n",
    "from pytorch3d.structures import Meshes, Textures\n",
    "\n",
    "# 3D transformations functions\n",
    "from pytorch3d.transforms import Rotate, Translate\n",
    "\n",
    "# rendering components\n",
    "from pytorch3d.renderer import (\n",
    "    OpenGLPerspectiveCameras, look_at_view_transform, look_at_rotation, \n",
    "    RasterizationSettings, MeshRenderer, MeshRasterizer, BlendParams,\n",
    "    SilhouetteShader, PhongShader, PointLights\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cpUf2UvirQdc"
   },
   "source": [
    "## 1. Load the Obj\n",
    "\n",
    "We will load an obj file and create a **Meshes** object. **Meshes** is a unique datastructure provided in PyTorch3d for working with **batches of meshes of different sizes**. It has several useful class methods which are used in the rendering pipeline. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8d-oREfkrt_Z"
   },
   "source": [
    "If you are running this notebook locally after cloning the PyTorch3d repository, the mesh will already be available. **If using Google Colab, fetch the mesh and save it at the path `data/`**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 204
    },
    "colab_type": "code",
    "collapsed": true,
    "id": "sD5KcLuJr0PL",
    "outputId": "e65061fa-dbd5-4c06-b559-3592632983ee"
   },
   "outputs": [],
   "source": [
    "!mkdir -p data\n",
    "!wget -P data https://dl.fbaipublicfiles.com/pytorch3d/data/teapot/teapot.obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "VWiPKnEIrQdd"
   },
   "outputs": [],
   "source": [
    "# Set the cuda device \n",
    "device = torch.device(\"cuda:0\")\n",
    "torch.cuda.set_device(device)\n",
    "\n",
    "# Load the obj and ignore the textures and materials.\n",
    "verts, faces_idx, _ = load_obj(\"./data/teapot.obj\")\n",
    "faces = faces_idx.verts_idx\n",
    "\n",
    "# Initialize each vertex to be white in color.\n",
    "verts_rgb = torch.ones_like(verts)[None]  # (1, V, 3)\n",
    "textures = Textures(verts_rgb=verts_rgb.to(device))\n",
    "\n",
    "# Create a Meshes object for the teapot. Here we have only one mesh in the batch.\n",
    "teapot_mesh = Meshes(\n",
    "    verts=[verts.to(device)],   \n",
    "    faces=[faces.to(device)], \n",
    "    textures=textures\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mgtGbQktrQdh"
   },
   "source": [
    "\n",
    "\n",
    "## 2. Optimization setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Q6PzKD_NrQdi"
   },
   "source": [
    "### Create a renderer\n",
    "\n",
    "A **renderer** in PyTorch3d is composed of a **rasterizer** and a **shader** which each have a number of subcomponents such as a **camera** (orthgraphic/perspective). Here we initialize some of these components and use default values for the rest. \n",
    "\n",
    "For optimizing the camera position we will use a renderer which produces a **silhouette** of the object only and does not apply any **lighting** or **shading**. We will also initialize another renderer which applies full **phong shading** and use this for visualizing the outputs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "KPlby75GrQdj"
   },
   "outputs": [],
   "source": [
    "# Initialize an OpenGL perspective camera.\n",
    "cameras = OpenGLPerspectiveCameras(device=device)\n",
    "\n",
    "# To blend the 100 faces we set a few parameters which control the opacity and the sharpness of \n",
    "# edges. Refer to blending.py for more details. \n",
    "blend_params = BlendParams(sigma=1e-4, gamma=1e-4)\n",
    "\n",
    "# Define the settings for rasterization and shading. Here we set the output image to be of size\n",
    "# 256x256. To form the blended image we use 100 faces for each pixel. Refer to rasterize_meshes.py\n",
    "# for an explanation of this parameter. \n",
    "raster_settings = RasterizationSettings(\n",
    "    image_size=256, \n",
    "    blur_radius=np.log(1. / 1e-4 - 1.) * blend_params.sigma, \n",
    "    faces_per_pixel=100, \n",
    "    bin_size=0\n",
    ")\n",
    "\n",
    "# Create a silhouette mesh renderer by composing a rasterizer and a shader. \n",
    "silhouette_renderer = MeshRenderer(\n",
    "    rasterizer=MeshRasterizer(\n",
    "        cameras=cameras, \n",
    "        raster_settings=raster_settings\n",
    "    ),\n",
    "    shader=SilhouetteShader(blend_params=blend_params)\n",
    ")\n",
    "\n",
    "\n",
    "# We will also create a phong renderer. This is simpler and only needs to render one face per pixel.\n",
    "raster_settings = RasterizationSettings(\n",
    "    image_size=256, \n",
    "    blur_radius=0.0, \n",
    "    faces_per_pixel=1, \n",
    "    bin_size=0\n",
    ")\n",
    "# We can add a point light in front of the object. \n",
    "lights = PointLights(device=device, location=((2.0, 2.0, -2.0),))\n",
    "phong_renderer = MeshRenderer(\n",
    "    rasterizer=MeshRasterizer(\n",
    "        cameras=cameras, \n",
    "        raster_settings=raster_settings\n",
    "    ),\n",
    "    shader=PhongShader(device=device, lights=lights)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "osOy2OIJrQdn"
   },
   "source": [
    "### Create a reference image\n",
    "\n",
    "We will first position the teapot and generate an image. We use helper functions to rotate the teapot to a desired viewpoint. Then we can use the renderers to produce an image. Here we will use both renderers and visualize the silhouette and full shaded image. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 305
    },
    "colab_type": "code",
    "id": "EjJrW7qerQdo",
    "outputId": "93545b65-269e-4719-f4a2-52cbc6c9c974"
   },
   "outputs": [
    {
     "data": {
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zz0YpxejoKFrrOA04PDzM3XffTTabJZvN1qX3gLpUX5pk6i6ZBkzXUhmRlVxlmM/nGRwc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\nQmCC\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Select the viewpoint using spherical angles  \n",
    "distance = 3   # distance from camera to the object\n",
    "elevation = 40.0   # angle of elevation in degrees\n",
    "azimuth = 10.0  # angle of azimuth rotation in degrees\n",
    "\n",
    "# Get the position of the camera based on the spherical angles\n",
    "R, T = look_at_view_transform(distance, elevation, azimuth, device=device)\n",
    "\n",
    "# Render the teapot providing the values of R and T. \n",
    "silhouete = silhouette_renderer(meshes_world=teapot_mesh, R=R, T=T)\n",
    "image_ref = phong_renderer(meshes_world=teapot_mesh, R=R, T=T)\n",
    "\n",
    "silhouete = silhouete.cpu().numpy()\n",
    "image_ref = image_ref.cpu().numpy()\n",
    "\n",
    "plt.figure(figsize=(10, 10))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(silhouete.squeeze()[..., 3])  # only plot the alpha channel of the RGBA image\n",
    "plt.grid(\"off\")\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(image_ref.squeeze())\n",
    "plt.grid(\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "plBJwEslrQdt"
   },
   "source": [
    "### Set up a basic model \n",
    "\n",
    "Here we create a simple model class and initialize a parameter for the camera position. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "YBbP1-EDrQdu"
   },
   "outputs": [],
   "source": [
    "class Model(nn.Module):\n",
    "    def __init__(self, meshes, renderer, image_ref):\n",
    "        super().__init__()\n",
    "        self.meshes = meshes\n",
    "        self.device = meshes.device\n",
    "        self.renderer = renderer\n",
    "        \n",
    "        # Get the silhouette of the reference RGB image by finding all the non zero values. \n",
    "        image_ref = torch.from_numpy((image_ref[..., :3].max(-1) != 0).astype(np.float32))\n",
    "        self.register_buffer('image_ref', image_ref)\n",
    "        \n",
    "        # Create an optimizable parameter for the x, y, z position of the camera. \n",
    "        self.camera_position = nn.Parameter(\n",
    "            torch.from_numpy(np.array([3.0,  6.9, -2.5], dtype=np.float32)).to(meshes.device))\n",
    "\n",
    "    def forward(self):\n",
    "        \n",
    "        # Render the image using the updated camera position. Based on the new position of the \n",
    "        # camer we calculate the rotation and translation matrices\n",
    "        R = look_at_rotation(self.camera_position[None, :], device=self.device)  # (1, 3, 3)\n",
    "        T = -torch.bmm(R.transpose(1, 2), self.camera_position[None, :, None])[:, :, 0]   # (1, 3)\n",
    "        \n",
    "        image = self.renderer(meshes_world=self.meshes.clone(), R=R, T=T)\n",
    "        \n",
    "        # Calculate the silhouette loss\n",
    "        loss = torch.sum((image[..., 3] - self.image_ref) ** 2)\n",
    "        return loss, image\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qCGLSJtfrQdy"
   },
   "source": [
    "## 3. Initialize the model and optimizer\n",
    "\n",
    "Now we can create an instance of the **model** above and set up an **optimizer** for the camera position parameter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "collapsed": true,
    "id": "srZPBU7_rQdz"
   },
   "outputs": [],
   "source": [
    "# We will save images periodically and compose them into a GIF.\n",
    "filename_output = \"./teapot_optimization_demo.gif\"\n",
    "writer = imageio.get_writer(filename_output, mode='I', duration=0.3)\n",
    "\n",
    "# Initialize a model using the renderer, mesh and reference image\n",
    "model = Model(meshes=teapot_mesh, renderer=silhouette_renderer, image_ref=image_ref).to(device)\n",
    "\n",
    "# Create an optimizer. Here we are using Adam and we pass in the parameters of the model\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dvTLnrWorQd2"
   },
   "source": [
    "### Visualise the starting position and the reference position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 335
    },
    "colab_type": "code",
    "id": "qyRXpP3mrQd3",
    "outputId": "47ecb12a-e68c-47f5-92fc-821a7a9bd661"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Reference silhouette')"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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C+QuyXWscjXY+Vo2qQg1QjTqqUAOMv44xnzqMiD0jYuaOx8CbgFuBy4F3F6u9G/jemFsn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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "\n",
    "_, image_init = model()\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(image_init.detach().squeeze().cpu().numpy()[..., 3])\n",
    "plt.grid(\"off\")\n",
    "plt.title(\"Starting position\")\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(model.image_ref.cpu().numpy().squeeze())\n",
    "plt.grid(\"off\")\n",
    "plt.title(\"Reference silhouette\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aGJu7h-lrQd5"
   },
   "source": [
    "## 4. Run the optimization \n",
    "\n",
    "We run several iterations of the forward and backward pass and save outputs every 10 iterations. When this has finished take a look at `./teapot_optimization_demo.gif` for a cool gif of the optimization process!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000,
     "referenced_widgets": [
      "79d7fc84b5564206ab64b2759474da04",
      "02acadb61c3949fcaeab177fd184c388",
      "efd9860908c64bfe9d47118be4734648",
      "f8df7c6efb7d47f5be760a39b4bdbcf8",
      "d8a109658c364a00ab4d298112dac6db",
      "2d05db82cc99482bb3d62b6d4e5b1a98",
      "c621d425e2c8426c8cd4f9136d392af1",
      "3df8063f307040ebb8ff8e2f26ccf729"
     ]
    },
    "colab_type": "code",
    "id": "HvnK5VI5rQd6",
    "outputId": "4019c697-3fc6-4c7b-cdfe-225633cc0d60"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "79d7fc84b5564206ab64b2759474da04",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=200), HTML(value='')))"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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xSnGKOKU4RZxSnCJOKU4RpxSniFOKU8QpxSnilOIUcUpxijilOEWcUpwiTilOEacUp4hT\nilPEKcUp4pTiFHFKcYo4pThFnFKcIk4pThGnFKeIU4pTxCnFKeKU4hRxSnGKOKU4RZxSnCJOKU4R\npxSniFOKU8QpxSnilOIUcUpxijilOEWcUpwiTilOEacUp4hTilPEKcUp4pTiFHFKcYo4pThFnFKc\nIk4pThGnFKeIU4pTxCnFKeKU4hRxSnGKOKU4RZxSnCJOKU4RpxSniFOKU8QpxSnilOIUcUpxijil\nOEWcUpwiTilOEacUp4hTilPEKcUp4pTiFHFKcYo4pThFnFKcIk4pThGnFKeIU4pTxCnFKeKU4hRx\nykIIS70PItKBRk4RpxSniFOKU8QpxSnilOIUcUpxijj1/4bRIP/CDC5NAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JJ+jv7+84tW8xO37yP0zdvce21Wplf3ulVqsxNTXF1NQU9Xo9e2y691a/8Gtp6G+lnMWe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\nSnGKOKU4RZxSnCJO/T+EYu27z/EzsAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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po3COSNiZE4YgDBewKBBLHXsOO/+ZfO6wW5kMW8dKLuaW00vhHJF4AMJmZbyjJt7zmnxe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\nH21MNb2uWcwlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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48ccf58orrwRQONeQWmv7cO+99zIyMkK5XE4C0G63OXbsGDfccENf83Atvq603b17N4cO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\nClEDPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sFhdUTTLvSmmA/vL9tZ9hFSQm/puZAWBiYgKAm36aKW2jZowoQc155r4lEgkA7lhBhUIB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\nKZSTEEv5f5tSHDOzyDx2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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eUywWI4GaUVxbjJ2KM0l0FkBT4EeLMwgC7Nu3b13Ox2aD4rwAKBaLyGazzkCR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\nT/n//95PBraYcUcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hUMAdd9zR6Sw1pastZy6Xwyte8Qq/HlBPdgTTdA+DLIMdqTQf0p/85CcN5xwaGsLQ0BAm\nJib8ekizNVAzF1f/LlWci51vtq1ZhFnfv2eeeQbnn38+UqmU31VtdnYWV1xxRbO/aUW45557MDY2\nhnXr1iEej/vd7XTZ2IwZ6Mh2uVzGVVddtep57UnLqa2Hrn7QfRvz+TyKxSIKhQLuvPPOwGNzuRwA\n+K6waXX12Dy6sbp5rnK5jHw+j02bNmFycrJhW5Ala1Wc9np7W9C+YetanQ97KQHwGzwopTA5OYm3\nvOUtDdFuEWm4P6vFrl27MDw8jHQ6jYmJCQwNDfnCtF/CZl718C/33XcfACCZTHbsxaLpast51113\nYfPmzb61BIBCodC2pmbj4+P+w6rvoy5n6mlqasoXctCDvpRyZKvly6jtYcIOyl+QxdT5np6exsjI\niL+f3Tl8ampq1bqZffrTn8bAwAAGBgb8POlqrHK5jPn5eWzcuHFBxP3w4cM4efKk3+b4tNNOW9VR\nCnvSclarVaTTafT19fl/Rjqdblv6pjD1vH44dU8QXeadn59vsKBRLq3+XYwYWxVi2Lowd9sWql7e\nu3cvLrjgAqxfv76hbtO+xnbe7zDGx8eRSCQwMDDgj60Uj8cbPB7dOsusc9br1q9fj0qlgsnJSRw4\ncMCZ4UO7Xpwigmw26/9Zp59+Oh599FG8973vbdt5zAddC1O/lfv6+lCr1ZBKpRCPx1Eul/1jooQa\n5sIuRnBRLnMrk7Y8ev7gwYNYt24dMpkMLr74Yt96AmjorWIeu9LivOuuuzAwMNDQ8D+RSCCTyTTk\nHUBDmbNcLmNmZgYnTpzAJz7xiRXN41LpanHqNq06ICMiOH78OJLJ5Iqd07Sg9iQiDVHMMEsaJSpz\nnb09aP+g4+1uauYDHBQIO3r0KIaHh7Fly5YF4w+Z1xHUZ9R2n9tJLpfzu8rpiLwWqH0d2nMqlUqY\nm5vD8ePH8dGPfnTF8tYOulqcO3fuxAMPPIBqtdowqHIikcAjjzyC973vfcs+R1BViZ7slkR6f/PB\n13WEqVQqUCyturnLEWdQY4wDBw5gYGAAGzZswOjoaEM50xSiGbOIesm0m1wuh0Qi4VtMPen6ZHsE\nQh1BPnToEG644YYVyVO76WpxAkCpVPKDQfrP0gMuL4dcLrdAmGGjDdiDOeuHW7e91VZdi7larSKT\nyfj7mmk2mzd/gxo72OVIPU1OTvqjKSQSCYyNjTWUy2yRmQINwkz7W9/6VlurKHQkXY/Za/ZjNdsy\nm/ezWCzi2LFja0aYQA+Is1gsolwu+w+Sfqsmk0k89thjeM973rPsc9juKbDQiugHRW/Tv2aXLS0a\n7frq7bovZjabXbSFtLe9/PLLvquvBwNLpVLYtGlToHjNc5nXa2IL1b72lahSsQc0M0e9F5GGwNyx\nY8fWZD/Trhfn/v37/Tfp8PBwQ/lTRPDEE0/g0ksvXVSa+s2tH0pTDEGV9vayGco3G0SY5SSdfiwW\na9rcMKxBfdD+r3rVq0JfInpZ04pLat8DO12d//vuu2/ZVSraW0kmk8hmsw2W3mz5Va1WMTU11fF6\nyuXS9f05c7kcjhw5gnw+j/n5eT8wYzYkeOyxx5aUdqvlLr3e3sdeH9Tzxe4sbRN0vrBWPeYx9rlX\nAvPc/f39bUvTDP7oa7VHf5idnW3L+TpJ14sTqPfLnJ6eRj6f9z9fYAv04YcfXtY5ggQQ5XLqZfPX\nngeCe8EETfYxrXYTazdhZdzltrXV3oodlTW/DwPAb463Ft1Ym54QJwBMTEz4zfbMiKkuf7ZaH6cf\nkmblTJsokZr7RK2LElWYUDtB2EtqucRiMaRSKb/bn9nAAPjdCPZzc3PLPpcL9Iw477jjDhw6dKih\nmZa2njp6++CDD7acnv2wRVnNMMvYrKwXdY7VYDFCDxKgfQ+WOoSJfiHqwbfNgbN1OVO7s/l8Hlde\neeWSzuMaPSNOANixYwcOHz7cUPY0BZpOp5sKtJXqg6DlKNe1E+XBlSIoMKR/l9L4QwtT/z/andWT\nGWQrFov44Ac/2J4LcYCubvgexv33349TTjkF2WzWLwvp1iO6gfT8/PyCzsJmQ3cTXa4K+gS8nsyv\nT5tRWbOJWVhAJ6y7WlTnbXt/e1srZWF7XhNUfrWDWOa8Hi+3Uqm03PBDi1IzMjKCwcFBv6mebhUk\nUu8JtJajs2EN33vKcmqee+45HDt2DDMzM34dqCkiXa556KGHFhwb9DJrJRik1wcRZSWblV+Xk85q\nlU/Ne/HAAw803X98fBwA/ECSdmXNzxzql6Aev2itCjOKrq/nDCKXy2F8fBznnHMOlFIYGhpqCCxo\nRAQPP/ww3v/+9zesC2OpgZ6w9YsVYBRRIyMsZtSEKEwXUy/bgTNzFAoTs8WV6X3oOmpbmNrjqFQq\nyOfzy867i/SkW6sZHx/HWWedhVNPPdUXqDk6uu4dPzs7i8svvzzUrTXHkbXbdpruq+3Smm6t7YYG\nDUAdNih1K40Q9Lqg/cxt5jqNvRzm1gJYUDer27Sa9/PFF1/0l3XPIfO+1Gq1hiJBMpnE4OAgMpkM\nMpmM38MHqPcnNV+ea5Ge7M/ZjJ07dwKA/xn2devWNXSD0qTTaf/NbhMWobS3t+LeuspSLGuQ1dTT\n0NAQqtVqQ2DOPJdep4Vp12uaTfS6pdokiJ4sc9ps27YNBw8e9L9vYls289uZYYS5tOZxyxHlago6\n6CW0nHpU2zr39/ejv7/f7xhtR2D1pBu2m581NBu1VyoVXH311cu+Xlfpactpsn37duRyOZx11lnY\nsGEDBgcH/SoWs7MuEF5XaS43K39GuY7LEWKQlWvV8rWr7Kkxy5/aXRWpj46gO6JHDbamy5jxeBzZ\nbLZh3KJSqYSZmZm25dVFKE4DHb7/3Oc+h1e+8pX+59zNQJF+eIMeZBfd1TDBmR2ko7a3EzMoZDYE\nCerlosvYuteJ2dhAj2TQzS4tQLc2kB07duDZZ5/FkSNHGt7OUW7rclzaVq3aau3TToKu3ywyaOuo\ny5V2tYl2cTU6wDQ3N4frrrtuVa9ltaHlDEEHi3bv3o3zzjtvwfYo0TUTWzvKoDbLcWfDjml2/GKF\nrl1VM+hjWtCgCLLZqF2XM/P5fFfWa9rQcjbh5ptvxvPPP99yMKQT0dlWRRLUxW2xabRC1PWaVU72\nWMBmGd8c1UC7vnrc4ampqbbl1WUozhb4yEc+Eum6apa7fbWJEmurx7aCXfdqurW2KE3hml8Br1Qq\nKJVKOHnyJLZt27bo/K5F6Na2yEoESKLOtZj1zQI6QVHmsPTtIJHdkTwoH7bIm/Ud1emYg5zZDSbM\nY6vVKmZmZnDZZZdF5r/boDiXQKtC7ZSlbKWp3lKite0OJgW1TgrqXK5Hju81KM4WWUoZshP1i3Za\ni017MQEhvU8raZqiC3sZaMymf7qZXzeMbLBYKM4uopkww6xlq25v0PmC5qMIis6aaZii1PWZ3TAe\n0FKgOFeI5VrD5Vi85R7TivVspVwcVBY1x3Cy3Vk96f6fpVIJJ06ccH5k9pWC4lwC9sMbFCAJskxB\n5b2wY8zjmtU1NqvjNNOJKnNGzUedP+g6g4SplEKhUFggTF3fqV3YiYkJ7NixI/ScvQKrUlrE7JVi\nCquZa7eY6oooaxQUKFmM9Wr13Is5NkqYQVOtVkOxWAydCoUCjh07RmF60HIukiBr10rAwz4marnV\nY5vt06zMGVUGbVYNE+W+hu1Tq9V8y6nTNOsxjx49ik996lOR19dLUJyLIKiRdpSlaaVKo9l+rdLM\nBW4littM2FHnDbKcetn8mFM+n/fd10KhgGq1umC8IFKnp0dCWAp6fBvgd0Kwm5zZg3vpNqJmCxlt\nNcJGQgga1KvVzzHY63VezfVm/sN+7XmbKGFqUeoAjxbkWh+1YCVQHOCrvQQFhGwrGrUtiLAya9QU\ntr89b6Yf9huUj6DrCAv4BG3XFlOLk7QOxblIdG8V8wHW33+0LUaUoMJE1izYE0RYOvZ2c30zqxcW\n0AlaNn/NSY8RpOsqu2lM2dWA4lwCO3fuXOAumg+uSZj4zOWg9ea6xVjP5VjOqHzaRIlbi1PPF4vF\nrh5OZKVgQGiJKLWwrjLIYtrub1DdoZ4PCjgtJj86jaj8BuU/qO61WR1nmLW3rWi1WkWhUFjSNfU6\ntJxLRLu3tvjCXFpNWJnN3GbvFySQpVjPsHM32zfseoLcXnPSH6/dunXrku9zL0PLuQxMa2S6tvb4\nOLYlta2UKS7zGNvS2fuZ20zsNFq1zM3qNu3zhQlXi7NUKtFqLgOKc5nYItLDb0SJNEiYUe5u2LIm\nrBF72LyZ7zBXO0rItvW0g2E6Mjs/P49rrrkm5M6RZrCesw2Y3+y0R3dvVv9pjwwfVP8ZVc+p1wML\nh+W026+GzQf92oS55rYo5+fnUalUemKMn3ahWM+5cmhxatdWVyE0K4cGBVGalfWiyoBAsHDM9eZ+\n9m+Uixo2r0VZLpdRLpdRKpUozDZBy9lmzA/ymOPjJBKJBd9Hsa2o/R2VqM8CRrUQAhBoUYPmNa20\nBDLntUjN78rQYi6NMMvJMmebMctwlUrFt0DmKHL6Qz3m8JDmB3zs9cDCTsrmZIsnrPxqljGDyqRR\nQSbb0mpRmsIslUptvZe9Di3nCmBaT6D+8OsvY5llz7AyZ9jXx8LKnM0mnQf9uxjLGeb2akFqlzaf\nz2P79u0rdk+7mTDLSXGuEHZPCz3Uo/4N+uK1+Rv2xeuwgFAzt9b+bdWlDWuyVy6X/QYGc3Nz+PjH\nP97O29dTUJwdRvdmsQVqR3G1qGwL24o4gWC3V683t5vYbrApRh3Ysgfduvbaa1flvvUCFKcDaIGK\niB8gCqpiCaqOMa3pYi2nXjaxl8PcVy1O8wO4xWKRlrKNUJwOocuksVis4ZuTUeIMi9Y2K4sCixtV\nz7aSZl/MSqVCUa4AFKeD6M/Ya6tofpYgzKKulDjNKhIzEjs/P498Po9bbrllRe9FL0NxOorZughA\nQ72o/Q2RpYozClOUZgMKPYzIrbfeumLXTupQnGuIMMHaZc5WqljMdKJaAJVKJdx+++0dud5eh+Jc\no+ggUiKRaBjmI6jaxRYqsLAMWavVkEqlkE6nUa1WcdNNN3XkusjvoDi7hPHxcT/Sq13eoDa6tVoN\ng4OD6Ovra2gscNttt3X6EogFxUmIo7BXCiFrDIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqT\nEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEeh\nOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlx\nFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqT\nEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEeh\nOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlx\nFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqT\nEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFIqTEEehOAlxFFFKdToPhJAAaDkJcRSKkxBHoTgJcRSK\nkxBHoTgJcRSKkxBH+X/aoRrtktm6nQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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E6hodoVcTSy9MS6nbK4MgoBA3EYpzG6GbY1xf3HIJMq04k5pjwjCkILcIinOb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\nPIXiJMRT/j+THJIQ/UO5mQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UZVCAS1vLm2++ebEvYcdDcbYZPfetFqZ+94f5LlC7zhlkUZupc0ZZTvPTXgcO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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Akb3f7pTQr1ur++11HG6kVt9zYkdkOY3IYKE4A6NUKkFEkM/nU78QKelFRklu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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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YNJPJYGxsLLwp7d27F9u3b1/Q9kkfi3PXrl0YGBhAoVAIk8lti2mLE5jvUkbhuoHGGDz3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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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op74Ogc9frh2Kc8CoFbVf4mP3f7r9m91YznYL0N1rB+1Akc7W7gaBhu0V74Mk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\nOAkJFIqTkEChOAkJFIqTkED5/zlzTf5ThpLoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jgfRQOt38VC6XEQQBKpUK3vve967ZMdv0ZUCoWCxGQ6k2b94MoLW3TLlcXtaBXN9cuvnC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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dfo/7dL/bdY8LBtmCZILB6jAJT6VQnGuMilSF6Ao0bbBpd36SODtNWr5+diNM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\nQjzl/wPI78CAnl3IGQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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y6U6TSus8fIve7vq0v5uYgjRdW/3eUrZhbh6Kc4joSK4tUD3+0x7naVrOuDGe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\nJyGBQnESEih/DwZFmCjQVasbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Y/UBNgTZ72W6zPp5RlhOIfkmu/rTF6OpUrZQK223teubJkydpLdsExdlhTIGa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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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btVot0tr1El3UPubxrvUoknaP2PlHbTdfaOa6UgqpVAq5XC4Ubi6XS5QvcTOy4gQQdsyb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\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NWu77dOdtfG651l8uLS3hIx/5yIZdv60CxbmJ2CK1Berr/+la1LQ+nkmWE0h+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\nk5BA+f8EUo6wXcG7tAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "loop = tqdm_notebook(range(200))\n",
    "for i in loop:\n",
    "    optimizer.zero_grad()\n",
    "    loss, _ = model()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    \n",
    "    loop.set_description('Optimizing (loss %.4f)' % loss.data)\n",
    "    \n",
    "    if loss.item() < 200:\n",
    "        break\n",
    "    \n",
    "    # Save outputs to create a GIF. \n",
    "    if i % 10 == 0:\n",
    "        R = look_at_rotation(model.camera_position[None, :], device=model.device)\n",
    "        T = -torch.bmm(R.transpose(1, 2), model.camera_position[None, :, None])[:, :, 0]   # (1, 3)\n",
    "        image = phong_renderer(meshes_world=model.meshes.clone(), R=R, T=T)\n",
    "        image = image[0, ..., :3].detach().squeeze().cpu().numpy()\n",
    "        image = img_as_ubyte(image)\n",
    "        writer.append_data(image)\n",
    "        \n",
    "        plt.figure()\n",
    "        plt.imshow(image[..., :3])\n",
    "        plt.title(\"iter: %d, loss: %0.2f\" % (i, loss.data))\n",
    "        plt.grid(\"off\")\n",
    "        plt.axis(\"off\")\n",
    "    \n",
    "writer.close()"
   ]
  },
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    "## 5. Conclusion \n",
    "\n",
    "In this tutorial we learnt how to **load** a mesh from an obj file, initialize a PyTorch3d datastructure called **Meshes**, set up an **Renderer** consisting of a **Rasterizer** and a **Shader**, set up an optimization loop including a **Model** and a **loss function**, and run  the optimization. "
   ]
  }
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