{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mesh Extraction from a fixed Signed Distance Field (SDF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we demonstrate how to use FlexiCubes to extract a mesh from a fixed signed distance field (SDF) **without** optimization. Note that in this case, the extraction scheme used is the original Dual Marching Cubes [Nielson 2004] algorithm, with minor improvements in splitting. To begin with, we will establish two functions: one for calculating the SDF of a cube, and another for determining its analytic gradient. In your specific application, the SDF might be predicted by a network, with gradients computed through methods such as finite differences or autograd."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import kaolin as kal\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import render"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cube_sdf(x_nx3):\n",
    "    sdf_values = 0.5 - torch.abs(x_nx3)\n",
    "    sdf_values = torch.clamp(sdf_values, min=0.0)\n",
    "    sdf_values = sdf_values[:, 0] * sdf_values[:, 1] * sdf_values[:, 2]\n",
    "    sdf_values = -1.0 * sdf_values\n",
    "\n",
    "    return sdf_values\n",
    "\n",
    "\n",
    "def cube_sdf_gradient(x_nx3):\n",
    "    gradients = []\n",
    "    for i in range(x_nx3.shape[0]):\n",
    "        x, y, z = x_nx3[i]\n",
    "        grad_x, grad_y, grad_z = 0, 0, 0\n",
    "\n",
    "        max_val = max(abs(x) - 0.5, abs(y) - 0.5, abs(z) - 0.5)\n",
    "\n",
    "        if max_val == abs(x) - 0.5:\n",
    "            grad_x = 1.0 if x > 0 else -1.0\n",
    "        if max_val == abs(y) - 0.5:\n",
    "            grad_y = 1.0 if y > 0 else -1.0\n",
    "        if max_val == abs(z) - 0.5:\n",
    "            grad_z = 1.0 if z > 0 else -1.0\n",
    "\n",
    "        gradients.append(torch.tensor([grad_x, grad_y, grad_z]))\n",
    "\n",
    "    return torch.stack(gradients).to(x_nx3.device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's call upon FlexiCubes to extract the mesh from this SDF, both with and without providing the gradient information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = 5\n",
    "device='cuda'\n",
    "fc = kal.non_commercial.FlexiCubes(device)\n",
    "voxelgrid_vertices, cube_idx = fc.construct_voxel_grid(res)\n",
    "voxelgrid_vertices *= 1.1 # add small margin to boundary\n",
    "scalar_field = cube_sdf(voxelgrid_vertices)\n",
    "\n",
    "mesh_with_grad_v, mesh_with_grad_f, _ = fc(\n",
    "    voxelgrid_vertices, scalar_field, cube_idx, res, grad_func=cube_sdf_gradient)\n",
    "\n",
    "mesh_with_grad = kal.rep.SurfaceMesh(vertices=mesh_with_grad_v, faces=mesh_with_grad_f)\n",
    "mesh_no_grad_v, mesh_no_grad_f, _ = fc(\n",
    "    voxelgrid_vertices, scalar_field, cube_idx, res)\n",
    "\n",
    "mesh_no_grad = kal.rep.SurfaceMesh(vertices=mesh_no_grad_v, faces=mesh_no_grad_f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we visualize the two meshes. Without the gradient information (left), the extracted vertex locations are positioned at the centroids of the primal (Marching Cubes) mesh. Consequently, this method fails to reconstruct the sharp features present in the cube."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "camera = render.get_rotate_camera(0, iter_res=[512, 512], device=device)\n",
    "f, ax = plt.subplots(1, 2)\n",
    "output = render.render_mesh(mesh_no_grad, camera, [512, 512], return_types=['normals'])\n",
    "ax[0].imshow(((output['normals'][0] + 1) / 2.).cpu())\n",
    "output = render.render_mesh(mesh_with_grad, camera, [512, 512], return_types=['normals'])\n",
    "ax[1].imshow(((output['normals'][0] + 1) / 2.).cpu())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize interactively with [kaolin's interactive visualizer](https://kaolin.readthedocs.io/en/latest/modules/kaolin.visualize.html), by moving around the camera and adjusting a wireframe to see the topology of the meshes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9adcd325a6664219aeb6a2a4843ede3b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "VBox(children=(Canvas(height=512, width=1024), interactive(children=(FloatLogSlider(value=0.3981071705534972, …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "95aa177aef744427b5061f5cd1547f5c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "render.SplitVisualizer(mesh_no_grad, mesh_with_grad, 512, 512).show(camera)"
   ]
  }
 ],
 "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": "3.9.18"
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "0310e1f1b5744d52bad42a93c0b4cacd": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_cad2738b444c452ebf92880dbd7c86f1"
      }
     },
     "0fc858ce475b4c5b854ee31d1ff0ce35": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_2e7fc70235424294be5f51f4ba00c6a8"
      }
     },
     "10785ebff0264da2a584b1cbdc280d7c": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "2.0.0",
      "model_name": "LayoutModel",
      "state": {}
     },
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      "buffers": [
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        "path": [
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      "model_module": "@jupyter-widgets/controls",
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_d7995ce46a94421881e055f652521fac"
      }
     },
     "23d0f8680d6d4eecb025638aba77cc8f": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_3fdfab044d404ec8b21a1eed31705844"
      }
     },
     "331d1e10b4d3476297f4f5d27508aeba": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_203326cb43394e3eb0a75166ddccf87d"
      }
     },
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      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_e046c6442bc34b1eb9dfa1629f4552c3"
      }
     },
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        "path": [
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      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
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      }
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_cfed2b9aa96e4204aa505002deb6e0fe"
      }
     },
     "53fd909a138245578e6033ab51e712e0": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_747776a93eb041ae85ec7aee3c06b451"
      }
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        "path": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_09357156e94142fe8abc1f70c30e70ec"
      }
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_08a6bc9e8c2441998aa15ebc4c69667d"
      }
     },
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      "buffers": [
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      "model_name": "ImageModel",
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        "path": [
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      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
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      }
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_c83af41cbb3542708293e7f95bfed76d"
      }
     },
     "82717cc25b2c44a4a70742d2ec263435": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_365398449b8a4739988051896039fa3a"
      }
     },
     "9fd4f2bfca9541819bcb629c760281ed": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_9b1dd5b7ae08434780df8c2e64a00d65"
      }
     },
     "9fda09fe038f44bda7c14162a767c606": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_4887c0e8468349cbafcbd8b3d8aa6fbd"
      }
     },
     "a127ce11df8942c49b6bee68d7700778": {
      "buffers": [
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        "encoding": "base64",
        "path": [
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        ]
       }
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      "model_module": "@jupyter-widgets/controls",
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_883050fc8e244613b62e9aee196b7ae4"
      }
     },
     "c74d79409bc0415c85ff0e0ab84b90cc": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_5e1d0da65fef47868fe59005668870da"
      }
     },
     "c814137f17234c62af85b056cd34e3e3": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_a288de127d224e0e82c1712ebbf8deaf"
      }
     },
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      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_9548190091d34d27a44714164b565f8b"
      }
     },
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_10785ebff0264da2a584b1cbdc280d7c"
      }
     },
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_687d435e027b48e984eb2789ad6f2d03"
      }
     },
     "db7c6da2896d474caab9f3273acd25e9": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_d7790747ebbf424ca165460ce9d6033e"
      }
     },
     "f05d0264cb5b449b9543509c2bedc711": {
      "buffers": [
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        "path": [
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        ]
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        "encoding": "base64",
        "path": [
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        ]
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      "model_module": "@jupyter-widgets/controls",
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_076373e179904a4ea7bb68807ef129a9"
      }
     },
     "fd76f2be3af54b05977e47137750f95f": {
      "buffers": [
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        "encoding": "base64",
        "path": [
         "value"
        ]
       }
      ],
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "2.0.0",
      "model_name": "ImageModel",
      "state": {
       "layout": "IPY_MODEL_570818bdbfe7490abbd09a27602e7dde"
      }
     }
    },
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}