Marching Cubes SDF.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fbe4e2d2",
   "metadata": {},
   "source": [
    "- break bounding box into grid\n",
    "- record every voxel center\n",
    "- compute distance voxel center from mesh\n",
    "- marching on voxel grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "faa3cb41",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import igl\n",
    "from meshplot import plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b5652a8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_cube(x,y,z,delta):\n",
    "#     print(x,y,z,delta)\n",
    "    return np.array([[x+delta, y+delta, z], [x+delta, y, z], [x, y, z], [x, y+delta,z],\\\n",
    "        [x, y+delta, z+delta], [x,y,z+delta], [x+delta, y+delta, z+delta],[x+delta,y,z+delta]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bc7d5e27",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_grid( bounds, delta=1):\n",
    "    min_bounds = bounds[0]\n",
    "    max_bounds = bounds[1]\n",
    "    x_b = round((max_bounds[0] - min_bounds[0])/delta+1)\n",
    "    y_b = round((max_bounds[1] - min_bounds[1])/delta+1)\n",
    "    z_b = round((max_bounds[2] - min_bounds[2])/delta+1)\n",
    "    grid_cells = []\n",
    "    centers = []\n",
    "    points  = []\n",
    "\n",
    "#     print(bounds)\n",
    "    for i in range(x_b-1):\n",
    "        for j in range(y_b-1):\n",
    "            for k in range(z_b-1) :\n",
    "                x = min_bounds[0] + i * delta\n",
    "                y = min_bounds[1] + j * delta\n",
    "                z = min_bounds[2] + k * delta\n",
    "                points.append([x,y,z])\n",
    "                grid_cube = get_cube(x,y,z,delta)\n",
    "                center = grid_cube.mean(0)\n",
    "                centers.append(center)\n",
    "                grid_cells.append(grid_cube)\n",
    "    \n",
    "    return np.array(grid_cells), np.array(centers), np.array(points),[x_b-1,y_b-1,z_b-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "27b9558d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(27, 8, 3) (27, 3) (27, 3)\n"
     ]
    }
   ],
   "source": [
    "bounds = np.array([[0., 0., 0.], [2.5, 2.5, 2.5]])\n",
    "grid_cells,centers,points,sizes = create_grid(bounds)\n",
    "print(grid_cells.shape, centers.shape, points.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ab3a6af3",
   "metadata": {},
   "outputs": [],
   "source": [
    "v,t,f = igl.read_mesh('bunny.mesh')\n",
    "\n",
    "zmin = v[:,-1].min() #+ 0.1 * v[:,-1].min()\n",
    "zmax = v[:,-1].max() #+ 0.1 * v[:,-1].max()\n",
    "ymin = v[:,-2].min() #+ 0.1 * v[:,-2].min() \n",
    "ymax = v[:, -2].max() #+ 0.1 * v[:, -2].max() \n",
    "xmin = v[:, -3].min() #+ 0.1 * v[:, -3].min() \n",
    "xmax = v[:, -3].max() #+ v[:, -3].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b8006440",
   "metadata": {},
   "outputs": [],
   "source": [
    "bounds = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]]) # bounds for bunny\n",
    "grid_cells,centers,points,sizes = create_grid(bounds,delta=0.004) #0.004-0.009"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "649b8546",
   "metadata": {},
   "source": [
    "### Signed Distance Field\n",
    "![signed distance](https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQFzpcjrhR0Qivr-89wvmof4gDN-5ylSXRrSQ&usqp=CAU)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8e323f28",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = igl.signed_distance(centers, v, f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "355af9d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "c_reshape = d[0].reshape((sizes[0],sizes[1],sizes[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "530e70b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(39, 39, 30)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_reshape.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c9635d90",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "version_minor": 0
      },
      "text/plain": [
       "Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-0.016860…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f560853f160>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig= plt.figure(figsize=(10,10))\n",
    "plot(v,f)\n",
    "plt.imshow(np.rot90(c_reshape[:,:,15]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "cd648149",
   "metadata": {},
   "outputs": [],
   "source": [
    "from skimage import measure"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1be651b9",
   "metadata": {},
   "source": [
    "### Marching Cubes\n",
    "![marching cubes](http://www.cs.utah.edu/~whitaker/sceneRecon/pics/sparse-field4.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a82e4334",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "verts, faces, normals, values = measure.marching_cubes(c_reshape,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "dee650eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8e0f622750c7455f80ace1208ffd0e35",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(19.0, 18.…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<meshplot.Viewer.Viewer at 0x7f55ebed2cf8>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(verts, faces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af1138dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "voxel = 3dconv\n",
    "point clouds = conv1d\n",
    "mesh = geometric deep learning (vertices, adjacency) "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}