{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dual Contouring\n",
    "\n",
    "Dual Contouring extracts a **triangle mesh** with vertices placed optimally within each cell. Unlike Marching Cubes, it can preserve sharp features when given accurate surface normals.\n",
    "\n",
    "## Simple Usage\n",
    "\n",
    "For most cases, you can use the simple one-liner interface:\n",
    "\n",
    "```python\n",
    "vertices, faces = isoext.dual_contouring(grid, level=0.0)\n",
    "```\n",
    "\n",
    "This automatically computes intersection points and normals from the grid values.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running cmake --build & --install in /home/gcnick/Documents/code/isoext/build/cp312-abi3-linux_x86_64\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import isoext\n",
    "from isoext.sdf import CuboidSDF, get_sdf_normal\n",
    "from _viz import show_mesh\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vertices: torch.Size([6146, 3])\n",
      "Faces: torch.Size([12288, 3])\n"
     ]
    },
    {
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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=600x400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simple usage - just call dual_contouring directly\n",
    "grid = isoext.UniformGrid([64, 64, 64])\n",
    "cube = CuboidSDF(size=[1.0, 1.0, 1.0])\n",
    "grid.set_values(cube(grid.get_points()))\n",
    "\n",
    "# One-liner: normals computed automatically from grid values\n",
    "vertices, faces = isoext.dual_contouring(grid, level=0.0)\n",
    "\n",
    "print(f\"Vertices: {vertices.shape}\")\n",
    "print(f\"Faces: {faces.shape}\")\n",
    "\n",
    "show_mesh(vertices, faces, color=\"lightblue\", smooth_shading=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Custom Normals for Sharp Features\n",
    "\n",
    "For shapes with sharp features (like cubes), you can provide custom normals computed from the SDF gradient for better results:\n",
    "\n",
    "1. **Get intersections** — Call `get_intersection()` to get intersection points\n",
    "2. **Compute normals** — Use SDF gradient for accurate surface normals\n",
    "3. **Run dual contouring** — Pass the intersection with custom normals\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intersection shape: torch.Size([24576, 3])\n"
     ]
    }
   ],
   "source": [
    "# Step 1: Find edge-surface intersections\n",
    "intersection = isoext.get_intersection(grid, level=0.0)\n",
    "points = intersection.get_points()\n",
    "print(f\"Intersection shape: {points.shape}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normals shape: torch.Size([24576, 3])\n"
     ]
    }
   ],
   "source": [
    "# Step 2: Compute accurate normals using the SDF gradient\n",
    "normals = get_sdf_normal(cube, points)\n",
    "intersection.set_normals(normals)\n",
    "\n",
    "print(f\"Normals shape: {normals.shape}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vertices: torch.Size([6146, 3])\n",
      "Faces: torch.Size([12288, 3])\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=600x400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Step 3: Run dual contouring with custom normals\n",
    "vertices, faces = isoext.dual_contouring(grid, level=0.0, intersection=intersection)\n",
    "\n",
    "print(f\"Vertices: {vertices.shape}\")  # (N, 3) float32\n",
    "print(f\"Faces: {faces.shape}\")        # (M, 3) int32\n",
    "\n",
    "show_mesh(vertices, faces, color=\"salmon\", smooth_shading=False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.12.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}