code: def marching_cubes_naive(
      vol_batch: torch.Tensor,
      isolevel: Optional[float] = None,
      return_local_coords: bool = True,
  ) -> Tuple[List[torch.Tensor], List[torch.Tensor]]:
      """
      Runs the classic marching cubes algorithm, iterating over
      the coordinates of the volume and using a given isolevel
      for determining intersected edges of cubes.
      Returns vertices and faces of the obtained mesh.
      This operation is non-differentiable.
  
      Args:
          vol_batch: a Tensor of size (N, D, H, W) corresponding to
              a batch of 3D scalar fields
          isolevel: the isosurface value to use as the threshold to determine
              whether points are within a volume. If None, then the average of the
              maximum and minimum value of the scalar field will be used.
          return_local_coords: bool. If True the output vertices will be in local coordinates in
          the range [-1, 1] x [-1, 1] x [-1, 1]. If False they will be in the range
          [0, W-1] x [0, H-1] x [0, D-1]
      Returns:
          verts: [{V_0}, {V_1}, ...] List of N sets of vertices of shape (|V_i|, 3) in FloatTensor
          faces: [{F_0}, {F_1}, ...] List of N sets of faces of shape (|F_i|, 3) in LongTensors
      """
      batched_verts, batched_faces = [], []
      D, H, W = vol_batch.shape[1:]
  
      # each edge is represented with its two endpoints (represented with global id)
      for i in range(len(vol_batch)):
          vol = vol_batch[i]
          thresh = (
              ((vol.max() + vol.min()) / 2).item()
              if isolevel is None
              else isolevel
          )
          vpair_to_edge = (
              {}
          )  # maps from tuple of edge endpoints to edge_id
          edge_id_to_v = {}  # maps from edge ID to vertex position
          uniq_edge_id = {}  # unique edge IDs
          verts = []  # store vertex positions
          faces = []  # store face indices
          # enumerate each cell in the 3d grid
          for z in range(0, D - 1):
              for y in range(0, H - 1):
                  for x in range(0, W - 1):
                      cube = Cube((x, y, z), vol, thresh)
                      edge_indices = FACE_TABLE[cube.cube_index]
                      # cube is entirely in/out of the surface
                      if len(edge_indices) == 0:
                          continue
  
                      # gather mesh vertices/faces by processing each cube
                      interp_points = [[0.0, 0.0, 0.0]] * 12
                      # triangle vertex IDs and positions
                      tri = []
                      ps = []
                      for i, edge in enumerate(edge_indices):
                          interp_points[edge] = cube.vert_interp(
                              thresh, edge, vol
                          )
  
                          # Bind interpolated vertex with a global edge_id, which
                          # is represented by a pair of vertex ids (v1_id, v2_id)
                          # corresponding to a local edge.
                          (v1_id, v2_id) = cube.get_vpair_from_edge(
                              edge, W, H
                          )
                          edge_id = vpair_to_edge.setdefault(
                              (v1_id, v2_id), len(vpair_to_edge)
                          )
                          tri.append(edge_id)
                          ps.append(interp_points[edge])
                          # when the isolevel are the same as the edge endpoints, the interploated
                          # vertices can share the same values, and lead to degenerate triangles.
                          if (
                              (i + 1) % 3 == 0
                              and ps[0] != ps[1]
                              and ps[1] != ps[2]
                              and ps[2] != ps[0]
                          ):
                              for j, edge_id in enumerate(tri):
                                  edge_id_to_v[edge_id] = ps[j]
                                  if edge_id not in uniq_edge_id:
                                      uniq_edge_id[edge_id] = len(verts)
                                      verts.append(
                                          edge_id_to_v[edge_id]
                                      )
                              faces.append(
                                  [
                                      uniq_edge_id[tri[j]]
                                      for j in range(3)
                                  ]
                              )
                              tri = []
                              ps = []
  
          if len(faces) > 0 and len(verts) > 0:
              verts = torch.tensor(verts, dtype=vol.dtype)
              # Convert from world coordinates ([0, D-1], [0, H-1], [0, W-1]) to
              # local coordinates in the range [-1, 1]
              if return_local_coords:
                  verts = (
                      Translate(
                          x=+1.0,
                          y=+1.0,
                          z=+1.0,
                          device=vol_batch.device,
                      )
                      .scale(
                          (vol_batch.new_tensor([W, H, D])[None] - 1)
                          * 0.5
                      )
                      .inverse()
                  ).transform_points(verts[None])[0]
              batched_verts.append(verts)
              batched_faces.append(
                  torch.tensor(faces, dtype=torch.int64)
              )
          else:
              batched_verts.append([])
              batched_faces.append([])
      return batched_verts, batched_faces
  
file_path: pytorch3d/pytorch3d/ops/marching_cubes.py
imports: from typing import List, Optional, Tuple
  import torch
  from pytorch3d import _C
  from pytorch3d.ops.marching_cubes_data import EDGE_TO_VERTICES, FACE_TABLE, INDEX
  from pytorch3d.transforms import Translate
  from torch.autograd import Function
label_desc: Use image node_id 1 for calling a global function with example usage: marching_cubes_naive(vol_batch, isolevel, return_local_coords) and returns: batched_verts,  batched_faces