def forward(self, field: torch.Tensor, min_point: torch.Tensor, size: torch.Tensor):
        """
        For a signed distance field, produce a mesh using marching cubes.

        :param field: a 3D tensor of field values, where negative values correspond
                    to the outside of the shape. The dimensions correspond to the x, y, and z directions, respectively.
        :param min_point: a tensor of shape [3] containing the point corresponding
                        to (0, 0, 0) in the field.
        :param size: a tensor of shape [3] containing the per-axis distance from the
                    (0, 0, 0) field corner and the (-1, -1, -1) field corner.
        """
        assert len(field.shape) == 3, "input must be a 3D scalar field"
        dev = field.device

        cases = self.cases.to(dev)
        masks = self.masks.to(dev)

        min_point = min_point.to(dev)
        size = size.to(dev)

        grid_size = field.shape
        grid_size_tensor = torch.tensor(grid_size).to(size)

        # Create bitmasks between 0 and 255 (inclusive) indicating the state
        # of the eight corners of each cube.
        bitmasks = (field > 0).to(torch.uint8)
        bitmasks = bitmasks[:-1, :, :] | (bitmasks[1:, :, :] << 1)
        bitmasks = bitmasks[:, :-1, :] | (bitmasks[:, 1:, :] << 2)
        bitmasks = bitmasks[:, :, :-1] | (bitmasks[:, :, 1:] << 4)

        # Compute corner coordinates across the entire grid.
        corner_coords = torch.empty(*grid_size, 3, device=dev, dtype=field.dtype)
        corner_coords[range(grid_size[0]), :, :, 0] = torch.arange(grid_size[0], device=dev, dtype=field.dtype)[
            :, None, None
        ]
        corner_coords[:, range(grid_size[1]), :, 1] = torch.arange(grid_size[1], device=dev, dtype=field.dtype)[
            :, None
        ]
        corner_coords[:, :, range(grid_size[2]), 2] = torch.arange(grid_size[2], device=dev, dtype=field.dtype)

        # Compute all vertices across all edges in the grid, even though we will
        # throw some out later. We have (X-1)*Y*Z + X*(Y-1)*Z + X*Y*(Z-1) vertices.
        # These are all midpoints, and don't account for interpolation (which is
        # done later based on the used edge midpoints).
        edge_midpoints = torch.cat(
            [
                ((corner_coords[:-1] + corner_coords[1:]) / 2).reshape(-1, 3),
                ((corner_coords[:, :-1] + corner_coords[:, 1:]) / 2).reshape(-1, 3),
                ((corner_coords[:, :, :-1] + corner_coords[:, :, 1:]) / 2).reshape(-1, 3),
            ],
            dim=0,
        )

        # Create a flat array of [X, Y, Z] indices for each cube.
        cube_indices = torch.zeros(
            grid_size[0] - 1, grid_size[1] - 1, grid_size[2] - 1, 3, device=dev, dtype=torch.long
        )
        cube_indices[range(grid_size[0] - 1), :, :, 0] = torch.arange(grid_size[0] - 1, device=dev)[:, None, None]
        cube_indices[:, range(grid_size[1] - 1), :, 1] = torch.arange(grid_size[1] - 1, device=dev)[:, None]
        cube_indices[:, :, range(grid_size[2] - 1), 2] = torch.arange(grid_size[2] - 1, device=dev)
        flat_cube_indices = cube_indices.reshape(-1, 3)

        # Create a flat array mapping each cube to 12 global edge indices.
        edge_indices = _create_flat_edge_indices(flat_cube_indices, grid_size)

        # Apply the LUT to figure out the triangles.
        flat_bitmasks = bitmasks.reshape(-1).long()  # must cast to long for indexing to believe this not a mask
        local_tris = cases[flat_bitmasks]
        local_masks = masks[flat_bitmasks]
        # Compute the global edge indices for the triangles.
        global_tris = torch.gather(edge_indices, 1, local_tris.reshape(local_tris.shape[0], -1)).reshape(
            local_tris.shape
        )
        # Select the used triangles for each cube.
        selected_tris = global_tris.reshape(-1, 3)[local_masks.reshape(-1)]

        # Now we have a bunch of indices into the full list of possible vertices,
        # but we want to reduce this list to only the used vertices.
        used_vertex_indices = torch.unique(selected_tris.view(-1))
        used_edge_midpoints = edge_midpoints[used_vertex_indices]
        old_index_to_new_index = torch.zeros(len(edge_midpoints), device=dev, dtype=torch.long)
        old_index_to_new_index[used_vertex_indices] = torch.arange(
            len(used_vertex_indices), device=dev, dtype=torch.long
        )

        # Rewrite the triangles to use the new indices
        faces = torch.gather(old_index_to_new_index, 0, selected_tris.view(-1)).reshape(selected_tris.shape)

        # Compute the actual interpolated coordinates corresponding to edge midpoints.
        v1 = torch.floor(used_edge_midpoints).to(torch.long)
        v2 = torch.ceil(used_edge_midpoints).to(torch.long)
        s1 = field[v1[:, 0], v1[:, 1], v1[:, 2]]
        s2 = field[v2[:, 0], v2[:, 1], v2[:, 2]]
        p1 = (v1.float() / (grid_size_tensor - 1)) * size + min_point
        p2 = (v2.float() / (grid_size_tensor - 1)) * size + min_point
        # The signs of s1 and s2 should be different. We want to find
        # t such that t*s2 + (1-t)*s1 = 0.
        t = (s1 / (s1 - s2))[:, None]
        verts = t * p2 + (1 - t) * p1

        return MeshDecoderOutput(verts=verts, faces=faces, vertex_channels=None)

        For a signed distance field, produce a mesh using marching cubes.

        :param field: a 3D tensor of field values, where negative values correspond
                    to the outside of the shape. The dimensions correspond to the x, y, and z directions, respectively.
        :param min_point: a tensor of shape [3] containing the point corresponding
                        to (0, 0, 0) in the field.
        :param size: a tensor of shape [3] containing the per-axis distance from the
                    (0, 0, 0) field corner and the (-1, -1, -1) field corner.
        
src/diffusers/pipelines/shap_e/renderer.py