code: def is_inside(
      plane: torch.Tensor,
      n: torch.Tensor,
      points: torch.Tensor,
      return_proj: bool = True,
  ):
      """
      Computes whether point is "inside" the plane.
      The definition of "inside" means that the point
      has a positive component in the direction of the plane normal defined by n.
      For example,
                    plane
                      |
                      |         . (A)
                      |--> n
                      |
           .(B)       |
  
      Point (A) is "inside" the plane, while point (B) is "outside" the plane.
      Args:
        plane: tensor of shape (4,3) of vertices of a box plane
        n: tensor of shape (3,) of the unit "inside" direction on the plane
        points: tensor of shape (P, 3) of coordinates of a point
        return_proj: bool whether to return the projected point on the plane
      Returns:
        is_inside: bool of shape (P,) of whether point is inside
        p_proj: tensor of shape (P, 3) of the projected point on plane
      """
      device = plane.device
      v0, v1, v2, v3 = plane.unbind(0)
      plane_ctr = plane.mean(0)
      e0 = F.normalize(v0 - plane_ctr, dim=0)
      e1 = F.normalize(v1 - plane_ctr, dim=0)
      if not torch.allclose(
          e0.dot(n), torch.zeros((1,), device=device), atol=1e-2
      ):
          raise ValueError("Input n is not perpendicular to the plane")
      if not torch.allclose(
          e1.dot(n), torch.zeros((1,), device=device), atol=1e-2
      ):
          raise ValueError("Input n is not perpendicular to the plane")
  
      add_dim = False
      if points.ndim == 1:
          points = points.unsqueeze(0)
          add_dim = True
  
      assert points.shape[1] == 3
      # Every point p can be written as p = ctr + a e0 + b e1 + c n
  
      # If return_proj is True, we need to solve for (a, b)
      p_proj = None
      if return_proj:
          # solving for (a, b)
          A = torch.tensor(
              [[1.0, e0.dot(e1)], [e0.dot(e1), 1.0]],
              dtype=torch.float32,
              device=device,
          )
          B = torch.zeros(
              (2, points.shape[0]), dtype=torch.float32, device=device
          )
          B[0, :] = torch.sum(
              (points - plane_ctr.view(1, 3)) * e0.view(1, 3), dim=-1
          )
          B[1, :] = torch.sum(
              (points - plane_ctr.view(1, 3)) * e1.view(1, 3), dim=-1
          )
          ab = A.inverse() @ B  # (2, P)
          p_proj = plane_ctr.view(1, 3) + ab.transpose(
              0, 1
          ) @ torch.stack((e0, e1), dim=0)
  
      # solving for c
      # c = (point - ctr - a * e0 - b * e1).dot(n)
      direc = torch.sum(
          (points - plane_ctr.view(1, 3)) * n.view(1, 3), dim=-1
      )
      ins = direc >= 0.0
  
      if add_dim:
          assert p_proj.shape[0] == 1
          p_proj = p_proj[0]
  
      return ins, p_proj
  
imports: import pickle
  import random
  import unittest
  from typing import List, Tuple, Union
  import torch
  import torch.nn.functional
  from pytorch3d.io import save_obj
  from pytorch3d.ops.iou_box3d import _box_planes, _box_triangles, box3d_overlap
  from pytorch3d.transforms.rotation_conversions import random_rotation
  from .common_testing import get_random_cuda_device, get_tests_dir, TestCaseMixin
label_desc: Use image node_id 10 for calling a global function with example usage: is_inside(plane, n, points, return_proj) and returns: ins,  p_proj