docstr: Case 3 triangles have exactly two vertices behind the clipping plane (z=0) so are
  clipped into a smaller triangle.
  
  Test with a single triangle parallel to the z axis which intersects with
  the image plane.
docstr_tok: ["Case","3","triangles","have","exactly","two","vertices","behind","the","clipping","plane","(","z=0",")","so","are","clipped","into","a","smaller","triangle",".","Test","with","a","single","triangle","parallel","to","the","z","axis","which","intersects","with","the","image","plane","."]
code: def test_case_3(self):
      """
      Case 3 triangles have exactly two vertices behind the clipping plane (z=0) so are
      clipped into a smaller triangle.
  
      Test with a single triangle parallel to the z axis which intersects with
      the image plane.
      """
  
      device = "cuda:0"
      verts = torch.tensor(
          [[-1.0, 0.0, -1.0], [0.0, 0.0, 1.0], [1.0, 0.0, -1.0]],
          dtype=torch.float32,
          device=device,
      )
      faces = torch.tensor(
          [
              [0, 1, 2],
          ],
          dtype=torch.int64,
          device=device,
      )
      meshes = Meshes(verts=[verts], faces=[faces])
      clipped_faces = self.clip_faces(meshes)
  
      zero_t = torch.zeros(size=(1,), dtype=torch.int64, device=device)
      clipped_face_verts = torch.tensor(
          [
              [
                  [0.4950, 0.0000, 0.0100],
                  [-0.4950, 0.0000, 0.0100],
                  [0.0000, 0.0000, 1.0000],
              ]
          ],
          device=device,
          dtype=torch.float32,
      )
  
      # barycentric_conversion[i, :, k] stores the barycentric weights
      # in terms of the world coordinates of the original
      # (big) triangle for the kth vertex in the clipped (small) triangle.
      barycentric_conversion = torch.tensor(
          [
              [
                  [0.0000, 0.4950, 0.0000],
                  [0.5050, 0.5050, 1.0000],
                  [0.4950, 0.0000, 0.0000],
              ]
          ],
          device=device,
          dtype=torch.float32,
      )
  
      self.assertClose(clipped_faces.face_verts, clipped_face_verts)
      self.assertEqual(clipped_faces.mesh_to_face_first_idx.item(), 0)
      self.assertEqual(clipped_faces.num_faces_per_mesh.item(), 1)
      self.assertClose(
          clipped_faces.faces_clipped_to_unclipped_idx, zero_t
      )
      self.assertClose(
          clipped_faces.faces_clipped_to_conversion_idx, zero_t
      )
      self.assertClose(
          clipped_faces.clipped_faces_neighbor_idx,
          zero_t - 1,  # default is -1
      )
      self.assertClose(
          clipped_faces.barycentric_conversion, barycentric_conversion
      )
  
imports: import unittest
  import imageio
  import numpy
  import torch
  from pytorch3d.io import save_obj
  from pytorch3d.renderer.cameras import FoVPerspectiveCameras, look_at_view_transform, PerspectiveCameras
  from pytorch3d.renderer.lighting import PointLights
  from pytorch3d.renderer.mesh import clip_faces, ClipFrustum, convert_clipped_rasterization_to_original_faces, TexturesUV
  from pytorch3d.renderer.mesh.rasterize_meshes import _RasterizeFaceVerts
  from pytorch3d.renderer.mesh.rasterizer import MeshRasterizer, RasterizationSettings
  from pytorch3d.renderer.mesh.renderer import MeshRenderer
  from pytorch3d.renderer.mesh.shader import SoftPhongShader
  from pytorch3d.renderer.mesh.textures import TexturesVertex
  from pytorch3d.structures.meshes import Meshes
  from pytorch3d.utils import torus
  from .common_testing import get_tests_dir, load_rgb_image, TestCaseMixin
label_desc: Use image node_id 7 for calling the TestRenderMeshesClipping obj's underlying member method code with example usage: obj.test_case_3() without return types