docstr: Instantiate random x_world, x_cam, R, T given a set of input
  2D projections y.
docstr_tok: ["Instantiate","random","x_world",",","x_cam",",","R",",","T","given","a","set","of","input","2D","projections","y","."]
code: def _generate_epnp_test_from_2d(cls, y):
      """
      Instantiate random x_world, x_cam, R, T given a set of input
      2D projections y.
      """
      batch_size = y.shape[0]
      x_cam = torch.cat(
          (y, torch.rand_like(y[:, :, :1]) * 2.0 + 3.5), dim=2
      )
      x_cam[:, :, :2] *= x_cam[:, :, 2:]  # unproject
      R = rotation_conversions.random_rotations(batch_size).to(y)
      T = torch.randn_like(R[:, :1, :])
      T[:, :, 2] = (T[:, :, 2] + 3.0).clamp(2.0)
      x_world = torch.matmul(x_cam - T, R.transpose(1, 2))
      return x_cam, x_world, R, T
  
file_path: pytorch3d/tests/test_perspective_n_points.py
imports: import unittest
  import torch
  from pytorch3d.ops import perspective_n_points
  from pytorch3d.transforms import rotation_conversions
  from .common_testing import TestCaseMixin
label_desc: Use image node_id 2 for calling the TestPerspectiveNPoints obj's underlying member method code with example usage: obj._generate_epnp_test_from_2d(cls, y) and returns: x_cam,  x_world,  R,  T