code: def test_simple_2d(self):
      radius = 7.0
      center = torch.tensor([9, 2.5])
      angles = torch.cumsum(torch.rand(17), dim=0)
      many = torch.stack([torch.cos(angles), torch.sin(angles)], dim=1)
      source_points = (many * radius) + center[None]
  
      result = fit_circle_in_2d(source_points)
      self.assertClose(result.radius, torch.tensor(radius))
      self.assertClose(result.center, center)
      self.assertEqual(result.generated_points.shape, (0, 2))
  
      # Generate 5 points around the circle
      n_new_points = 5
      result2 = fit_circle_in_2d(source_points, n_points=n_new_points)
      self.assertClose(result2.radius, torch.tensor(radius))
      self.assertClose(result2.center, center)
      self.assertEqual(result2.generated_points.shape, (5, 2))
  
      observed_points = result2.generated_points
      self.assertClose(observed_points[0], observed_points[4])
      self.assertClose(observed_points[0], source_points[0], atol=1e-5)
      diameters = observed_points[:2] - observed_points[2:4]
      self.assertClose(
          torch.norm(diameters, dim=1), torch.full((2,), 2 * radius)
      )
  
      # Regenerate the input points
      result3 = fit_circle_in_2d(
          source_points, angles=angles - angles[0]
      )
      self.assertClose(result3.radius, torch.tensor(radius))
      self.assertClose(result3.center, center)
      self.assertClose(
          result3.generated_points, source_points, atol=1e-5
      )
  
file_path: pytorch3d/tests/implicitron/test_circle_fitting.py
imports: import unittest
  from math import pi
  import torch
  from pytorch3d.implicitron.tools.circle_fitting import _signed_area, fit_circle_in_2d, fit_circle_in_3d, get_rotation_to_best_fit_xy
  from pytorch3d.transforms import random_rotation, random_rotations
  from tests.common_testing import TestCaseMixin
label_desc: Use image node_id 6 for calling the TestCircleFitting obj's underlying member method code with example usage: obj.test_simple_2d() without return types