code: def _simple_3d_test(self, radius, center, rot, offset, up):
      # angles are increasing so the points move in a well defined direction.
      angles = torch.cumsum(torch.rand(17, device=rot.device), dim=0)
      many = torch.stack(
          [
              torch.cos(angles),
              torch.sin(angles),
              torch.zeros_like(angles),
          ],
          dim=1,
      )
      source_points = (many * radius) @ rot + center[None]
  
      # case with no generation
      result = fit_circle_in_3d(source_points)
      self.assertClose(result.radius, radius)
      self.assertClose(result.center, center)
      self._assertParallel(result.normal, rot[2], atol=1e-5)
      self.assertEqual(result.generated_points.shape, (0, 3))
  
      # Generate 5 points around the circle
      n_new_points = 5
      result2 = fit_circle_in_3d(source_points, n_points=n_new_points)
      self.assertClose(result2.radius, radius)
      self.assertClose(result2.center, center)
      self.assertClose(result2.normal, result.normal)
      self.assertEqual(result2.generated_points.shape, (5, 3))
  
      observed_points = result2.generated_points
      self.assertClose(
          observed_points[0], observed_points[4], atol=1e-4
      )
      self.assertClose(observed_points[0], source_points[0], atol=1e-5)
      observed_normal = torch.cross(
          observed_points[0] - observed_points[2],
          observed_points[1] - observed_points[3],
          dim=-1,
      )
      self._assertParallel(observed_normal, result.normal, atol=1e-4)
      diameters = observed_points[:2] - observed_points[2:4]
      self.assertClose(
          torch.norm(diameters, dim=1),
          diameters.new_full((2,), 2 * radius),
      )
  
      # Regenerate the input points
      result3 = fit_circle_in_3d(
          source_points, angles=angles - angles[0]
      )
      self.assertClose(result3.radius, radius)
      self.assertClose(result3.center, center)
      self.assertClose(result3.normal, result.normal)
      self.assertClose(
          result3.generated_points, source_points, atol=1e-5
      )
  
      # Test with offset
      result4 = fit_circle_in_3d(
          source_points, angles=angles - angles[0], offset=offset, up=up
      )
      self.assertClose(result4.radius, radius)
      self.assertClose(result4.center, center)
      self.assertClose(result4.normal, result.normal)
      observed_offsets = result4.generated_points - source_points
  
      # observed_offset is constant
      self.assertClose(
          observed_offsets.min(0).values,
          observed_offsets.max(0).values,
          atol=1e-5,
      )
      # observed_offset has the right length
      self.assertClose(observed_offsets[0].norm(), offset.norm())
  
      self.assertClose(result.normal.norm(), torch.ones(()))
      # component of observed_offset along normal
      component = torch.dot(observed_offsets[0], result.normal)
      self.assertClose(component.abs(), offset[2].abs(), atol=1e-5)
      agree_normal = torch.dot(result.normal, up) > 0
      agree_signs = component * offset[2] > 0
      self.assertEqual(agree_normal, agree_signs)
  
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 5 for calling the TestCircleFitting obj's underlying member method code with example usage: obj._simple_3d_test(radius, center, rot, offset, up) without return types