code: def test_signed_area(self):
      n_points = 1001
      angles = torch.linspace(0, 2 * pi, n_points)
      radius = 0.85
      center = torch.rand(2)
      circle = center + radius * torch.stack(
          [torch.cos(angles), torch.sin(angles)], dim=1
      )
      circle_area = torch.tensor(pi * radius * radius)
      self.assertClose(_signed_area(circle), circle_area)
      # clockwise is negative
      self.assertClose(_signed_area(circle.flip(0)), -circle_area)
  
      # Semicircles
      self.assertClose(
          _signed_area(circle[: (n_points + 1) // 2]), circle_area / 2
      )
      self.assertClose(
          _signed_area(circle[n_points // 2 :]), circle_area / 2
      )
  
      # A straight line bounds no area
      self.assertClose(
          _signed_area(torch.rand(2, 2)), torch.tensor(0.0)
      )
  
      # Letter 'L' written anticlockwise.
      L_shape = [[0, 1], [0, 0], [1, 0]]
      # Triangle area is 0.5 * b * h.
      self.assertClose(
          _signed_area(torch.tensor(L_shape)), torch.tensor(0.5)
      )
  
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 8 for calling the TestCircleFitting obj's underlying member method code with example usage: obj.test_signed_area() without return types