docstr: Test vertex_areas.
  
  Vertex area is the area of all of the triangles who are in contact
  with a specific vertex, according to the formula:
  vertex_areas = 2 * sum_incident_areas / 3.0
docstr_tok: ["Test","vertex_areas",".","Vertex","area","is","the","area","of","all","of","the","triangles","who","are","in","contact","with","a","specific","vertex",",","according","to","the","formula",":","vertex_areas","=","2","*","sum_incident_areas","\/","3.0"]
code: def test_vertex_areas(self, point, expected, atol):
      """Test vertex_areas.
  
      Vertex area is the area of all of the triangles who are in contact
      with a specific vertex, according to the formula:
      vertex_areas = 2 * sum_incident_areas / 3.0
      """
      res = self.space.vertex_areas(point)
      self.assertAllClose(res, expected, atol=atol)
  
file_path: geomstats/geomstats/test_cases/geometry/discrete_surfaces.py
imports: import geomstats.backend
  from geomstats.test_cases.geometry.manifold import ManifoldTestCase
  from geomstats.test_cases.geometry.riemannian_metric import RiemannianMetricTestCase
  from geomstats.vectorization import get_n_points
label_desc: Use image node_id 1 for calling the DiscreteSurfacesTestCase obj's underlying member method code with example usage: obj.test_vertex_areas(point, expected, atol) without return types