text: # The MIT License (MIT)
  #
  # Copyright (c) 2021, NVIDIA CORPORATION.
  #
  # Permission is hereby granted, free of charge, to any person obtaining a copy of
  # this software and associated documentation files (the "Software"), to deal in
  # the Software without restriction, including without limitation the rights to
  # use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
  # the Software, and to permit persons to whom the Software is furnished to do so,
  # subject to the following conditions:
  #
  # The above copyright notice and this permission notice shall be included in all
  # copies or substantial portions of the Software.
  #
  # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
  # FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
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  import torch
  from .per_face_normals import per_face_normals
  
  def area_weighted_distribution(mesh : torch.Tensor, normals : torch.Tensor = None):
      """Construct discrete area weighted distribution over triangle mesh.
  
      Args:
          mesh (torch.Tensor): #F, 3, 3 array of vertices
          normals (torch.Tensor): normals (if precomputed)
          eps (float): epsilon
      """
  
      if normals is None:
          normals = per_face_normals(mesh)
      areas = torch.norm(normals, p=2, dim=1) * 0.5
      areas /= torch.sum(areas) + 1e-10
      
      # Discrete PDF over triangles
      return torch.distributions.Categorical(areas.view(-1))
  
  