content: # MIT License
  
  # Copyright (c) 2022 Petr Kellnhofer
  
  # 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 COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  # SOFTWARE.
  
  import torch
  
  def transform_vectors(matrix: torch.Tensor, vectors4: torch.Tensor) -> torch.Tensor:
      """
      Left-multiplies MxM @ NxM. Returns NxM.
      """
      res = torch.matmul(vectors4, matrix.T)
      return res
  
  
  def normalize_vecs(vectors: torch.Tensor) -> torch.Tensor:
      """
      Normalize vector lengths.
      """
      return vectors / (torch.norm(vectors, dim=-1, keepdim=True))
  
  def torch_dot(x: torch.Tensor, y: torch.Tensor):
      """
      Dot product of two tensors.
      """
      return (x * y).sum(-1)
  
  
  def get_ray_limits_box(rays_o: torch.Tensor, rays_d: torch.Tensor, box_side_length):
      """
      Author: Petr Kellnhofer
      Intersects rays with the [-1, 1] NDC volume.
      Returns min and max distance of entry.
      Returns -1 for no intersection.
      https://www.scratchapixel.com/lessons/3d-basic-rendering/minimal-ray-tracer-rendering-simple-shapes/ray-box-intersection
      """
      o_shape = rays_o.shape
      rays_o = rays_o.detach().reshape(-1, 3)
      rays_d = rays_d.detach().reshape(-1, 3)
  
  
      bb_min = [-1*(box_side_length/2), -1*(box_side_length/2), -1*(box_side_length/2)]
      bb_max = [1*(box_side_length/2), 1*(box_side_length/2), 1*(box_side_length/2)]
      bounds = torch.tensor([bb_min, bb_max], dtype=rays_o.dtype, device=rays_o.device)
      is_valid = torch.ones(rays_o.shape[:-1], dtype=bool, device=rays_o.device)
  
      # Precompute inverse for stability.
      invdir = 1 / rays_d
      sign = (invdir < 0).long()
  
      # Intersect with YZ plane.
      tmin = (bounds.index_select(0, sign[..., 0])[..., 0] - rays_o[..., 0]) * invdir[..., 0]
      tmax = (bounds.index_select(0, 1 - sign[..., 0])[..., 0] - rays_o[..., 0]) * invdir[..., 0]
  
      # Intersect with XZ plane.
      tymin = (bounds.index_select(0, sign[..., 1])[..., 1] - rays_o[..., 1]) * invdir[..., 1]
      tymax = (bounds.index_select(0, 1 - sign[..., 1])[..., 1] - rays_o[..., 1]) * invdir[..., 1]
  
      # Resolve parallel rays.
      is_valid[torch.logical_or(tmin > tymax, tymin > tmax)] = False
  
      # Use the shortest intersection.
      tmin = torch.max(tmin, tymin)
      tmax = torch.min(tmax, tymax)
  
      # Intersect with XY plane.
      tzmin = (bounds.index_select(0, sign[..., 2])[..., 2] - rays_o[..., 2]) * invdir[..., 2]
      tzmax = (bounds.index_select(0, 1 - sign[..., 2])[..., 2] - rays_o[..., 2]) * invdir[..., 2]
  
      # Resolve parallel rays.
      is_valid[torch.logical_or(tmin > tzmax, tzmin > tmax)] = False
  
      # Use the shortest intersection.
      tmin = torch.max(tmin, tzmin)
      tmax = torch.min(tmax, tzmax)
  
      # Mark invalid.
      tmin[torch.logical_not(is_valid)] = -1
      tmax[torch.logical_not(is_valid)] = -2
  
      return tmin.reshape(*o_shape[:-1], 1), tmax.reshape(*o_shape[:-1], 1)
  
  
  def linspace(start: torch.Tensor, stop: torch.Tensor, num: int):
      """
      Creates a tensor of shape [num, *start.shape] whose values are evenly spaced from start to end, inclusive.
      Replicates but the multi-dimensional bahaviour of numpy.linspace in PyTorch.
      """
      # create a tensor of 'num' steps from 0 to 1
      steps = torch.arange(num, dtype=torch.float32, device=start.device) / (num - 1)
  
      # reshape the 'steps' tensor to [-1, *([1]*start.ndim)] to allow for broadcastings
      # - using 'steps.reshape([-1, *([1]*start.ndim)])' would be nice here but torchscript
      #   "cannot statically infer the expected size of a list in this contex", hence the code below
      for i in range(start.ndim):
          steps = steps.unsqueeze(-1)
  
      # the output starts at 'start' and increments until 'stop' in each dimension
      out = start[None] + steps * (stop - start)[None]
  
      return out
  