content: from collections import defaultdict
  import math
  
  import numpy as np
  import torch
  import torch.nn as nn
  import torch.nn.functional as F
  from torch.autograd import Function
  from torch.amp import custom_bwd, custom_fwd
  
  from CharacterGen.Stage_3D import lrm
  from .typing import *
  
  
  def dot(x, y):
      return torch.sum(x * y, -1, keepdim=True)
  
  
  def reflect(x, n):
      return 2 * dot(x, n) * n - x
  
  
  ValidScale = Union[Tuple[float, float], Num[Tensor, "2 D"]]
  
  
  def scale_tensor(
      dat: Num[Tensor, "... D"], inp_scale: ValidScale, tgt_scale: ValidScale
  ):
      if inp_scale is None:
          inp_scale = (0, 1)
      if tgt_scale is None:
          tgt_scale = (0, 1)
      if isinstance(tgt_scale, Tensor):
          assert dat.shape[-1] == tgt_scale.shape[-1]
      dat = (dat - inp_scale[0]) / (inp_scale[1] - inp_scale[0])
      dat = dat * (tgt_scale[1] - tgt_scale[0]) + tgt_scale[0]
      return dat
  
  
  class _TruncExp(Function):  # pylint: disable=abstract-method
      # Implementation from torch-ngp:
      # https://github.com/ashawkey/torch-ngp/blob/93b08a0d4ec1cc6e69d85df7f0acdfb99603b628/activation.py
      @staticmethod
      @custom_fwd(cast_inputs=torch.float32, device_type="cuda")
      def forward(ctx, x):  # pylint: disable=arguments-differ
          ctx.save_for_backward(x)
          return torch.exp(x)
  
      @staticmethod
      @custom_bwd(device_type="cuda")
      def backward(ctx, g):  # pylint: disable=arguments-differ
          x = ctx.saved_tensors[0]
          return g * torch.exp(torch.clamp(x, max=15))
  
  
  trunc_exp = _TruncExp.apply
  
  
  def get_activation(name) -> Callable:
      if name is None:
          return lambda x: x
      name = name.lower()
      if name == "none":
          return lambda x: x
      elif name == "lin2srgb":
          return lambda x: torch.where(
              x > 0.0031308,
              torch.pow(torch.clamp(x, min=0.0031308), 1.0 / 2.4) * 1.055 - 0.055,
              12.92 * x,
          ).clamp(0.0, 1.0)
      elif name == "exp":
          return lambda x: torch.exp(x)
      elif name == "shifted_exp":
          return lambda x: torch.exp(x - 1.0)
      elif name == "trunc_exp":
          return trunc_exp
      elif name == "shifted_trunc_exp":
          return lambda x: trunc_exp(x - 1.0)
      elif name == "sigmoid":
          return lambda x: torch.sigmoid(x)
      elif name == "tanh":
          return lambda x: torch.tanh(x)
      elif name == "shifted_softplus":
          return lambda x: F.softplus(x - 1.0)
      elif name == "scale_-11_01":
          return lambda x: x * 0.5 + 0.5
      elif name == "negative":
          return lambda x: -x
      else:
          try:
              return getattr(F, name)
          except AttributeError:
              raise ValueError(f"Unknown activation function: {name}")
  
  
  def chunk_batch(func: Callable, chunk_size: int, *args, **kwargs) -> Any:
      if chunk_size <= 0:
          return func(*args, **kwargs)
      B = None
      for arg in list(args) + list(kwargs.values()):
          if isinstance(arg, torch.Tensor):
              B = arg.shape[0]
              break
      assert (
          B is not None
      ), "No tensor found in args or kwargs, cannot determine batch size."
      out = defaultdict(list)
      out_type = None
      # max(1, B) to support B == 0
      for i in range(0, max(1, B), chunk_size):
          out_chunk = func(
              *[
                  arg[i : i + chunk_size] if isinstance(arg, torch.Tensor) else arg
                  for arg in args
              ],
              **{
                  k: arg[i : i + chunk_size] if isinstance(arg, torch.Tensor) else arg
                  for k, arg in kwargs.items()
              },
          )
          if out_chunk is None:
              continue
          out_type = type(out_chunk)
          if isinstance(out_chunk, torch.Tensor):
              out_chunk = {0: out_chunk}
          elif isinstance(out_chunk, tuple) or isinstance(out_chunk, list):
              chunk_length = len(out_chunk)
              out_chunk = {i: chunk for i, chunk in enumerate(out_chunk)}
          elif isinstance(out_chunk, dict):
              pass
          else:
              print(
                  f"Return value of func must be in type [torch.Tensor, list, tuple, dict], get {type(out_chunk)}."
              )
              exit(1)
          for k, v in out_chunk.items():
              v = v if torch.is_grad_enabled() else v.detach()
              out[k].append(v)
  
      if out_type is None:
          return None
  
      out_merged: Dict[Any, Optional[torch.Tensor]] = {}
      for k, v in out.items():
          if all([vv is None for vv in v]):
              # allow None in return value
              out_merged[k] = None
          elif all([isinstance(vv, torch.Tensor) for vv in v]):
              out_merged[k] = torch.cat(v, dim=0)
          else:
              raise TypeError(
                  f"Unsupported types in return value of func: {[type(vv) for vv in v if not isinstance(vv, torch.Tensor)]}"
              )
  
      if out_type is torch.Tensor:
          return out_merged[0]
      elif out_type in [tuple, list]:
          return out_type([out_merged[i] for i in range(chunk_length)])
      elif out_type is dict:
          return out_merged
  
  
  def get_ray_directions(
      H: int,
      W: int,
      focal: Union[float, Tuple[float, float]],
      principal: Optional[Tuple[float, float]] = None,
      use_pixel_centers: bool = True,
      normalize: bool = True,
  ) -> Float[Tensor, "H W 3"]:
      """
      Get ray directions for all pixels in camera coordinate.
      Reference: https://www.scratchapixel.com/lessons/3d-basic-rendering/
                 ray-tracing-generating-camera-rays/standard-coordinate-systems
  
      Inputs:
          H, W, focal, principal, use_pixel_centers: image height, width, focal length, principal point and whether use pixel centers
      Outputs:
          directions: (H, W, 3), the direction of the rays in camera coordinate
      """
      pixel_center = 0.5 if use_pixel_centers else 0
  
      if isinstance(focal, float):
          fx, fy = focal, focal
          cx, cy = W / 2, H / 2
      else:
          fx, fy = focal
          assert principal is not None
          cx, cy = principal
  
      i, j = torch.meshgrid(
          torch.arange(W, dtype=torch.float32) + pixel_center,
          torch.arange(H, dtype=torch.float32) + pixel_center,
          indexing="xy",
      )
  
      directions: Float[Tensor, "H W 3"] = torch.stack(
          [(i - cx) / fx, -(j - cy) / fy, -torch.ones_like(i)], -1
      )
  
      if normalize:
          directions = F.normalize(directions, dim=-1)
  
      return directions
  
  
  def get_rays(
      directions: Float[Tensor, "... 3"],
      c2w: Float[Tensor, "... 4 4"],
      keepdim=False,
      noise_scale=0.0,
      normalize=False,
  ) -> Tuple[Float[Tensor, "... 3"], Float[Tensor, "... 3"]]:
      # Rotate ray directions from camera coordinate to the world coordinate
      assert directions.shape[-1] == 3
  
      if directions.ndim == 2:  # (N_rays, 3)
          if c2w.ndim == 2:  # (4, 4)
              c2w = c2w[None, :, :]
          assert c2w.ndim == 3  # (N_rays, 4, 4) or (1, 4, 4)
          rays_d = (directions[:, None, :] * c2w[:, :3, :3]).sum(-1)  # (N_rays, 3)
          rays_o = c2w[:, :3, 3].expand(rays_d.shape)
      elif directions.ndim == 3:  # (H, W, 3)
          assert c2w.ndim in [2, 3]
          if c2w.ndim == 2:  # (4, 4)
              rays_d = (directions[:, :, None, :] * c2w[None, None, :3, :3]).sum(
                  -1
              )  # (H, W, 3)
              rays_o = c2w[None, None, :3, 3].expand(rays_d.shape)
          elif c2w.ndim == 3:  # (B, 4, 4)
              rays_d = (directions[None, :, :, None, :] * c2w[:, None, None, :3, :3]).sum(
                  -1
              )  # (B, H, W, 3)
              rays_o = c2w[:, None, None, :3, 3].expand(rays_d.shape)
      elif directions.ndim == 4:  # (B, H, W, 3)
          assert c2w.ndim == 3  # (B, 4, 4)
          rays_d = (directions[:, :, :, None, :] * c2w[:, None, None, :3, :3]).sum(
              -1
          )  # (B, H, W, 3)
          rays_o = c2w[:, None, None, :3, 3].expand(rays_d.shape)
  
      # add camera noise to avoid grid-like artifect
      # https://github.com/ashawkey/stable-dreamfusion/blob/49c3d4fa01d68a4f027755acf94e1ff6020458cc/nerf/utils.py#L373
      if noise_scale > 0:
          rays_o = rays_o + torch.randn(3, device=rays_o.device) * noise_scale
          rays_d = rays_d + torch.randn(3, device=rays_d.device) * noise_scale
  
      if normalize:
          rays_d = F.normalize(rays_d, dim=-1)
      if not keepdim:
          rays_o, rays_d = rays_o.reshape(-1, 3), rays_d.reshape(-1, 3)
  
      return rays_o, rays_d
  
  
  def get_projection_matrix(
      fovy: Union[float, Float[Tensor, "B"]], aspect_wh: float, near: float, far: float
  ) -> Float[Tensor, "*B 4 4"]:
      if isinstance(fovy, float):
          proj_mtx = torch.zeros(4, 4, dtype=torch.float32)
          proj_mtx[0, 0] = 1.0 / (math.tan(fovy / 2.0) * aspect_wh)
          proj_mtx[1, 1] = -1.0 / math.tan(
              fovy / 2.0
          )  # add a negative sign here as the y axis is flipped in nvdiffrast output
          proj_mtx[2, 2] = -(far + near) / (far - near)
          proj_mtx[2, 3] = -2.0 * far * near / (far - near)
          proj_mtx[3, 2] = -1.0
      else:
          batch_size = fovy.shape[0]
          proj_mtx = torch.zeros(batch_size, 4, 4, dtype=torch.float32)
          proj_mtx[:, 0, 0] = 1.0 / (torch.tan(fovy / 2.0) * aspect_wh)
          proj_mtx[:, 1, 1] = -1.0 / torch.tan(
              fovy / 2.0
          )  # add a negative sign here as the y axis is flipped in nvdiffrast output
          proj_mtx[:, 2, 2] = -(far + near) / (far - near)
          proj_mtx[:, 2, 3] = -2.0 * far * near / (far - near)
          proj_mtx[:, 3, 2] = -1.0
      return proj_mtx
  
  
  def get_mvp_matrix(
      c2w: Float[Tensor, "*B 4 4"], proj_mtx: Float[Tensor, "*B 4 4"]
  ) -> Float[Tensor, "*B 4 4"]:
      # calculate w2c from c2w: R' = Rt, t' = -Rt * t
      # mathematically equivalent to (c2w)^-1
      if c2w.ndim == 2:
          assert proj_mtx.ndim == 2
          w2c: Float[Tensor, "4 4"] = torch.zeros(4, 4).to(c2w)
          w2c[:3, :3] = c2w[:3, :3].permute(1, 0)
          w2c[:3, 3:] = -c2w[:3, :3].permute(1, 0) @ c2w[:3, 3:]
          w2c[3, 3] = 1.0
      else:
          w2c: Float[Tensor, "B 4 4"] = torch.zeros(c2w.shape[0], 4, 4).to(c2w)
          w2c[:, :3, :3] = c2w[:, :3, :3].permute(0, 2, 1)
          w2c[:, :3, 3:] = -c2w[:, :3, :3].permute(0, 2, 1) @ c2w[:, :3, 3:]
          w2c[:, 3, 3] = 1.0
      # calculate mvp matrix by proj_mtx @ w2c (mv_mtx)
      mvp_mtx = proj_mtx @ w2c
      return mvp_mtx
  
  
  def get_intrinsic_from_fov(fov, H, W, bs=-1):
      focal_length = 0.5 * H / np.tan(0.5 * fov)
      intrinsic = np.identity(3, dtype=np.float32)
      intrinsic[0, 0] = focal_length
      intrinsic[1, 1] = focal_length
      intrinsic[0, 2] = W / 2.0
      intrinsic[1, 2] = H / 2.0
  
      if bs > 0:
          intrinsic = intrinsic[None].repeat(bs, axis=0)
  
      return torch.from_numpy(intrinsic)
  
  
  def binary_cross_entropy(input, target):
      """
      F.binary_cross_entropy is not numerically stable in mixed-precision training.
      """
      return -(target * torch.log(input) + (1 - target) * torch.log(1 - input)).mean()
  
  
  def tet_sdf_diff(
      vert_sdf: Float[Tensor, "Nv 1"], tet_edges: Integer[Tensor, "Ne 2"]
  ) -> Float[Tensor, ""]:
      sdf_f1x6x2 = vert_sdf[:, 0][tet_edges.reshape(-1)].reshape(-1, 2)
      mask = torch.sign(sdf_f1x6x2[..., 0]) != torch.sign(sdf_f1x6x2[..., 1])
      sdf_f1x6x2 = sdf_f1x6x2[mask]
      sdf_diff = F.binary_cross_entropy_with_logits(
          sdf_f1x6x2[..., 0], (sdf_f1x6x2[..., 1] > 0).float()
      ) + F.binary_cross_entropy_with_logits(
          sdf_f1x6x2[..., 1], (sdf_f1x6x2[..., 0] > 0).float()
      )
      return sdf_diff
  
  
  def validate_empty_rays(ray_indices, t_start, t_end):
      if ray_indices.nelement() == 0:
          lrm.warn("Empty rays_indices!")
          ray_indices = torch.LongTensor([0]).to(ray_indices)
          t_start = torch.Tensor([0]).to(ray_indices)
          t_end = torch.Tensor([0]).to(ray_indices)
      return ray_indices, t_start, t_end
  
  
  def rays_intersect_bbox(
      rays_o: Float[Tensor, "N 3"],
      rays_d: Float[Tensor, "N 3"],
      radius: Float,
      near: Float = 0.0,
      valid_thresh: Float = 0.01,
      background: bool = False,
  ):
      input_shape = rays_o.shape[:-1]
      rays_o, rays_d = rays_o.view(-1, 3), rays_d.view(-1, 3)
      rays_d_valid = torch.where(
          rays_d.abs() < 1e-6, torch.full_like(rays_d, 1e-6), rays_d
      )
      if type(radius) in [int, float]:
          radius = torch.FloatTensor(
              [[-radius, radius], [-radius, radius], [-radius, radius]]
          ).to(rays_o.device)
      radius = (
          1.0 - 1.0e-3
      ) * radius  # tighten the radius to make sure the intersection point lies in the bounding box
      interx0 = (radius[..., 1] - rays_o) / rays_d_valid
      interx1 = (radius[..., 0] - rays_o) / rays_d_valid
      t_near = torch.minimum(interx0, interx1).amax(dim=-1).clamp_min(near)
      t_far = torch.maximum(interx0, interx1).amin(dim=-1)
  
      # check wheter a ray intersects the bbox or not
      rays_valid = t_far - t_near > valid_thresh
  
      t_near_valid, t_far_valid = t_near[rays_valid], t_far[rays_valid]
      global_near = t_near_valid.min().item()
      global_far = t_far_valid.max().item()
  
      t_near[torch.where(~rays_valid)] = 0.0
      t_far[torch.where(~rays_valid)] = 0.0
  
      t_near = t_near.view(*input_shape, 1)
      t_far = t_far.view(*input_shape, 1)
      rays_valid = rays_valid.view(*input_shape)
  
      return t_near, t_far, rays_valid
  
  
  def get_plucker_rays(rays_o: Float[Tensor, "*N 3"], rays_d: Float[Tensor, "*N 3"]) -> Float[Tensor, "*N 6"]:
      rays_o = F.normalize(rays_o, dim=-1)
      rays_d = F.normalize(rays_d, dim=-1)
      return torch.cat([
          rays_o.cross(rays_d),
          rays_d
      ], dim=-1)
  
  
  def c2w_to_polar(c2w: Float[Tensor, "4 4"]) -> Tuple[float, float, float]:
      cam_pos = c2w[:3, 3]
      x, y, z = cam_pos.tolist()
      distance = cam_pos.norm().item()
      elevation = math.asin(z / distance)
      if abs(x) < 1.0e-5 and abs(y) < 1.0e-5:
          azimuth = 0
      else:
          azimuth = math.atan2(y, x)
          if azimuth < 0:
              azimuth += 2 * math.pi
  
      return elevation, azimuth, distance
  
  
  def polar_to_c2w(elevation: float, azimuth: float, distance: float) -> Float[Tensor, "4 4"]:
      """
      Compute L = p - C.
      Normalize L.
      Compute s = L x u. (cross product)
      Normalize s.
      Compute u' = s x L.
      rotation = [s, u, -l]
      """
      z = distance * math.sin(elevation)
      x = distance * math.cos(elevation) * math.cos(azimuth)
      y = distance * math.cos(elevation) * math.sin(azimuth)
      l = -torch.as_tensor([x, y, z]).float()
      l = F.normalize(l, dim=0)
      u = torch.as_tensor([0.0, 0.0, 1.0]).float()
      s = l.cross(u)
      s = F.normalize(s, dim=0)
      u = s.cross(l)
      rot = torch.stack([s, u, -l], dim=0).T
      c2w = torch.zeros((4, 4), dtype=torch.float32)
      c2w[:3, :3] = rot
      c2w[:3, 3] = torch.as_tensor([x, y, z])
      c2w[3, 3] = 1
      return c2w
  