
"""simple docstring"""

from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch
@dataclass
class   _UpperCAmelCase				:
      __SCREAMING_SNAKE_CASE :				torch.Tensor  # [batch_size x 3]
      __SCREAMING_SNAKE_CASE :				torch.Tensor  # [batch_size x 3]
      __SCREAMING_SNAKE_CASE :				torch.Tensor  # [batch_size x 3]
      __SCREAMING_SNAKE_CASE :				torch.Tensor  # [batch_size x 3]
      __SCREAMING_SNAKE_CASE :				int
      __SCREAMING_SNAKE_CASE :				int
      __SCREAMING_SNAKE_CASE :				float
      __SCREAMING_SNAKE_CASE :				float
      __SCREAMING_SNAKE_CASE :				Tuple[int]




      def      a_   (				self				)    ->       int:
          assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
          assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
          assert len(self.x.shape				) == len(self.y.shape				) == len(self.z.shape				) == len(self.origin.shape				) == 2




      def      a_   (				self				)    ->       str:
          return torch.from_numpy(np.array([self.width, self.height] ,							dtype=np.floataa				)				)




      def      a_   (				self				)    ->       List[Any]:
          return torch.from_numpy(np.array([self.x_fov, self.y_fov] ,							dtype=np.floataa				)				)




      def      a_   (				self				)    ->       torch.Tensor:
          UpperCAmelCase          =       torch.arange(self.height * self.width				)
          UpperCAmelCase          =       torch.stack(
              [
                  pixel_indices % self.width,
                  torch.div(lowercase_ ,							self.width ,							rounding_mode='trunc'				),
              ] ,							axis=1 ,							)
          return coords




      @property
      def      a_   (				self				)    ->       int:
          UpperCAmelCase      ,				*UpperCAmelCase          =       self.shape
          UpperCAmelCase          =       int(np.prod(lowercase_				)				)

          UpperCAmelCase          =       self.get_image_coords()
          UpperCAmelCase          =       torch.broadcast_to(coords.unsqueeze(0				) ,							[batch_size * inner_batch_size, *coords.shape]				)
          UpperCAmelCase          =       self.get_camera_rays(lowercase_				)

          UpperCAmelCase          =       rays.view(lowercase_ ,							inner_batch_size * self.height * self.width ,							2 ,							3				)

          return rays




      def      a_   (				self ,							lowercase_				)    ->       torch.Tensor:
          UpperCAmelCase      ,				*UpperCAmelCase      ,				UpperCAmelCase          =       coords.shape
          assert n_coords == 2
          assert batch_size == self.origin.shape[0]

          UpperCAmelCase          =       coords.view(lowercase_ ,							-1 ,							2				)

          UpperCAmelCase          =       self.resolution()
          UpperCAmelCase          =       self.fov()

          UpperCAmelCase          =       (flat.float() / (res - 1)) * 2 - 1
          UpperCAmelCase          =       fracs * torch.tan(fov / 2				)

          UpperCAmelCase          =       fracs.view(lowercase_ ,							-1 ,							2				)
          UpperCAmelCase          =       (
              self.z.view(lowercase_ ,							1 ,							3				)
              + self.x.view(lowercase_ ,							1 ,							3				) * fracs[:, :, :1]
              + self.y.view(lowercase_ ,							1 ,							3				) * fracs[:, :, 1:]
          )
          UpperCAmelCase          =       directions / directions.norm(dim=-1 ,							keepdim=lowercase_				)
          UpperCAmelCase          =       torch.stack(
              [
                  torch.broadcast_to(self.origin.view(lowercase_ ,							1 ,							3				) ,							[batch_size, directions.shape[1], 3]				),
                  directions,
              ] ,							dim=2 ,							)
          return rays.view(lowercase_ ,							*lowercase_ ,							2 ,							3				)




      def      a_   (				self ,							lowercase_ ,							lowercase_				)    ->       "DifferentiableProjectiveCamera":
          assert width * self.height == height * self.width, "The aspect ratio should not change."
          return DifferentiableProjectiveCamera(
              origin=self.origin ,							x=self.x ,							y=self.y ,							z=self.z ,							width=lowercase_ ,							height=lowercase_ ,							x_fov=self.x_fov ,							y_fov=self.y_fov ,							)




def      lowercase__    (       lowerCAmelCase					:       int			)			->   DifferentiableProjectiveCamera:






    """simple docstring"""




    UpperCAmelCase          =       []
    UpperCAmelCase          =       []
    UpperCAmelCase          =       []
    UpperCAmelCase          =       []
    for theta in np.linspace(0			,					2 * np.pi			,					num=20			):
        UpperCAmelCase          =       np.array([np.sin(lowerCAmelCase			), np.cos(lowerCAmelCase			), -0.5]			)
        z /= np.sqrt(np.sum(z**2			)			)
        UpperCAmelCase          =       -z * 4
        UpperCAmelCase          =       np.array([np.cos(lowerCAmelCase			), -np.sin(lowerCAmelCase			), 0.0]			)
        UpperCAmelCase          =       np.cross(lowerCAmelCase			,					lowerCAmelCase			)
        origins.append(lowerCAmelCase			)
        xs.append(lowerCAmelCase			)
        ys.append(lowerCAmelCase			)
        zs.append(lowerCAmelCase			)
    return DifferentiableProjectiveCamera(
        origin=torch.from_numpy(np.stack(lowerCAmelCase			,					axis=0			)			).float()			,					x=torch.from_numpy(np.stack(lowerCAmelCase			,					axis=0			)			).float()			,					y=torch.from_numpy(np.stack(lowerCAmelCase			,					axis=0			)			).float()			,					z=torch.from_numpy(np.stack(lowerCAmelCase			,					axis=0			)			).float()			,					width=lowerCAmelCase			,					height=lowerCAmelCase			,					x_fov=0.7			,					y_fov=0.7			,					shape=(1, len(lowerCAmelCase			))			,					)





"""simple docstring"""

from math import asin, atan, cos, radians, sin, sqrt, tan

SCREAMING_SNAKE_CASE_            =    6_3_7_8_1_3_7.0
SCREAMING_SNAKE_CASE_            =    6_3_5_6_7_5_2.3_1_4_2_4_5
SCREAMING_SNAKE_CASE_            =    637_8137




def      lowercase__    (       lowerCAmelCase					:       float			,					lowerCAmelCase					:       float			,					lowerCAmelCase					:       float			,					lowerCAmelCase					:       float			)			->   float:






    """simple docstring"""




    UpperCAmelCase          =       (AXIS_A - AXIS_B) / AXIS_A
    UpperCAmelCase          =       atan((1 - flattening) * tan(radians(lowerCAmelCase			)			)			)
    UpperCAmelCase          =       atan((1 - flattening) * tan(radians(lowerCAmelCase			)			)			)
    UpperCAmelCase          =       radians(lowerCAmelCase			)
    UpperCAmelCase          =       radians(lowerCAmelCase			)
    # Equation
    UpperCAmelCase          =       sin((phi_a - phi_a) / 2			)
    UpperCAmelCase          =       sin((lambda_a - lambda_a) / 2			)
    # Square both values
    sin_sq_phi *= sin_sq_phi
    sin_sq_lambda *= sin_sq_lambda
    UpperCAmelCase          =       sqrt(sin_sq_phi + (cos(lowerCAmelCase			) * cos(lowerCAmelCase			) * sin_sq_lambda)			)
    return 2 * RADIUS * asin(lowerCAmelCase			)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



