text: import torch
  import torch.nn as nn
  from utils import rend_util
  
  class RayTracing(nn.Module):
      def __init__(
              self,
              object_bounding_sphere=1.0,
              sdf_threshold=5.0e-5,
              line_search_step=0.5,
              line_step_iters=1,
              sphere_tracing_iters=10,
              n_steps=100,
              n_secant_steps=8,
      ):
          super().__init__()
  
          self.object_bounding_sphere = object_bounding_sphere
          self.sdf_threshold = sdf_threshold
          self.sphere_tracing_iters = sphere_tracing_iters
          self.line_step_iters = line_step_iters
          self.line_search_step = line_search_step
          self.n_steps = n_steps
          self.n_secant_steps = n_secant_steps
  
      def forward(self,
                  sdf,
                  cam_loc,
                  object_mask,
                  ray_directions
                  ):
  
          batch_size, num_pixels, _ = ray_directions.shape
  
          sphere_intersections, mask_intersect = rend_util.get_sphere_intersection(cam_loc, ray_directions, r=self.object_bounding_sphere)
  
          curr_start_points, unfinished_mask_start, acc_start_dis, acc_end_dis, min_dis, max_dis = \
              self.sphere_tracing(batch_size, num_pixels, sdf, cam_loc, ray_directions, mask_intersect, sphere_intersections)
  
          network_object_mask = (acc_start_dis < acc_end_dis)
  
          # The non convergent rays should be handled by the sampler
          sampler_mask = unfinished_mask_start
          sampler_net_obj_mask = torch.zeros_like(sampler_mask).bool().cuda()
          if sampler_mask.sum() > 0:
              sampler_min_max = torch.zeros((batch_size, num_pixels, 2)).cuda()
              sampler_min_max.reshape(-1, 2)[sampler_mask, 0] = acc_start_dis[sampler_mask]
              sampler_min_max.reshape(-1, 2)[sampler_mask, 1] = acc_end_dis[sampler_mask]
  
              sampler_pts, sampler_net_obj_mask, sampler_dists = self.ray_sampler(sdf,
                                                                                  cam_loc,
                                                                                  object_mask,
                                                                                  ray_directions,
                                                                                  sampler_min_max,
                                                                                  sampler_mask
                                                                                  )
  
              curr_start_points[sampler_mask] = sampler_pts[sampler_mask]
              acc_start_dis[sampler_mask] = sampler_dists[sampler_mask]
              network_object_mask[sampler_mask] = sampler_net_obj_mask[sampler_mask]
  
          print('----------------------------------------------------------------')
          print('RayTracing: object = {0}/{1}, secant on {2}/{3}.'
                .format(network_object_mask.sum(), len(network_object_mask), sampler_net_obj_mask.sum(), sampler_mask.sum()))
          print('----------------------------------------------------------------')
  
          if not self.training:
              return curr_start_points, \
                     network_object_mask, \
                     acc_start_dis
  
          ray_directions = ray_directions.reshape(-1, 3)
          mask_intersect = mask_intersect.reshape(-1)
  
          in_mask = ~network_object_mask & object_mask & ~sampler_mask
          out_mask = ~object_mask & ~sampler_mask
  
          mask_left_out = (in_mask | out_mask) & ~mask_intersect
          if mask_left_out.sum() > 0:  # project the origin to the not intersect points on the sphere
              cam_left_out = cam_loc.unsqueeze(1).repeat(1, num_pixels, 1).reshape(-1, 3)[mask_left_out]
              rays_left_out = ray_directions[mask_left_out]
              acc_start_dis[mask_left_out] = -torch.bmm(rays_left_out.view(-1, 1, 3), cam_left_out.view(-1, 3, 1)).squeeze()
              curr_start_points[mask_left_out] = cam_left_out + acc_start_dis[mask_left_out].unsqueeze(1) * rays_left_out
  
          mask = (in_mask | out_mask) & mask_intersect
  
          if mask.sum() > 0:
              min_dis[network_object_mask & out_mask] = acc_start_dis[network_object_mask & out_mask]
  
              min_mask_points, min_mask_dist = self.minimal_sdf_points(num_pixels, sdf, cam_loc, ray_directions, mask, min_dis, max_dis)
  
              curr_start_points[mask] = min_mask_points
              acc_start_dis[mask] = min_mask_dist
  
          return curr_start_points, \
                 network_object_mask, \
                 acc_start_dis
  
  
      def sphere_tracing(self, batch_size, num_pixels, sdf, cam_loc, ray_directions, mask_intersect, sphere_intersections):
          ''' Run sphere tracing algorithm for max iterations from both sides of unit sphere intersection '''
  
          sphere_intersections_points = cam_loc.reshape(batch_size, 1, 1, 3) + sphere_intersections.unsqueeze(-1) * ray_directions.unsqueeze(2)
          unfinished_mask_start = mask_intersect.reshape(-1).clone()
          unfinished_mask_end = mask_intersect.reshape(-1).clone()
  
          # Initialize start current points
          curr_start_points = torch.zeros(batch_size * num_pixels, 3).cuda().float()
          curr_start_points[unfinished_mask_start] = sphere_intersections_points[:,:,0,:].reshape(-1,3)[unfinished_mask_start]
          acc_start_dis = torch.zeros(batch_size * num_pixels).cuda().float()
          acc_start_dis[unfinished_mask_start] = sphere_intersections.reshape(-1,2)[unfinished_mask_start,0]
  
          # Initialize end current points
          curr_end_points = torch.zeros(batch_size * num_pixels, 3).cuda().float()
          curr_end_points[unfinished_mask_end] = sphere_intersections_points[:,:,1,:].reshape(-1,3)[unfinished_mask_end]
          acc_end_dis = torch.zeros(batch_size * num_pixels).cuda().float()
          acc_end_dis[unfinished_mask_end] = sphere_intersections.reshape(-1,2)[unfinished_mask_end,1]
  
          # Initizliae min and max depth
          min_dis = acc_start_dis.clone()
          max_dis = acc_end_dis.clone()
  
          # Iterate on the rays (from both sides) till finding a surface
          iters = 0
  
          next_sdf_start = torch.zeros_like(acc_start_dis).cuda()
          next_sdf_start[unfinished_mask_start] = sdf(curr_start_points[unfinished_mask_start])
  
          next_sdf_end = torch.zeros_like(acc_end_dis).cuda()
          next_sdf_end[unfinished_mask_end] = sdf(curr_end_points[unfinished_mask_end])
  
          while True:
              # Update sdf
              curr_sdf_start = torch.zeros_like(acc_start_dis).cuda()
              curr_sdf_start[unfinished_mask_start] = next_sdf_start[unfinished_mask_start]
              curr_sdf_start[curr_sdf_start <= self.sdf_threshold] = 0
  
              curr_sdf_end = torch.zeros_like(acc_end_dis).cuda()
              curr_sdf_end[unfinished_mask_end] = next_sdf_end[unfinished_mask_end]
              curr_sdf_end[curr_sdf_end <= self.sdf_threshold] = 0
  
              # Update masks
              unfinished_mask_start = unfinished_mask_start & (curr_sdf_start > self.sdf_threshold)
              unfinished_mask_end = unfinished_mask_end & (curr_sdf_end > self.sdf_threshold)
  
              if (unfinished_mask_start.sum() == 0 and unfinished_mask_end.sum() == 0) or iters == self.sphere_tracing_iters:
                  break
              iters += 1
  
              # Make step
              # Update distance
              acc_start_dis = acc_start_dis + curr_sdf_start
              acc_end_dis = acc_end_dis - curr_sdf_end
  
              # Update points
              curr_start_points = (cam_loc.unsqueeze(1) + acc_start_dis.reshape(batch_size, num_pixels, 1) * ray_directions).reshape(-1, 3)
              curr_end_points = (cam_loc.unsqueeze(1) + acc_end_dis.reshape(batch_size, num_pixels, 1) * ray_directions).reshape(-1, 3)
  
              # Fix points which wrongly crossed the surface
              next_sdf_start = torch.zeros_like(acc_start_dis).cuda()
              next_sdf_start[unfinished_mask_start] = sdf(curr_start_points[unfinished_mask_start])
  
              next_sdf_end = torch.zeros_like(acc_end_dis).cuda()
              next_sdf_end[unfinished_mask_end] = sdf(curr_end_points[unfinished_mask_end])
  
              not_projected_start = next_sdf_start < 0
              not_projected_end = next_sdf_end < 0
              not_proj_iters = 0
              while (not_projected_start.sum() > 0 or not_projected_end.sum() > 0) and not_proj_iters < self.line_step_iters:
                  # Step backwards
                  acc_start_dis[not_projected_start] -= ((1 - self.line_search_step) / (2 ** not_proj_iters)) * curr_sdf_start[not_projected_start]
                  curr_start_points[not_projected_start] = (cam_loc.unsqueeze(1) + acc_start_dis.reshape(batch_size, num_pixels, 1) * ray_directions).reshape(-1, 3)[not_projected_start]
  
                  acc_end_dis[not_projected_end] += ((1 - self.line_search_step) / (2 ** not_proj_iters)) * curr_sdf_end[not_projected_end]
                  curr_end_points[not_projected_end] = (cam_loc.unsqueeze(1) + acc_end_dis.reshape(batch_size, num_pixels, 1) * ray_directions).reshape(-1, 3)[not_projected_end]
  
                  # Calc sdf
                  next_sdf_start[not_projected_start] = sdf(curr_start_points[not_projected_start])
                  next_sdf_end[not_projected_end] = sdf(curr_end_points[not_projected_end])
  
                  # Update mask
                  not_projected_start = next_sdf_start < 0
                  not_projected_end = next_sdf_end < 0
                  not_proj_iters += 1
  
              unfinished_mask_start = unfinished_mask_start & (acc_start_dis < acc_end_dis)
              unfinished_mask_end = unfinished_mask_end & (acc_start_dis < acc_end_dis)
  
          return curr_start_points, unfinished_mask_start, acc_start_dis, acc_end_dis, min_dis, max_dis
  
      def ray_sampler(self, sdf, cam_loc, object_mask, ray_directions, sampler_min_max, sampler_mask):
          ''' Sample the ray in a given range and run secant on rays which have sign transition '''
  
          batch_size, num_pixels, _ = ray_directions.shape
          n_total_pxl = batch_size * num_pixels
          sampler_pts = torch.zeros(n_total_pxl, 3).cuda().float()
          sampler_dists = torch.zeros(n_total_pxl).cuda().float()
  
          intervals_dist = torch.linspace(0, 1, steps=self.n_steps).cuda().view(1, 1, -1)
  
          pts_intervals = sampler_min_max[:, :, 0].unsqueeze(-1) + intervals_dist * (sampler_min_max[:, :, 1] - sampler_min_max[:, :, 0]).unsqueeze(-1)
          points = cam_loc.reshape(batch_size, 1, 1, 3) + pts_intervals.unsqueeze(-1) * ray_directions.unsqueeze(2)
  
          # Get the non convergent rays
          mask_intersect_idx = torch.nonzero(sampler_mask).flatten()
          points = points.reshape((-1, self.n_steps, 3))[sampler_mask, :, :]
          pts_intervals = pts_intervals.reshape((-1, self.n_steps))[sampler_mask]
  
          sdf_val_all = []
          for pnts in torch.split(points.reshape(-1, 3), 100000, dim=0):
              sdf_val_all.append(sdf(pnts))
          sdf_val = torch.cat(sdf_val_all).reshape(-1, self.n_steps)
  
          tmp = torch.sign(sdf_val) * torch.arange(self.n_steps, 0, -1).cuda().float().reshape((1, self.n_steps))  # Force argmin to return the first min value
          sampler_pts_ind = torch.argmin(tmp, -1)
          sampler_pts[mask_intersect_idx] = points[torch.arange(points.shape[0]), sampler_pts_ind, :]
          sampler_dists[mask_intersect_idx] = pts_intervals[torch.arange(pts_intervals.shape[0]), sampler_pts_ind]
  
          true_surface_pts = object_mask[sampler_mask]
          net_surface_pts = (sdf_val[torch.arange(sdf_val.shape[0]), sampler_pts_ind] < 0)
  
          # take points with minimal SDF value for P_out pixels
          p_out_mask = ~(true_surface_pts & net_surface_pts)
          n_p_out = p_out_mask.sum()
          if n_p_out > 0:
              out_pts_idx = torch.argmin(sdf_val[p_out_mask, :], -1)
              sampler_pts[mask_intersect_idx[p_out_mask]] = points[p_out_mask, :, :][torch.arange(n_p_out), out_pts_idx, :]
              sampler_dists[mask_intersect_idx[p_out_mask]] = pts_intervals[p_out_mask, :][torch.arange(n_p_out), out_pts_idx]
  
          # Get Network object mask
          sampler_net_obj_mask = sampler_mask.clone()
          sampler_net_obj_mask[mask_intersect_idx[~net_surface_pts]] = False
  
          # Run Secant method
          secant_pts = net_surface_pts & true_surface_pts if self.training else net_surface_pts
          n_secant_pts = secant_pts.sum()
          if n_secant_pts > 0:
              # Get secant z predictions
              z_high = pts_intervals[torch.arange(pts_intervals.shape[0]), sampler_pts_ind][secant_pts]
              sdf_high = sdf_val[torch.arange(sdf_val.shape[0]), sampler_pts_ind][secant_pts]
              z_low = pts_intervals[secant_pts][torch.arange(n_secant_pts), sampler_pts_ind[secant_pts] - 1]
              sdf_low = sdf_val[secant_pts][torch.arange(n_secant_pts), sampler_pts_ind[secant_pts] - 1]
              cam_loc_secant = cam_loc.unsqueeze(1).repeat(1, num_pixels, 1).reshape((-1, 3))[mask_intersect_idx[secant_pts]]
              ray_directions_secant = ray_directions.reshape((-1, 3))[mask_intersect_idx[secant_pts]]
              z_pred_secant = self.secant(sdf_low, sdf_high, z_low, z_high, cam_loc_secant, ray_directions_secant, sdf)
  
              # Get points
              sampler_pts[mask_intersect_idx[secant_pts]] = cam_loc_secant + z_pred_secant.unsqueeze(-1) * ray_directions_secant
              sampler_dists[mask_intersect_idx[secant_pts]] = z_pred_secant
  
          return sampler_pts, sampler_net_obj_mask, sampler_dists
  
      def secant(self, sdf_low, sdf_high, z_low, z_high, cam_loc, ray_directions, sdf):
          ''' Runs the secant method for interval [z_low, z_high] for n_secant_steps '''
  
          z_pred = - sdf_low * (z_high - z_low) / (sdf_high - sdf_low) + z_low
          for i in range(self.n_secant_steps):
              p_mid = cam_loc + z_pred.unsqueeze(-1) * ray_directions
              sdf_mid = sdf(p_mid)
              ind_low = sdf_mid > 0
              if ind_low.sum() > 0:
                  z_low[ind_low] = z_pred[ind_low]
                  sdf_low[ind_low] = sdf_mid[ind_low]
              ind_high = sdf_mid < 0
              if ind_high.sum() > 0:
                  z_high[ind_high] = z_pred[ind_high]
                  sdf_high[ind_high] = sdf_mid[ind_high]
  
              z_pred = - sdf_low * (z_high - z_low) / (sdf_high - sdf_low) + z_low
  
          return z_pred
  
      def minimal_sdf_points(self, num_pixels, sdf, cam_loc, ray_directions, mask, min_dis, max_dis):
          ''' Find points with minimal SDF value on rays for P_out pixels '''
  
          n_mask_points = mask.sum()
  
          n = self.n_steps
          # steps = torch.linspace(0.0, 1.0,n).cuda()
          steps = torch.empty(n).uniform_(0.0, 1.0).cuda()
          mask_max_dis = max_dis[mask].unsqueeze(-1)
          mask_min_dis = min_dis[mask].unsqueeze(-1)
          steps = steps.unsqueeze(0).repeat(n_mask_points, 1) * (mask_max_dis - mask_min_dis) + mask_min_dis
  
          mask_points = cam_loc.unsqueeze(1).repeat(1, num_pixels, 1).reshape(-1, 3)[mask]
          mask_rays = ray_directions[mask, :]
  
          mask_points_all = mask_points.unsqueeze(1).repeat(1, n, 1) + steps.unsqueeze(-1) * mask_rays.unsqueeze(
              1).repeat(1, n, 1)
          points = mask_points_all.reshape(-1, 3)
  
          mask_sdf_all = []
          for pnts in torch.split(points, 100000, dim=0):
              mask_sdf_all.append(sdf(pnts))
  
          mask_sdf_all = torch.cat(mask_sdf_all).reshape(-1, n)
          min_vals, min_idx = mask_sdf_all.min(-1)
          min_mask_points = mask_points_all.reshape(-1, n, 3)[torch.arange(0, n_mask_points), min_idx]
          min_mask_dist = steps.reshape(-1, n)[torch.arange(0, n_mask_points), min_idx]
  
          return min_mask_points, min_mask_dist
  