code: def densify_and_split(self, grads, grad_threshold, scene_extent, N=2):
      n_init_points = self.get_xyz.shape[0]
      # Extract points that satisfy the gradient condition
      padded_grad = torch.zeros((n_init_points), device="cuda")
      padded_grad[: grads.shape[0]] = grads.squeeze()
      selected_pts_mask = torch.where(
          padded_grad >= grad_threshold, True, False
      )
      selected_pts_mask = torch.logical_and(
          selected_pts_mask,
          torch.max(self.get_scaling, dim=1).values
          > self.percent_dense * scene_extent,
      )
  
      stds = self.get_scaling[selected_pts_mask].repeat(N, 1)
      means = torch.zeros((stds.size(0), 3), device="cuda")
      samples = torch.normal(mean=means, std=stds)
      rots = build_rotation(self._rotation[selected_pts_mask]).repeat(
          N, 1, 1
      )
      new_xyz = torch.bmm(rots, samples.unsqueeze(-1)).squeeze(
          -1
      ) + self.get_xyz[selected_pts_mask].repeat(N, 1)
      new_scaling = self.scaling_inverse_activation(
          self.get_scaling[selected_pts_mask].repeat(N, 1) / (0.8 * N)
      )
      new_rotation = self._rotation[selected_pts_mask].repeat(N, 1)
      new_features_dc = self._features_dc[selected_pts_mask].repeat(
          N, 1, 1
      )
      new_features_rest = self._features_rest[selected_pts_mask].repeat(
          N, 1, 1
      )
      new_opacity = self._opacity[selected_pts_mask].repeat(N, 1)
  
      self.densification_postfix(
          new_xyz,
          new_features_dc,
          new_features_rest,
          new_opacity,
          new_scaling,
          new_rotation,
      )
  
      prune_filter = torch.cat(
          (
              selected_pts_mask,
              torch.zeros(
                  N * selected_pts_mask.sum(), device="cuda", dtype=bool
              ),
          )
      )
      self.prune_points(prune_filter)
  
imports: import torch
  import numpy
  from utils.general_utils import inverse_sigmoid, get_expon_lr_func, build_rotation
  from torch import nn
  import os
  from utils.system_utils import mkdir_p
  from plyfile import PlyData, PlyElement
  from utils.sh_utils import RGB2SH
  from simple_knn._C import distCUDA2
  from utils.graphics_utils import BasicPointCloud
  from utils.general_utils import strip_symmetric, build_scaling_rotation
label_desc: Use image node_id 24 for calling the GaussianModel obj's underlying member method code with example usage: obj.densify_and_split(grads, grad_threshold, scene_extent, N) without return types